Magical Glace Posted August 22, 2014 Share Posted August 22, 2014 I'm evil. Quote Link to comment Share on other sites More sharing options...
Nobody Posted August 22, 2014 Share Posted August 22, 2014 notto disu shitto agen Quote Link to comment Share on other sites More sharing options...
DreadFighter Posted August 22, 2014 Share Posted August 22, 2014 K Quote Link to comment Share on other sites More sharing options...
Lance Masayoshi Posted August 22, 2014 Share Posted August 22, 2014 y do u do dis Quote Link to comment Share on other sites More sharing options...
ZemZem Posted August 22, 2014 Share Posted August 22, 2014 Gonna be honest with you, Glac. This is stupid. Quote Link to comment Share on other sites More sharing options...
Nobody Posted August 22, 2014 Share Posted August 22, 2014 Welcome to Wikipedia, the free encyclopedia that anyone can edit. 4,586,381 articles in English Arts Biography Geography History Mathematics Science Society Technology All portals From today's featured article One of the two surviving complete manuscripts of Liber Eliensis The Liber Eliensis ("Book of Ely") is a 12th-century English chronicle and history, written in Latin. Composed in three books, it was written at Ely Abbey on the island of Ely in the fenlands of eastern Cambridgeshire. Ely Abbey became the cathedral of a newly formed bishopric in 1109. The Liber covers the period from the founding of the abbey in 673 until the middle of the 12th century, building on a number of earlier historical works. It incorporates documents and stories of saints' lives and is a typical example of a kind of local history produced during the latter part of the 12th century. The longest of the contemporary local histories, it describes the devastation caused by the disorders during the reign of King Stephen, as well as the career of Nigel (Bishop of Ely 1133–69) and his disputes with the king. The two surviving complete manuscripts of the work are complemented by a number of partial manuscripts. A printed version of the Latin text appeared in 1963 and an English translation was published in 2005. The Liber Eliensis is an important source of historical information for the region and period it covers, and particularly for the abbey and bishopric of Ely. (Full article...) Recently featured: Horse Protection Act of 1970 – Thirty Flights of Loving – Cyclura nubila Archive – By email – More featured articles... Did you know... From Wikipedia's new and recently improved content: Claude Debussy ... that Des pas sur la neige, Ce qu'a vu le vent d'ouest, and La fille aux cheveux de lin by Claude Debussy (pictured) form "the central arch" of the structure of his first book of Préludes? ... that 100 years ago today the French 3rd Colonial Division was virtually destroyed at the Battle of Rossignol? ... that the Hindu deity Heramba, protector of the weak, is associated with rites for inflicting harm on one's enemies? ... that Valentin Wolfenstein owned the first successful photography studio in Los Angeles? ... that the noble Roman Altieri family, which ascended the papal throne in 1670 with Clement X, pretended to be descended from an unknown ancient Roman citizen named Lucius Alterius? ... that approximately 200 bird species have been observed on or near Lake Chillisquaque in Montour County, Pennsylvania? ... that three protesters were killed near a Cape Town school by armed police hidden in a "Trojan Horse"? ... that Marina Frolova-Walker has delivered lectures on music at venues ranging from Carnegie Hall to factories in Kazakhstan? Archive – Start a new article – Nominate an article In the news Robin Williams At least 39 people are killed in a series of landslides in Hiroshima Prefecture, Japan. The 41st Chess Olympiad concludes with China winning the open section and Russia winning the women's section of the tournament. Mathematicians Artur Ávila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani are awarded the Fields Medal; Mirzakhani is its first female recipient. Actor and comedian Robin Williams (pictured) dies at the age of 63. Recep Tayyip Erdoğan wins Turkey's first direct presidential election. Ongoing: Ebola outbreak – Gaza conflict – Ukrainian unrest Recent deaths: B. K. S. Iyengar On this day... August 22: Feast day of the Queenship of Mary (Roman Catholic Church); Paryushana begins (Svetambar Jains, 2014); Madras Day in Chennai, Tamil Nadu, India Henry Dunant 1642 – King Charles I of England raised the royal standard at Nottingham, marking the beginning of the First English Civil War. 1864 – The Red Cross movement led by Henry Dunant (pictured) officially began when twelve European nations signed the First Geneva Convention, establishing the International Committee of the Red Cross. 1922 – Irish Civil War: Irish National Army commander-in-chief Michael Collins was assassinated in an ambush while en route through County Cork at the village of Béal na mBláth. 1944 – World War II: Wehrmacht infantry carried out an assault operation against the civilian residents of nine villages located in the Amari Valley on the Greek island of Crete. 2012 – A series of ethnic clashes between the Orma and Pokomo tribes of Kenya's Tana River District resulted in the deaths of at least 52 people. More anniversaries: August 21 – August 22 – August 23 Archive – By email – List of historical anniversaries It is now August 22, 2014 (UTC) – Reload this page From today's featured list Rani Mukerji is looking away from the camera Rani Mukerji's acting career has been dominated by work in Bollywood films. Mukerji, an Indian actress, made her screen debut with a supporting role in Biyer Phool (1992), and had her first leading role with the drama Raja Ki Aayegi Baraat (1997). In 1998, she achieved success by playing a supporting role in the romance Kuch Kuch Hota Hai. After three years of poorly received films, Mukerji's career prospects improved in 2002 when she played the lead role in Saathiya. For her roles in the 2004 romantic comedy Hum Tum and the drama Yuva, Mukerji became the only actress to win the Filmfare Awards both for Best Actress and for Best Supporting Actress, respectively, in the same year. She subsequently garnered praise for portraying a blind, deaf and mute woman in Black (2005) and an unfaithful wife in Kabhi Alvida Naa Kehna (2006). Following a series of box office flops, Mukerji starred in two successful thrillers—No One Killed Jessica (2011) and Talaash: The Answer Lies Within (2012). (Full list...) Recently featured: Recessions in the United States – Sega Genesis games – International cricket five-wicket hauls by Shoaib Akhtar Archive – More featured lists... Today's featured picture Thermal power station A diagram of a typical coal-fired thermal power station, a type of power plant in which the prime mover is steam driven. Water is heated, turns into steam and spins a steam turbine, which drives an electrical generator. After it passes through the turbine, the steam is condensed in a condenser and recycled to where it was heated; this is known as a Rankine cycle. For a more detailed overview of the process, consult the diagram's description. Diagram: BillC; modifications: MaCRoEco Recently featured: Osaka Castle – Benjamin Harrison – Charles Bolden Archive – More featured pictures... Other areas of Wikipedia Community portal – Bulletin board, projects, resources and activities covering a wide range of Wikipedia areas. Help desk – Ask questions about using Wikipedia. Local embassy – For Wikipedia-related communication in languages other than English. Reference desk – Serving as virtual librarians, Wikipedia volunteers tackle your questions on a wide range of subjects. Site news – Announcements, updates, articles and press releases on Wikipedia and the Wikimedia Foundation. Village pump – For discussions about Wikipedia itself, including areas for technical issues and policies. 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Roxas Posted August 22, 2014 Share Posted August 22, 2014 KORRA FINALE AHHHHHHH Quote Link to comment Share on other sites More sharing options...
DreadFighter Posted August 22, 2014 Share Posted August 22, 2014 Waluigi (Japanese: ワルイージ, Waruīji) is Luigi's very tall and skinny rival, and Wario's partner. Waluigi made his debut in Mario Tennis, and since then, he has made playable appearances in many of the Mario series' spin-off titles. He has been voiced by Charles Martinet ever since his debut. His name is a portmanteau of the Japanese words, Warui and Ruīji, meaning "bad" and "Luigi". In addition, his name is an anagram to the Japanese word Ijiwaru, which can mean "ill-tempered" or "cruel". The details of Waluigi's past are unclear since he has no confirmed background, although he has evidently been antagonizing the Mario Bros., especially Luigi, for quite some time before his debut as seen in the opening of Mario Tennis, where he and Luigi confront each other. He has a particularly strong rivalry with Luigi, who he constantly harasses, but he seems to have animosity towards pretty much everyone else in the Mushroom Kingdom, with the exception of his partner in crime, Wario. Quote Link to comment Share on other sites More sharing options...
Magical Glace Posted August 22, 2014 Author Share Posted August 22, 2014 Gonna be honest with you, Glac. This is stupid. I'm aware. Quote Link to comment Share on other sites More sharing options...
Nobody Posted August 22, 2014 Share Posted August 22, 2014 Gonna be stupid with you, Glac. This is honest. Quote Link to comment Share on other sites More sharing options...
Magical Glace Posted August 22, 2014 Author Share Posted August 22, 2014 Gonna be stupid with you, Glac. This is honest. Goof. Quote Link to comment Share on other sites More sharing options...
Elieson Posted August 22, 2014 Share Posted August 22, 2014 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut efficitur cursus justo et fringilla. Duis semper orci enim, a scelerisque turpis mattis sed. Aenean dignissim vehicula nisi, eu tempor nisl lacinia sit amet. Sed eu arcu eget velit cursus posuere vitae quis leo. Fusce vestibulum feugiat feugiat. Duis ligula velit, faucibus sit amet arcu at, efficitur congue massa. Quisque euismod, nibh sed egestas luctus, turpis est tincidunt nisl, quis dapibus diam lectus sed risus. Aliquam erat volutpat. Vivamus viverra orci augue, at molestie turpis tristique ut. Etiam ut quam purus. Donec faucibus lacinia rutrum. Maecenas ut dolor in ligula finibus facilisis eu eget ex. Proin placerat pellentesque venenatis. Praesent eu laoreet felis. Proin mollis molestie purus, in feugiat ligula tempor eget. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Morbi auctor justo neque, vel mattis massa ullamcorper nec. Pellentesque metus arcu, fringilla id dui a, faucibus molestie lacus. Aliquam a aliquam ligula. Donec nisl dolor, varius id dolor nec, feugiat fermentum arcu. Ut laoreet ipsum ut gravida imperdiet. Mauris eleifend justo at orci lobortis euismod. Duis non lectus nisl. Vestibulum eget dui sollicitudin dui efficitur volutpat vitae sit amet lorem. In sapien quam, dapibus vitae euismod at, convallis quis dui. Curabitur sit amet ultrices purus, a bibendum diam. Morbi nec felis nunc. Aenean lacinia, tortor eu dictum mattis, tortor enim commodo arcu, sed tristique ex mauris ut sem. Nulla molestie ut nunc at molestie. Integer vehicula id risus eu dictum. Nunc vitae laoreet nunc, id maximus justo. Donec luctus urna id magna scelerisque, quis dapibus libero fermentum. Vestibulum molestie massa ac leo volutpat, in porttitor tellus porttitor. Pellentesque dapibus iaculis orci, eu imperdiet est eleifend sed. Nam vitae maximus libero. Vestibulum scelerisque nisi massa, id finibus nibh efficitur non. Nullam sit amet efficitur erat. Nunc semper lacus eu turpis ultrices mollis eget quis ligula. Ut vel mi sodales, sagittis tellus sed, dictum diam. Phasellus lobortis faucibus tortor. Donec posuere lacus nibh, sit amet dignissim magna vehicula sed. Donec blandit neque sit amet imperdiet tincidunt. Maecenas gravida convallis sem, in maximus turpis tempor in. Sed eu odio condimentum, maximus ipsum ut, consectetur neque. Fusce mattis mi quis sollicitudin viverra. Nullam gravida nisl arcu, a malesuada augue finibus in. Nunc quis tellus elit. Morbi aliquam ligula euismod ligula scelerisque commodo. Aliquam erat risus, ultrices ut leo eget, luctus aliquam est. Duis quis fringilla nisi, et vehicula dolor. Phasellus massa velit, tempus id hendrerit eget, bibendum ac tortor. In rhoncus ex ut varius sollicitudin. Ut imperdiet pharetra faucibus. Fusce sed nunc in nunc convallis scelerisque. Phasellus posuere gravida sagittis. In a augue feugiat, pellentesque odio quis, dictum nisi. In sed pharetra lectus, vitae vehicula neque. Nullam ultrices cursus ex, et gravida mi ornare vitae. Aliquam at nisl nunc. Donec aliquet diam vitae ex iaculis lacinia. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nullam viverra enim tortor, ut efficitur dui accumsan nec. Nulla placerat erat ut nunc bibendum, sed molestie felis consequat. Curabitur bibendum, nisi sed laoreet facilisis, justo mi ullamcorper libero, vel ullamcorper dolor lacus eu lorem. Quisque eget consectetur tortor. Phasellus lacinia eget sapien vel vehicula. Nullam sit amet vestibulum turpis, quis consectetur arcu. Nunc dapibus dapibus eros sed blandit. Nunc imperdiet pharetra felis nec iaculis. Suspendisse nec erat quis risus tincidunt laoreet. Suspendisse accumsan ex erat. Praesent at nisi bibendum, laoreet sem ut, sollicitudin velit. Pellentesque aliquam elit leo, sit amet congue libero eleifend non. Morbi sodales, tortor a congue finibus, felis nibh vehicula urna, sed suscipit risus sapien pharetra est. Etiam ultricies libero sed libero laoreet malesuada. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Quisque in ornare quam. Nam ut tincidunt dolor, vitae dapibus mi. Curabitur eu sagittis diam, nec lacinia nisl. Quisque fermentum ex in odio mollis, at pretium orci vestibulum. Sed ultricies libero dui, at venenatis diam pulvinar nec. Praesent tortor felis, gravida eu nisl id, aliquet faucibus nibh. Nullam sed lorem et purus luctus auctor. Fusce tempor nunc a feugiat porta. Cras nulla ligula, congue ut arcu vitae, tempor euismod nisl. Phasellus imperdiet interdum enim. Quisque eleifend turpis eget tincidunt placerat. Donec finibus tristique magna et interdum. Ut nisl lorem, facilisis sed bibendum sed, eleifend vel eros. Maecenas quis dui tortor. Aliquam vulputate aliquam neque a tincidunt. Vestibulum ut scelerisque est, nec efficitur odio. Phasellus at enim sit amet eros congue bibendum. Donec finibus lacinia quam et pellentesque. Proin suscipit varius lectus a laoreet. Praesent ut finibus augue. Nulla pellentesque lectus et tellus porttitor aliquet. Praesent sed arcu eu dolor blandit efficitur ac eu elit. Etiam id ligula lacinia, dapibus metus id, lobortis tortor. Nullam vehicula interdum elit non tempus. Nulla eget sagittis turpis, nec commodo purus. Vestibulum rhoncus, ligula ac aliquam tempus, ligula erat euismod velit, et volutpat ex eros a elit. Nam ornare metus nec lorem pellentesque feugiat. Integer at ante a augue placerat sagittis quis eget ligula. Quisque elementum, dolor quis cursus facilisis, dui erat dictum sapien, ac mollis turpis turpis nec massa. Sed pharetra accumsan pulvinar. Fusce volutpat, enim a sollicitudin molestie, ex odio eleifend metus, sit amet pretium nunc arcu porttitor elit. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Duis ultricies rutrum tortor, in pellentesque sapien vestibulum eu. Sed ac cursus augue, eget venenatis mauris. Quisque dapibus pretium ipsum, vel sagittis elit suscipit quis. Aliquam condimentum malesuada nibh vitae accumsan. Fusce dignissim tellus eu justo porta, ac consequat augue viverra. Sed rutrum, metus sed eleifend finibus, lorem diam vestibulum magna, ac molestie orci erat vitae felis. Etiam leo quam, molestie id nunc feugiat, sagittis sollicitudin arcu. Quisque porta dolor augue, at gravida lectus tincidunt nec. Nulla non nisl neque. Praesent malesuada felis neque, a egestas massa feugiat et. Proin et arcu semper, dignissim enim quis, vehicula velit. Sed et accumsan risus, eu consectetur lectus. Fusce a dictum ante. Quisque molestie consequat mauris, nec ultrices diam consequat in. Donec non dapibus leo. Nulla dignissim arcu feugiat erat semper, ut interdum est scelerisque. Vestibulum tincidunt nisi quis leo auctor mattis. Cras ac viverra orci. Fusce at nisl sit amet enim pharetra tempor eu in risus. Cras nec consequat nisl, quis molestie lorem. Ut ac fermentum justo, vitae pretium ex. In eleifend, enim sed varius posuere, felis tortor congue urna, id euismod lorem est non elit. Quisque a nibh neque. Phasellus ornare ligula vel diam accumsan posuere. Vestibulum eget tellus metus. Praesent vitae mattis justo. Maecenas tempus viverra hendrerit. Maecenas porttitor, dolor ut tincidunt fermentum, nulla quam feugiat sem, et rutrum turpis sapien vel est. Sed a metus ut ante eleifend consequat. In hac habitasse platea dictumst. Nam eu mauris dignissim, pulvinar quam ut, euismod massa. Sed varius, mauris quis ullamcorper tincidunt, enim massa pretium massa, nec placerat purus urna vel mauris. Nulla facilisi. Proin facilisis ultricies purus eu dignissim. Duis vitae ligula nibh. Quisque rutrum porta efficitur. Proin nec tellus egestas, laoreet arcu in, congue odio. Maecenas eget vulputate libero. Nulla tristique, leo nec iaculis auctor, tellus sapien vestibulum orci, ac posuere nunc nibh a magna. Nulla consequat porta libero, laoreet pharetra nisl fermentum sit amet. Vivamus a nibh et diam feugiat bibendum a id eros. Phasellus quis lectus auctor elit ornare ultricies et sit amet diam. Nullam quam lacus, dapibus vitae tristique vel, aliquet eget eros. Etiam pulvinar purus ut nulla malesuada, et pellentesque sem dapibus. Nulla pharetra leo elit. In convallis ornare quam, eu gravida massa rhoncus at. Fusce vulputate iaculis sagittis. Nam non quam enim. Vestibulum aliquet eu leo eget auctor. Duis sollicitudin, metus sed egestas egestas, neque ex interdum nulla, ac congue metus lectus a quam. Fusce quis tellus erat. Sed ut erat purus. Morbi eget purus ac magna sollicitudin consequat. Nunc semper fringilla lacus, eget auctor nisi varius quis. Vivamus mi erat, bibendum eu ex sed, lobortis iaculis urna. Etiam lacinia, enim pulvinar tempus accumsan, purus velit condimentum purus, varius accumsan sem felis at enim. Praesent tincidunt elit ex, nec sodales ipsum tincidunt quis. Duis quis ipsum volutpat, commodo nisl quis, viverra purus. Sed risus lectus, posuere quis sem ut, fermentum interdum enim. Nam sed erat faucibus est pharetra finibus id eget velit. Suspendisse sit amet felis nisi. Duis id erat at dui commodo eleifend. Ut faucibus cursus mi in dapibus. Etiam pretium ligula quis neque tristique, vel imperdiet metus pellentesque. Nulla id justo hendrerit, tempus est id, posuere mauris. Praesent scelerisque porta ultricies. Phasellus id ante a nisl tristique feugiat quis at diam. Donec tristique sit amet neque a malesuada. Duis varius lorem ante, eu fringilla dui malesuada id. Aliquam pharetra velit nec erat dapibus malesuada. Aliquam fermentum mi est. Nullam cursus sapien nec dui volutpat hendrerit. Donec at tortor quis mi dictum feugiat. Nam non dui non nisl finibus pulvinar sit amet quis metus. Integer nisl orci, venenatis in libero quis, commodo scelerisque nibh. Integer sit amet tempus mauris. Suspendisse turpis sem, ultrices a libero id, posuere iaculis risus. Praesent ex sem, egestas at nisl nec, venenatis consectetur orci. Mauris tristique est maximus quam finibus vulputate. Nulla ut sollicitudin nisl. Phasellus eu efficitur purus, vitae laoreet enim. Cras consectetur urna ac nisi hendrerit mollis. Nunc id quam nunc. Aliquam erat volutpat. Sed aliquet commodo mauris, sit amet consectetur enim laoreet nec. Donec et diam sit amet orci rutrum pulvinar id a magna. Aliquam aliquam eleifend ligula, eget rutrum nulla ultrices eu. Fusce sagittis efficitur ullamcorper. Nam pellentesque est nec ullamcorper pellentesque. Aliquam erat volutpat. Curabitur sit amet lobortis libero, sit amet cursus quam. Sed luctus erat ultricies, hendrerit ante vel, aliquam ipsum. Integer euismod nisl ac nisi ultrices auctor. Aenean malesuada turpis in ante tincidunt egestas. Pellentesque ac purus sed diam varius fermentum. Fusce commodo dui at sem molestie vehicula. Suspendisse finibus vitae lectus vitae efficitur. Aliquam viverra est et massa commodo sollicitudin. In fringilla felis dui, eu varius dui consectetur vel. Suspendisse potenti. Proin gravida sagittis lacinia. Cras posuere suscipit ex lobortis imperdiet. Vivamus mauris magna, feugiat sed tristique eget, consequat sit amet risus. Aliquam eu rutrum ligula. Aliquam imperdiet convallis mauris, at lacinia nisl pretium vel. Donec eu cursus libero. Morbi at scelerisque arcu. Nulla semper fringilla leo sed mattis. Ut volutpat nulla est, quis ultrices diam interdum malesuada. Suspendisse vulputate purus arcu, nec tincidunt justo commodo in. Cras sit amet fringilla mauris. Curabitur mollis ex at commodo mattis. Sed scelerisque ut risus sed tempus. Nunc blandit, augue at cursus consectetur, elit erat imperdiet nisl, vitae dapibus dui magna at lacus. Phasellus felis orci, lobortis at molestie eu, rhoncus quis dui. Vestibulum id fringilla leo. Etiam posuere justo libero, ac tristique massa dictum a. Ut metus magna, tristique a odio at, vehicula tempus dolor. Fusce at sollicitudin est, ac tincidunt quam. Maecenas a orci ex. Donec ut sagittis dui, sit amet interdum enim. Mauris sollicitudin lectus sed leo dictum finibus. Integer non aliquam turpis. Vivamus fermentum odio at sem varius porta. Donec porttitor quis est et aliquet. Fusce faucibus metus leo, ut auctor nulla fringilla eleifend. Ut interdum, libero quis varius varius, metus libero convallis nibh, nec elementum velit nibh vel dui. Praesent felis mauris, dictum non auctor sit amet, facilisis quis metus. Cras tempor metus et sodales sagittis. Cras blandit elit ac magna facilisis, a pharetra elit venenatis. Suspendisse eu velit velit. Nullam porta consectetur hendrerit. Donec non lacus ullamcorper, elementum magna vel, gravida massa. Nullam quis mi ante. Maecenas odio dui, scelerisque id egestas ornare, maximus at lacus. Morbi efficitur velit et facilisis molestie. Aliquam sed urna ipsum. Nulla sed tempor leo. Nullam at diam nisi. Nunc risus nibh, feugiat nec dolor in, sagittis pharetra nisl. Fusce vulputate euismod arcu ac luctus. Donec vitae feugiat lorem, et iaculis dolor. Sed lacus libero, interdum ac enim eget, pellentesque consequat nunc. Proin ipsum turpis, venenatis in dapibus eget, lobortis sed enim. Donec mauris dui, fermentum et purus id, imperdiet dignissim lectus. Suspendisse felis lorem, semper tincidunt efficitur vel, condimentum vel felis. Fusce in feugiat augue. Proin fringilla urna sed congue volutpat. Curabitur semper rutrum tellus, sit amet ullamcorper ligula posuere eu. Donec luctus, urna a fermentum interdum, lorem libero vestibulum lectus, vestibulum dapibus urna mi id elit. Vestibulum sollicitudin risus nulla, eu suscipit nisi scelerisque vitae. Mauris hendrerit a tellus non semper. Praesent quis urna sollicitudin, luctus lorem a, lacinia risus. Ut sit amet facilisis mauris. Sed nulla risus, commodo eu malesuada eget, scelerisque et nunc. Proin ullamcorper commodo pharetra. Curabitur eget egestas dolor. Vestibulum volutpat aliquet elit ac efficitur. Praesent dictum tincidunt sapien, id molestie augue semper et. Aenean volutpat velit magna. Ut tempus facilisis enim quis imperdiet. Fusce commodo venenatis nisi in blandit. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur eget iaculis augue. Sed vel pharetra sem, vel pharetra felis. Morbi nec tincidunt turpis, a semper massa. Interdum et malesuada fames ac ante ipsum primis in faucibus. Ut ut massa rhoncus, mollis lorem ut, hendrerit dolor. Nullam condimentum magna vel ligula finibus, quis pellentesque magna vestibulum. Suspendisse efficitur sit amet nisi nec lobortis. Fusce aliquet ornare sagittis. Vestibulum maximus lorem venenatis lorem lacinia mollis. Morbi elit eros, pulvinar ac tempus et, scelerisque sed dolor. Suspendisse sagittis eget augue id ultrices. Nam felis velit, convallis in ornare vitae, consequat eu sem. Donec auctor suscipit arcu in congue. Praesent viverra eros ut pharetra luctus. Suspendisse at tempor urna, tincidunt porttitor orci. Quisque gravida suscipit nulla, vitae dictum sem faucibus vel. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Curabitur placerat ultricies dolor. Ut nec leo vulputate, pharetra urna quis, accumsan dolor. Sed fringilla ultrices metus. Suspendisse consequat consectetur turpis, non dictum quam ultricies et. Donec cursus libero risus, vitae dapibus ipsum lacinia a. Nulla facilisi. Integer fringilla justo sed sodales interdum. Vivamus vulputate ornare dolor, eu tincidunt ex placerat vel. Duis turpis neque, bibendum vel aliquam sit amet, rhoncus sit amet augue. Sed leo risus, pharetra eget mattis pellentesque, faucibus et urna. Donec viverra gravida dolor eu sollicitudin. Nullam nec felis tortor. Nullam ut sodales odio. Etiam imperdiet consequat nulla non elementum. Maecenas viverra tellus vitae ante volutpat, eget finibus nibh ultrices. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Phasellus eu lorem gravida, tempor ex id, pretium lacus. Nulla in tempor magna. Suspendisse auctor, ex sed blandit dapibus, risus ante pulvinar mi, vel rhoncus diam sem ut velit. Nam vitae auctor mauris. Donec tincidunt efficitur congue. In hac habitasse platea dictumst. Nam dapibus cursus pulvinar. Sed neque diam, pulvinar vel nisl quis, tristique viverra ligula. Maecenas a nunc libero. Duis tristique augue sit amet massa malesuada pulvinar. Etiam vitae libero eros. Vestibulum at ipsum eros. Mauris efficitur, felis vel tristique blandit, orci nisi ullamcorper eros, ac euismod nisl libero at mi. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nunc auctor venenatis erat ac malesuada. Mauris sit amet aliquam ex. Nulla facilisis augue id diam gravida facilisis. Maecenas at nibh scelerisque, congue enim consectetur, dignissim dolor. Pellentesque eu lacinia mi. Vestibulum dignissim sem non metus convallis, vel laoreet diam consequat. Quisque a mollis turpis, a tristique quam. Praesent hendrerit ultrices tempor. Mauris imperdiet enim at lorem venenatis, vitae consequat erat mollis. Nam massa tellus, scelerisque non lorem eu, venenatis pharetra eros. Morbi fringilla odio sed quam tempus aliquam. Vivamus in lorem non libero porta sollicitudin. Maecenas at consectetur risus. Aenean velit nisl, porta sed mollis bibendum, tincidunt non tellus. Nam sed dictum ante. Praesent quis commodo dui, in viverra mauris. Maecenas sodales dapibus nisl, sit amet maximus nisi bibendum sed. Duis nec orci elit. Curabitur ut ligula non ligula vestibulum ultricies in eu justo. Duis non sagittis enim, nec lacinia nisi. Duis viverra sit amet nulla sed tempor. Proin sollicitudin turpis enim, vel aliquam lectus varius a. Quisque semper nisi at est pharetra suscipit. Nullam condimentum ligula vitae velit dignissim accumsan. Nam mauris ante, porta non venenatis eu, hendrerit et tellus. Phasellus felis libero, auctor consequat velit sed, auctor fringilla felis. Donec felis diam, elementum eget odio ut, vulputate commodo nunc. Duis sed ornare mauris, nec suscipit est. In auctor elementum nunc. Mauris euismod, felis consectetur iaculis lacinia, diam elit consequat lectus, commodo rutrum orci nunc ac arcu. Quisque consequat, diam vel tincidunt volutpat, massa odio mattis elit, in lacinia est risus eu massa. Mauris felis ligula, lobortis at rhoncus et, egestas aliquam metus. Integer sit amet efficitur purus. Suspendisse quis neque ligula. Donec felis sapien, commodo id elit ut, pretium malesuada leo. Praesent rutrum lobortis erat. Nullam mollis semper lectus. Maecenas egestas faucibus magna, sodales sagittis leo. Integer a facilisis tortor. Quisque sem magna, semper eget accumsan vitae, porta at lacus. Nam sit amet condimentum sapien. Fusce porttitor et mauris sed ornare. Etiam ut ornare neque. Sed sit amet ligula ac mauris ultricies tincidunt sed ut enim. Maecenas ornare sapien sit amet nunc volutpat bibendum. Ut vel elit pretium, tincidunt nisl et, fringilla quam. Curabitur hendrerit nisl vitae ipsum iaculis aliquet. Vestibulum commodo id felis quis vulputate. Vestibulum a commodo tortor, sit amet vehicula urna. Etiam gravida imperdiet diam vitae aliquet. Suspendisse risus magna, vestibulum eget sem quis, varius ornare velit. Quisque et turpis a dui dictum aliquet eu sit amet risus. Duis enim diam, sagittis et consectetur sed, euismod ut magna. Duis suscipit scelerisque sapien a vulputate. Fusce id dolor suscipit, malesuada ex non, molestie ligula. Duis id orci vitae enim elementum ornare. Nam non massa et tellus rhoncus auctor. Praesent non lorem quis mauris dignissim pulvinar. Donec ut est non lorem posuere posuere. Vivamus efficitur a diam ut volutpat. Nullam tincidunt tellus justo, non accumsan odio varius ut. Maecenas augue velit, bibendum eget ornare non, pellentesque id justo. Nullam aliquam a urna sit amet tempor. Vivamus ut diam hendrerit, convallis massa eu, posuere velit. Ut at aliquet est, faucibus commodo neque. Maecenas hendrerit hendrerit lectus vel scelerisque. Etiam sit amet nulla vitae leo scelerisque pretium et quis lectus. Morbi lectus nisl, tempor eget erat in, maximus interdum ex. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aenean egestas ipsum vitae facilisis tincidunt. Fusce tristique eros et ante mattis, sit amet semper justo placerat. In facilisis imperdiet ex in finibus. Proin dapibus, est vel imperdiet consequat, metus leo efficitur urna, sit amet tempus erat urna non velit. Donec sagittis sollicitudin tempus. Duis eu tortor eros. Donec vehicula tempor sodales. Cras placerat interdum nunc ut efficitur. Fusce quis finibus quam. Nunc in elementum nisi. Nunc fringilla iaculis gravida. Cras malesuada, nunc nec vehicula pretium, neque metus mollis nisi, sed malesuada lorem ante a felis. Donec venenatis lorem et nisl posuere, dapibus euismod turpis tristique. In hac habitasse platea dictumst. Praesent accumsan sem eu ex consequat, et rhoncus massa accumsan. Praesent aliquet ornare justo, in fermentum mauris tristique sit amet. Praesent fringilla aliquam mi, in egestas dui accumsan eu. Ut tincidunt in risus in faucibus. Ut volutpat nunc urna, at fermentum magna posuere non. Fusce venenatis nisi urna, vitae vehicula risus ullamcorper maximus. Donec ac leo accumsan, convallis eros in, pellentesque nulla. Nunc euismod lacinia tincidunt. Vivamus rhoncus massa ut hendrerit cursus. Interdum et malesuada fames ac ante ipsum primis in faucibus. Sed quis mi dignissim, tempor purus a, mollis nisi. Nullam malesuada commodo lacus, et fringilla justo faucibus eget. Sed vitae quam vitae dolor elementum condimentum. Proin fringilla a arcu in posuere. Nulla placerat, ligula et commodo fermentum, mauris ante condimentum ante, et sollicitudin dui quam sed sem. Donec euismod pulvinar massa, malesuada imperdiet risus mattis eu. Fusce et est ultricies, pretium quam quis, tristique odio. Donec quis lorem interdum, condimentum sem vel, lacinia nisi. In ornare ex vel dui imperdiet scelerisque. Phasellus eget sodales felis, in rutrum velit. Pellentesque molestie ex libero, eget tincidunt neque hendrerit sit amet. Donec dictum nisi risus, et rhoncus arcu commodo et. Sed finibus diam id malesuada placerat. Sed ut tempor nibh. Donec convallis feugiat orci, vel tempor justo. Sed tempus nunc nunc, ut facilisis turpis varius sed. Sed maximus lobortis ipsum, tempus fermentum mi malesuada quis. Suspendisse tempor, ex vel cursus finibus, neque leo eleifend velit, ut tempor nibh urna et diam. Sed ullamcorper vel massa sit amet viverra. Integer vitae pulvinar lectus. Nulla dignissim purus enim, quis fringilla ligula hendrerit gravida. Donec congue leo mi, eget suscipit velit imperdiet a. Donec congue auctor tellus, ac ornare ligula gravida in. Aenean sagittis nibh sit amet urna mollis, in laoreet urna suscipit. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aenean non vestibulum dui, tincidunt euismod metus. Nunc non fermentum leo, et pretium diam. Morbi sed sapien enim. Cras id tincidunt lacus. Duis varius maximus porta. Ut ac massa lectus. Sed viverra accumsan tortor, at tempus nulla commodo et. Pellentesque in vehicula augue. Cras efficitur suscipit mollis. Sed ultricies sapien in sapien commodo, sed semper augue scelerisque. Cras ornare dignissim augue. Pellentesque suscipit odio erat, nec efficitur augue gravida non. Interdum et malesuada fames ac ante ipsum primis in faucibus. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Morbi vestibulum, nunc non lacinia hendrerit, nisl leo interdum dolor, sed sodales libero augue faucibus tellus. Nullam vel maximus ligula. Sed fermentum nisi at nisl viverra, in tristique nisi elementum. Phasellus pharetra et elit quis dictum. Cras rutrum ornare pulvinar. Donec viverra tristique quam, in vehicula metus pharetra maximus. Cras lacinia ornare posuere. Nulla eros justo, rhoncus sed leo sit amet, volutpat scelerisque elit. Proin facilisis nisi sit amet libero faucibus iaculis. Duis a est sagittis, commodo nisi vitae, auctor eros. Aliquam at diam augue. Vestibulum tortor nulla, eleifend nec nunc eget, gravida pretium nisl. Cras luctus finibus sem ac mattis. Proin pharetra turpis nec suscipit rhoncus. Proin vel dolor sit amet neque euismod dapibus a sit amet ligula. Aenean ut enim sit amet nunc commodo pellentesque. Maecenas imperdiet magna ac elit varius, vel hendrerit ipsum malesuada. Etiam pellentesque ante et nisl pretium posuere. Donec malesuada magna vel auctor convallis. Donec nisl tortor, consectetur et lectus eu, finibus molestie est. Praesent auctor metus lacus, ut pulvinar magna imperdiet nec. Fusce scelerisque dolor et ligula condimentum, ut fringilla orci blandit. Aliquam ut sagittis leo, in feugiat mauris. Donec ut lectus orci. Morbi imperdiet elementum venenatis. Morbi blandit pretium accumsan. Phasellus suscipit tincidunt ligula id cursus. Duis tincidunt vehicula mauris, sed malesuada ligula. Duis consectetur lorem in metus sollicitudin, vitae lobortis risus efficitur. In a pulvinar arcu. Curabitur mattis pretium pellentesque. Ut vitae ornare odio. Fusce mattis cursus tellus eu euismod. Cras at interdum risus. Vestibulum et mollis tellus. Vivamus hendrerit quam nec elit luctus, a faucibus purus finibus. Mauris sit amet augue velit. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Proin scelerisque ligula at est hendrerit efficitur. Proin elementum vestibulum ipsum, sit amet mollis ipsum interdum ac. Maecenas nec mi venenatis nulla consequat laoreet sit amet eu dolor. Cras hendrerit nisl eget ante tempus, id tincidunt tortor cursus. Phasellus orci turpis, convallis eu lacinia et, convallis et arcu. Ut ut venenatis ex. Curabitur eu dolor sit amet diam vestibulum sagittis convallis in eros. Praesent accumsan mi vitae diam tempus egestas. Vivamus sit amet tempor dui, et blandit odio. Sed sagittis eu lacus maximus interdum. Quisque laoreet volutpat rhoncus. Etiam bibendum sapien at magna pharetra commodo. Aenean eu tincidunt turpis. Aenean eros diam, mattis ut purus sed, consectetur pellentesque magna. Duis tempor dolor arcu, in dictum velit mattis non. In dignissim lectus velit, vel pharetra eros lacinia elementum. Donec varius risus ante, at tristique ex luctus vel. Donec laoreet libero at diam auctor elementum. Donec volutpat posuere luctus. Phasellus augue orci, pulvinar vel pharetra nec, imperdiet volutpat nulla. Maecenas cursus nibh lorem, ut pretium enim efficitur ut. Cras vel laoreet orci, vitae semper leo. In accumsan nisi magna, ut consequat velit facilisis nec. Phasellus faucibus vehicula auctor. Morbi eget luctus turpis, sit amet vestibulum nunc. Integer bibendum malesuada posuere. Morbi ligula augue, maximus sed convallis id, vehicula ac neque. Praesent diam mi, interdum sit amet volutpat ut, eleifend et leo. Nulla cursus ultricies libero, ut semper dolor tempor eu. Nam euismod nisi pellentesque orci tincidunt, sit amet dictum magna suscipit. Cras ac nulla urna. Maecenas vel mi ac nisi gravida cursus in id purus. In tincidunt ligula id felis tincidunt feugiat. Cras dapibus ullamcorper quam non rutrum. Cras a blandit mi, ut gravida erat. Nunc condimentum, diam sit amet dapibus congue, erat massa imperdiet dui, sit amet varius ligula lorem a nisi. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Cras nisl ex, dictum quis facilisis a, vulputate non eros. Nullam lacinia, dolor vel blandit imperdiet, ex dui laoreet dolor, non dignissim enim urna in quam. Sed placerat dolor vel nibh varius tristique. Fusce volutpat consequat tellus quis eleifend. Mauris condimentum dui mi, eget sollicitudin eros ultrices vitae. Praesent nulla metus, molestie id sapien a, ultrices mattis augue. Sed commodo vitae velit a pharetra. In dictum diam laoreet justo consequat laoreet. Morbi nec auctor lectus. Nullam iaculis arcu et rhoncus scelerisque. Quisque orci dolor, ornare a malesuada et, consectetur eu urna. Vestibulum aliquam, justo quis bibendum maximus, ante nisi auctor magna, id pellentesque nunc justo in sem. Donec ac lectus vel metus pellentesque ullamcorper id a est. Suspendisse elit metus, vestibulum id consectetur a, consequat a erat. Proin vel tortor nisi. Donec facilisis in neque vel pharetra. Nullam convallis efficitur tortor, quis aliquet augue volutpat et. Sed sit amet malesuada sem. Suspendisse enim felis, porttitor cursus venenatis non, maximus vitae est. Donec pharetra neque urna, ut aliquam libero tincidunt sit amet. Aenean ut enim nulla. Phasellus finibus viverra mi at molestie. Nullam in diam urna. Donec eget sapien tincidunt, lacinia eros a, tempus eros. Quisque efficitur porttitor lorem id porttitor. Ut vitae ex auctor, blandit magna ut, vulputate leo. Cras a tincidunt dolor, nec egestas felis. Quisque et lacus quis orci placerat pulvinar et nec ante. In imperdiet ultricies ante nec pellentesque. Nulla facilisi. Donec tincidunt ipsum et quam faucibus porta. Vivamus sagittis leo et leo viverra molestie. Sed tincidunt aliquet sem eu mollis. Proin imperdiet porttitor volutpat. Aenean ornare velit tellus, vulputate pellentesque neque convallis et. Etiam vestibulum ut libero nec cursus. Sed ornare semper lobortis. Sed feugiat enim in porttitor fermentum. Cras cursus elementum tortor. Etiam at congue ligula, ac tempor arcu. Proin nulla mauris, consequat non lobortis sed, fringilla condimentum urna. Fusce quis libero turpis. Integer vitae felis ac mi efficitur mattis a convallis quam. Nam bibendum est ut purus feugiat, vel ultrices ante porttitor. Nam molestie ante erat, vel tincidunt mi aliquam condimentum. In hac habitasse platea dictumst. Praesent efficitur mi sit amet efficitur molestie. Sed egestas mi purus, eget rhoncus leo vulputate vel. Mauris ut libero ut ante hendrerit viverra nec eget sapien. Aenean gravida libero vitae elementum bibendum. Fusce in ante et est convallis imperdiet nec vel nisi. Nunc vitae libero malesuada, efficitur magna a, suscipit neque. Nunc feugiat ante pretium nisi pellentesque, et finibus quam porta. Nulla ipsum turpis, ultricies eget nibh vitae, efficitur luctus leo. Sed consectetur arcu leo, eget tempor sapien aliquet sed. Praesent finibus leo a dignissim mattis. Aliquam nec imperdiet arcu, ut accumsan massa. Morbi sed luctus risus. Suspendisse potenti. Curabitur viverra tortor tempor elit lacinia hendrerit. Aenean semper justo ante, sit amet blandit enim blandit vel. Phasellus lectus felis, mattis at arcu nec, consectetur suscipit orci. Fusce pharetra fringilla imperdiet. Duis vel tristique massa. Pellentesque porttitor tempor ligula, vel euismod ipsum dictum ac. Curabitur ullamcorper dui risus, eget scelerisque libero accumsan eu. Nullam ut pellentesque arcu. Vivamus congue at risus a auctor. Fusce vulputate sem tortor, eget ultricies risus interdum non. Praesent fermentum justo mauris, eget consectetur ante accumsan id. Mauris in orci eu turpis placerat ultrices. Praesent pellentesque velit arcu, id egestas velit dignissim at. Nam feugiat lacus vel diam vehicula, vitae fermentum orci euismod. Proin egestas enim dui, quis rutrum leo rhoncus in. Nulla et quam sed nisi auctor laoreet. Nulla id porta mi. Aliquam aliquam neque quis ultricies pellentesque. Vestibulum consectetur felis nulla, eget feugiat purus pretium eget. Duis vulputate nunc sed leo commodo, vel vestibulum enim semper. Suspendisse ut ante ut neque consequat tincidunt. Sed et ullamcorper nunc. Vestibulum urna velit, tristique a elit in, euismod consectetur tortor. Suspendisse vel risus nulla. Sed ac tellus ac felis aliquam suscipit. Suspendisse ligula ante, scelerisque sed tellus a, accumsan accumsan lectus. Quote Link to comment Share on other sites More sharing options...
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Nobody Posted August 22, 2014 Share Posted August 22, 2014 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut efficitur cursus justo et fringilla. Duis semper orci enim, a scelerisque turpis mattis sed. Aenean dignissim vehicula nisi, eu tempor nisl lacinia sit amet. Sed eu arcu eget velit cursus posuere vitae quis leo. Fusce vestibulum feugiat feugiat. Duis ligula velit, faucibus sit amet arcu at, efficitur congue massa. Quisque euismod, nibh sed egestas luctus, turpis est tincidunt nisl, quis dapibus diam lectus sed risus. Aliquam erat volutpat. Vivamus viverra orci augue, at molestie turpis tristique ut. Etiam ut quam purus. Donec faucibus lacinia rutrum. Maecenas ut dolor in ligula finibus facilisis eu eget ex. Proin placerat pellentesque venenatis. Praesent eu laoreet felis. Proin mollis molestie purus, in feugiat ligula tempor eget. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Morbi auctor justo neque, vel mattis massa ullamcorper nec. Pellentesque metus arcu, fringilla id dui a, faucibus molestie lacus. Aliquam a aliquam ligula. Donec nisl dolor, varius id dolor nec, feugiat fermentum arcu. Ut laoreet ipsum ut gravida imperdiet. Mauris eleifend justo at orci lobortis euismod. Duis non lectus nisl. Vestibulum eget dui sollicitudin dui efficitur volutpat vitae sit amet lorem. In sapien quam, dapibus vitae euismod at, convallis quis dui. Curabitur sit amet ultrices purus, a bibendum diam. Morbi nec felis nunc. Aenean lacinia, tortor eu dictum mattis, tortor enim commodo arcu, sed tristique ex mauris ut sem. Nulla molestie ut nunc at molestie. Integer vehicula id risus eu dictum. Nunc vitae laoreet nunc, id maximus justo. Donec luctus urna id magna scelerisque, quis dapibus libero fermentum. Vestibulum molestie massa ac leo volutpat, in porttitor tellus porttitor. Pellentesque dapibus iaculis orci, eu imperdiet est eleifend sed. Nam vitae maximus libero. Vestibulum scelerisque nisi massa, id finibus nibh efficitur non. Nullam sit amet efficitur erat. Nunc semper lacus eu turpis ultrices mollis eget quis ligula. Ut vel mi sodales, sagittis tellus sed, dictum diam. Phasellus lobortis faucibus tortor. Donec posuere lacus nibh, sit amet dignissim magna vehicula sed. Donec blandit neque sit amet imperdiet tincidunt. Maecenas gravida convallis sem, in maximus turpis tempor in. Sed eu odio condimentum, maximus ipsum ut, consectetur neque. Fusce mattis mi quis sollicitudin viverra. Nullam gravida nisl arcu, a malesuada augue finibus in. Nunc quis tellus elit. Morbi aliquam ligula euismod ligula scelerisque commodo. Aliquam erat risus, ultrices ut leo eget, luctus aliquam est. Duis quis fringilla nisi, et vehicula dolor. Phasellus massa velit, tempus id hendrerit eget, bibendum ac tortor. In rhoncus ex ut varius sollicitudin. Ut imperdiet pharetra faucibus. Fusce sed nunc in nunc convallis scelerisque. Phasellus posuere gravida sagittis. In a augue feugiat, pellentesque odio quis, dictum nisi. In sed pharetra lectus, vitae vehicula neque. Nullam ultrices cursus ex, et gravida mi ornare vitae. Aliquam at nisl nunc. Donec aliquet diam vitae ex iaculis lacinia. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nullam viverra enim tortor, ut efficitur dui accumsan nec. Nulla placerat erat ut nunc bibendum, sed molestie felis consequat. Curabitur bibendum, nisi sed laoreet facilisis, justo mi ullamcorper libero, vel ullamcorper dolor lacus eu lorem. Quisque eget consectetur tortor. Phasellus lacinia eget sapien vel vehicula. Nullam sit amet vestibulum turpis, quis consectetur arcu. Nunc dapibus dapibus eros sed blandit. Nunc imperdiet pharetra felis nec iaculis. Suspendisse nec erat quis risus tincidunt laoreet. Suspendisse accumsan ex erat. Praesent at nisi bibendum, laoreet sem ut, sollicitudin velit. Pellentesque aliquam elit leo, sit amet congue libero eleifend non. Morbi sodales, tortor a congue finibus, felis nibh vehicula urna, sed suscipit risus sapien pharetra est. Etiam ultricies libero sed libero laoreet malesuada. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Quisque in ornare quam. Nam ut tincidunt dolor, vitae dapibus mi. Curabitur eu sagittis diam, nec lacinia nisl. Quisque fermentum ex in odio mollis, at pretium orci vestibulum. Sed ultricies libero dui, at venenatis diam pulvinar nec. Praesent tortor felis, gravida eu nisl id, aliquet faucibus nibh. Nullam sed lorem et purus luctus auctor. Fusce tempor nunc a feugiat porta. Cras nulla ligula, congue ut arcu vitae, tempor euismod nisl. Phasellus imperdiet interdum enim. Quisque eleifend turpis eget tincidunt placerat. Donec finibus tristique magna et interdum. Ut nisl lorem, facilisis sed bibendum sed, eleifend vel eros. Maecenas quis dui tortor. Aliquam vulputate aliquam neque a tincidunt. Vestibulum ut scelerisque est, nec efficitur odio. Phasellus at enim sit amet eros congue bibendum. Donec finibus lacinia quam et pellentesque. Proin suscipit varius lectus a laoreet. Praesent ut finibus augue. Nulla pellentesque lectus et tellus porttitor aliquet. Praesent sed arcu eu dolor blandit efficitur ac eu elit. Etiam id ligula lacinia, dapibus metus id, lobortis tortor. Nullam vehicula interdum elit non tempus. Nulla eget sagittis turpis, nec commodo purus. Vestibulum rhoncus, ligula ac aliquam tempus, ligula erat euismod velit, et volutpat ex eros a elit. Nam ornare metus nec lorem pellentesque feugiat. Integer at ante a augue placerat sagittis quis eget ligula. Quisque elementum, dolor quis cursus facilisis, dui erat dictum sapien, ac mollis turpis turpis nec massa. Sed pharetra accumsan pulvinar. Fusce volutpat, enim a sollicitudin molestie, ex odio eleifend metus, sit amet pretium nunc arcu porttitor elit. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Duis ultricies rutrum tortor, in pellentesque sapien vestibulum eu. Sed ac cursus augue, eget venenatis mauris. Quisque dapibus pretium ipsum, vel sagittis elit suscipit quis. Aliquam condimentum malesuada nibh vitae accumsan. Fusce dignissim tellus eu justo porta, ac consequat augue viverra. Sed rutrum, metus sed eleifend finibus, lorem diam vestibulum magna, ac molestie orci erat vitae felis. Etiam leo quam, molestie id nunc feugiat, sagittis sollicitudin arcu. Quisque porta dolor augue, at gravida lectus tincidunt nec. Nulla non nisl neque. Praesent malesuada felis neque, a egestas massa feugiat et. Proin et arcu semper, dignissim enim quis, vehicula velit. Sed et accumsan risus, eu consectetur lectus. Fusce a dictum ante. Quisque molestie consequat mauris, nec ultrices diam consequat in. Donec non dapibus leo. Nulla dignissim arcu feugiat erat semper, ut interdum est scelerisque. Vestibulum tincidunt nisi quis leo auctor mattis. Cras ac viverra orci. Fusce at nisl sit amet enim pharetra tempor eu in risus. Cras nec consequat nisl, quis molestie lorem. Ut ac fermentum justo, vitae pretium ex. In eleifend, enim sed varius posuere, felis tortor congue urna, id euismod lorem est non elit. Quisque a nibh neque. Phasellus ornare ligula vel diam accumsan posuere. Vestibulum eget tellus metus. Praesent vitae mattis justo. Maecenas tempus viverra hendrerit. Maecenas porttitor, dolor ut tincidunt fermentum, nulla quam feugiat sem, et rutrum turpis sapien vel est. Sed a metus ut ante eleifend consequat. In hac habitasse platea dictumst. Nam eu mauris dignissim, pulvinar quam ut, euismod massa. Sed varius, mauris quis ullamcorper tincidunt, enim massa pretium massa, nec placerat purus urna vel mauris. Nulla facilisi. Proin facilisis ultricies purus eu dignissim. Duis vitae ligula nibh. Quisque rutrum porta efficitur. Proin nec tellus egestas, laoreet arcu in, congue odio. Maecenas eget vulputate libero. Nulla tristique, leo nec iaculis auctor, tellus sapien vestibulum orci, ac posuere nunc nibh a magna. Nulla consequat porta libero, laoreet pharetra nisl fermentum sit amet. Vivamus a nibh et diam feugiat bibendum a id eros. Phasellus quis lectus auctor elit ornare ultricies et sit amet diam. Nullam quam lacus, dapibus vitae tristique vel, aliquet eget eros. Etiam pulvinar purus ut nulla malesuada, et pellentesque sem dapibus. Nulla pharetra leo elit. In convallis ornare quam, eu gravida massa rhoncus at. Fusce vulputate iaculis sagittis. Nam non quam enim. Vestibulum aliquet eu leo eget auctor. Duis sollicitudin, metus sed egestas egestas, neque ex interdum nulla, ac congue metus lectus a quam. Fusce quis tellus erat. Sed ut erat purus. Morbi eget purus ac magna sollicitudin consequat. Nunc semper fringilla lacus, eget auctor nisi varius quis. Vivamus mi erat, bibendum eu ex sed, lobortis iaculis urna. Etiam lacinia, enim pulvinar tempus accumsan, purus velit condimentum purus, varius accumsan sem felis at enim. Praesent tincidunt elit ex, nec sodales ipsum tincidunt quis. Duis quis ipsum volutpat, commodo nisl quis, viverra purus. Sed risus lectus, posuere quis sem ut, fermentum interdum enim. Nam sed erat faucibus est pharetra finibus id eget velit. Suspendisse sit amet felis nisi. Duis id erat at dui commodo eleifend. Ut faucibus cursus mi in dapibus. Etiam pretium ligula quis neque tristique, vel imperdiet metus pellentesque. Nulla id justo hendrerit, tempus est id, posuere mauris. Praesent scelerisque porta ultricies. Phasellus id ante a nisl tristique feugiat quis at diam. Donec tristique sit amet neque a malesuada. Duis varius lorem ante, eu fringilla dui malesuada id. Aliquam pharetra velit nec erat dapibus malesuada. Aliquam fermentum mi est. Nullam cursus sapien nec dui volutpat hendrerit. Donec at tortor quis mi dictum feugiat. Nam non dui non nisl finibus pulvinar sit amet quis metus. Integer nisl orci, venenatis in libero quis, commodo scelerisque nibh. Integer sit amet tempus mauris. Suspendisse turpis sem, ultrices a libero id, posuere iaculis risus. Praesent ex sem, egestas at nisl nec, venenatis consectetur orci. Mauris tristique est maximus quam finibus vulputate. Nulla ut sollicitudin nisl. Phasellus eu efficitur purus, vitae laoreet enim. Cras consectetur urna ac nisi hendrerit mollis. Nunc id quam nunc. Aliquam erat volutpat. Sed aliquet commodo mauris, sit amet consectetur enim laoreet nec. Donec et diam sit amet orci rutrum pulvinar id a magna. Aliquam aliquam eleifend ligula, eget rutrum nulla ultrices eu. Fusce sagittis efficitur ullamcorper. Nam pellentesque est nec ullamcorper pellentesque. Aliquam erat volutpat. Curabitur sit amet lobortis libero, sit amet cursus quam. Sed luctus erat ultricies, hendrerit ante vel, aliquam ipsum. Integer euismod nisl ac nisi ultrices auctor. Aenean malesuada turpis in ante tincidunt egestas. Pellentesque ac purus sed diam varius fermentum. Fusce commodo dui at sem molestie vehicula. Suspendisse finibus vitae lectus vitae efficitur. Aliquam viverra est et massa commodo sollicitudin. In fringilla felis dui, eu varius dui consectetur vel. Suspendisse potenti. Proin gravida sagittis lacinia. Cras posuere suscipit ex lobortis imperdiet. Vivamus mauris magna, feugiat sed tristique eget, consequat sit amet risus. Aliquam eu rutrum ligula. Aliquam imperdiet convallis mauris, at lacinia nisl pretium vel. Donec eu cursus libero. Morbi at scelerisque arcu. Nulla semper fringilla leo sed mattis. Ut volutpat nulla est, quis ultrices diam interdum malesuada. Suspendisse vulputate purus arcu, nec tincidunt justo commodo in. Cras sit amet fringilla mauris. Curabitur mollis ex at commodo mattis. Sed scelerisque ut risus sed tempus. Nunc blandit, augue at cursus consectetur, elit erat imperdiet nisl, vitae dapibus dui magna at lacus. Phasellus felis orci, lobortis at molestie eu, rhoncus quis dui. Vestibulum id fringilla leo. Etiam posuere justo libero, ac tristique massa dictum a. Ut metus magna, tristique a odio at, vehicula tempus dolor. Fusce at sollicitudin est, ac tincidunt quam. Maecenas a orci ex. Donec ut sagittis dui, sit amet interdum enim. Mauris sollicitudin lectus sed leo dictum finibus. Integer non aliquam turpis. Vivamus fermentum odio at sem varius porta. Donec porttitor quis est et aliquet. Fusce faucibus metus leo, ut auctor nulla fringilla eleifend. Ut interdum, libero quis varius varius, metus libero convallis nibh, nec elementum velit nibh vel dui. Praesent felis mauris, dictum non auctor sit amet, facilisis quis metus. Cras tempor metus et sodales sagittis. Cras blandit elit ac magna facilisis, a pharetra elit venenatis. Suspendisse eu velit velit. Nullam porta consectetur hendrerit. Donec non lacus ullamcorper, elementum magna vel, gravida massa. Nullam quis mi ante. Maecenas odio dui, scelerisque id egestas ornare, maximus at lacus. Morbi efficitur velit et facilisis molestie. Aliquam sed urna ipsum. Nulla sed tempor leo. Nullam at diam nisi. Nunc risus nibh, feugiat nec dolor in, sagittis pharetra nisl. Fusce vulputate euismod arcu ac luctus. Donec vitae feugiat lorem, et iaculis dolor. Sed lacus libero, interdum ac enim eget, pellentesque consequat nunc. Proin ipsum turpis, venenatis in dapibus eget, lobortis sed enim. Donec mauris dui, fermentum et purus id, imperdiet dignissim lectus. Suspendisse felis lorem, semper tincidunt efficitur vel, condimentum vel felis. Fusce in feugiat augue. Proin fringilla urna sed congue volutpat. Curabitur semper rutrum tellus, sit amet ullamcorper ligula posuere eu. Donec luctus, urna a fermentum interdum, lorem libero vestibulum lectus, vestibulum dapibus urna mi id elit. Vestibulum sollicitudin risus nulla, eu suscipit nisi scelerisque vitae. Mauris hendrerit a tellus non semper. Praesent quis urna sollicitudin, luctus lorem a, lacinia risus. Ut sit amet facilisis mauris. Sed nulla risus, commodo eu malesuada eget, scelerisque et nunc. Proin ullamcorper commodo pharetra. Curabitur eget egestas dolor. Vestibulum volutpat aliquet elit ac efficitur. Praesent dictum tincidunt sapien, id molestie augue semper et. Aenean volutpat velit magna. Ut tempus facilisis enim quis imperdiet. Fusce commodo venenatis nisi in blandit. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur eget iaculis augue. Sed vel pharetra sem, vel pharetra felis. Morbi nec tincidunt turpis, a semper massa. Interdum et malesuada fames ac ante ipsum primis in faucibus. Ut ut massa rhoncus, mollis lorem ut, hendrerit dolor. Nullam condimentum magna vel ligula finibus, quis pellentesque magna vestibulum. Suspendisse efficitur sit amet nisi nec lobortis. Fusce aliquet ornare sagittis. Vestibulum maximus lorem venenatis lorem lacinia mollis. Morbi elit eros, pulvinar ac tempus et, scelerisque sed dolor. Suspendisse sagittis eget augue id ultrices. Nam felis velit, convallis in ornare vitae, consequat eu sem. Donec auctor suscipit arcu in congue. Praesent viverra eros ut pharetra luctus. Suspendisse at tempor urna, tincidunt porttitor orci. Quisque gravida suscipit nulla, vitae dictum sem faucibus vel. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Curabitur placerat ultricies dolor. Ut nec leo vulputate, pharetra urna quis, accumsan dolor. Sed fringilla ultrices metus. Suspendisse consequat consectetur turpis, non dictum quam ultricies et. Donec cursus libero risus, vitae dapibus ipsum lacinia a. Nulla facilisi. Integer fringilla justo sed sodales interdum. Vivamus vulputate ornare dolor, eu tincidunt ex placerat vel. Duis turpis neque, bibendum vel aliquam sit amet, rhoncus sit amet augue. Sed leo risus, pharetra eget mattis pellentesque, faucibus et urna. Donec viverra gravida dolor eu sollicitudin. Nullam nec felis tortor. Nullam ut sodales odio. Etiam imperdiet consequat nulla non elementum. Maecenas viverra tellus vitae ante volutpat, eget finibus nibh ultrices. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Phasellus eu lorem gravida, tempor ex id, pretium lacus. Nulla in tempor magna. Suspendisse auctor, ex sed blandit dapibus, risus ante pulvinar mi, vel rhoncus diam sem ut velit. Nam vitae auctor mauris. Donec tincidunt efficitur congue. In hac habitasse platea dictumst. Nam dapibus cursus pulvinar. Sed neque diam, pulvinar vel nisl quis, tristique viverra ligula. Maecenas a nunc libero. Duis tristique augue sit amet massa malesuada pulvinar. Etiam vitae libero eros. Vestibulum at ipsum eros. Mauris efficitur, felis vel tristique blandit, orci nisi ullamcorper eros, ac euismod nisl libero at mi. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Nunc auctor venenatis erat ac malesuada. Mauris sit amet aliquam ex. Nulla facilisis augue id diam gravida facilisis. Maecenas at nibh scelerisque, congue enim consectetur, dignissim dolor. Pellentesque eu lacinia mi. Vestibulum dignissim sem non metus convallis, vel laoreet diam consequat. Quisque a mollis turpis, a tristique quam. Praesent hendrerit ultrices tempor. Mauris imperdiet enim at lorem venenatis, vitae consequat erat mollis. Nam massa tellus, scelerisque non lorem eu, venenatis pharetra eros. Morbi fringilla odio sed quam tempus aliquam. Vivamus in lorem non libero porta sollicitudin. Maecenas at consectetur risus. Aenean velit nisl, porta sed mollis bibendum, tincidunt non tellus. Nam sed dictum ante. Praesent quis commodo dui, in viverra mauris. Maecenas sodales dapibus nisl, sit amet maximus nisi bibendum sed. Duis nec orci elit. Curabitur ut ligula non ligula vestibulum ultricies in eu justo. Duis non sagittis enim, nec lacinia nisi. Duis viverra sit amet nulla sed tempor. Proin sollicitudin turpis enim, vel aliquam lectus varius a. Quisque semper nisi at est pharetra suscipit. Nullam condimentum ligula vitae velit dignissim accumsan. Nam mauris ante, porta non venenatis eu, hendrerit et tellus. Phasellus felis libero, auctor consequat velit sed, auctor fringilla felis. Donec felis diam, elementum eget odio ut, vulputate commodo nunc. Duis sed ornare mauris, nec suscipit est. In auctor elementum nunc. Mauris euismod, felis consectetur iaculis lacinia, diam elit consequat lectus, commodo rutrum orci nunc ac arcu. Quisque consequat, diam vel tincidunt volutpat, massa odio mattis elit, in lacinia est risus eu massa. Mauris felis ligula, lobortis at rhoncus et, egestas aliquam metus. Integer sit amet efficitur purus. Suspendisse quis neque ligula. Donec felis sapien, commodo id elit ut, pretium malesuada leo. Praesent rutrum lobortis erat. Nullam mollis semper lectus. Maecenas egestas faucibus magna, sodales sagittis leo. Integer a facilisis tortor. Quisque sem magna, semper eget accumsan vitae, porta at lacus. Nam sit amet condimentum sapien. Fusce porttitor et mauris sed ornare. Etiam ut ornare neque. Sed sit amet ligula ac mauris ultricies tincidunt sed ut enim. Maecenas ornare sapien sit amet nunc volutpat bibendum. Ut vel elit pretium, tincidunt nisl et, fringilla quam. Curabitur hendrerit nisl vitae ipsum iaculis aliquet. Vestibulum commodo id felis quis vulputate. Vestibulum a commodo tortor, sit amet vehicula urna. Etiam gravida imperdiet diam vitae aliquet. Suspendisse risus magna, vestibulum eget sem quis, varius ornare velit. Quisque et turpis a dui dictum aliquet eu sit amet risus. Duis enim diam, sagittis et consectetur sed, euismod ut magna. Duis suscipit scelerisque sapien a vulputate. Fusce id dolor suscipit, malesuada ex non, molestie ligula. Duis id orci vitae enim elementum ornare. Nam non massa et tellus rhoncus auctor. Praesent non lorem quis mauris dignissim pulvinar. Donec ut est non lorem posuere posuere. Vivamus efficitur a diam ut volutpat. Nullam tincidunt tellus justo, non accumsan odio varius ut. Maecenas augue velit, bibendum eget ornare non, pellentesque id justo. Nullam aliquam a urna sit amet tempor. Vivamus ut diam hendrerit, convallis massa eu, posuere velit. Ut at aliquet est, faucibus commodo neque. Maecenas hendrerit hendrerit lectus vel scelerisque. Etiam sit amet nulla vitae leo scelerisque pretium et quis lectus. Morbi lectus nisl, tempor eget erat in, maximus interdum ex. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aenean egestas ipsum vitae facilisis tincidunt. Fusce tristique eros et ante mattis, sit amet semper justo placerat. In facilisis imperdiet ex in finibus. Proin dapibus, est vel imperdiet consequat, metus leo efficitur urna, sit amet tempus erat urna non velit. Donec sagittis sollicitudin tempus. Duis eu tortor eros. Donec vehicula tempor sodales. Cras placerat interdum nunc ut efficitur. Fusce quis finibus quam. Nunc in elementum nisi. Nunc fringilla iaculis gravida. Cras malesuada, nunc nec vehicula pretium, neque metus mollis nisi, sed malesuada lorem ante a felis. Donec venenatis lorem et nisl posuere, dapibus euismod turpis tristique. In hac habitasse platea dictumst. Praesent accumsan sem eu ex consequat, et rhoncus massa accumsan. Praesent aliquet ornare justo, in fermentum mauris tristique sit amet. Praesent fringilla aliquam mi, in egestas dui accumsan eu. Ut tincidunt in risus in faucibus. Ut volutpat nunc urna, at fermentum magna posuere non. Fusce venenatis nisi urna, vitae vehicula risus ullamcorper maximus. Donec ac leo accumsan, convallis eros in, pellentesque nulla. Nunc euismod lacinia tincidunt. Vivamus rhoncus massa ut hendrerit cursus. Interdum et malesuada fames ac ante ipsum primis in faucibus. Sed quis mi dignissim, tempor purus a, mollis nisi. Nullam malesuada commodo lacus, et fringilla justo faucibus eget. Sed vitae quam vitae dolor elementum condimentum. Proin fringilla a arcu in posuere. Nulla placerat, ligula et commodo fermentum, mauris ante condimentum ante, et sollicitudin dui quam sed sem. Donec euismod pulvinar massa, malesuada imperdiet risus mattis eu. Fusce et est ultricies, pretium quam quis, tristique odio. Donec quis lorem interdum, condimentum sem vel, lacinia nisi. In ornare ex vel dui imperdiet scelerisque. Phasellus eget sodales felis, in rutrum velit. Pellentesque molestie ex libero, eget tincidunt neque hendrerit sit amet. Donec dictum nisi risus, et rhoncus arcu commodo et. Sed finibus diam id malesuada placerat. Sed ut tempor nibh. Donec convallis feugiat orci, vel tempor justo. Sed tempus nunc nunc, ut facilisis turpis varius sed. Sed maximus lobortis ipsum, tempus fermentum mi malesuada quis. Suspendisse tempor, ex vel cursus finibus, neque leo eleifend velit, ut tempor nibh urna et diam. Sed ullamcorper vel massa sit amet viverra. Integer vitae pulvinar lectus. Nulla dignissim purus enim, quis fringilla ligula hendrerit gravida. Donec congue leo mi, eget suscipit velit imperdiet a. Donec congue auctor tellus, ac ornare ligula gravida in. Aenean sagittis nibh sit amet urna mollis, in laoreet urna suscipit. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aenean non vestibulum dui, tincidunt euismod metus. Nunc non fermentum leo, et pretium diam. Morbi sed sapien enim. Cras id tincidunt lacus. Duis varius maximus porta. Ut ac massa lectus. Sed viverra accumsan tortor, at tempus nulla commodo et. Pellentesque in vehicula augue. Cras efficitur suscipit mollis. Sed ultricies sapien in sapien commodo, sed semper augue scelerisque. Cras ornare dignissim augue. Pellentesque suscipit odio erat, nec efficitur augue gravida non. Interdum et malesuada fames ac ante ipsum primis in faucibus. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Morbi vestibulum, nunc non lacinia hendrerit, nisl leo interdum dolor, sed sodales libero augue faucibus tellus. Nullam vel maximus ligula. Sed fermentum nisi at nisl viverra, in tristique nisi elementum. Phasellus pharetra et elit quis dictum. Cras rutrum ornare pulvinar. Donec viverra tristique quam, in vehicula metus pharetra maximus. Cras lacinia ornare posuere. Nulla eros justo, rhoncus sed leo sit amet, volutpat scelerisque elit. Proin facilisis nisi sit amet libero faucibus iaculis. Duis a est sagittis, commodo nisi vitae, auctor eros. Aliquam at diam augue. Vestibulum tortor nulla, eleifend nec nunc eget, gravida pretium nisl. Cras luctus finibus sem ac mattis. Proin pharetra turpis nec suscipit rhoncus. Proin vel dolor sit amet neque euismod dapibus a sit amet ligula. Aenean ut enim sit amet nunc commodo pellentesque. Maecenas imperdiet magna ac elit varius, vel hendrerit ipsum malesuada. Etiam pellentesque ante et nisl pretium posuere. Donec malesuada magna vel auctor convallis. Donec nisl tortor, consectetur et lectus eu, finibus molestie est. Praesent auctor metus lacus, ut pulvinar magna imperdiet nec. Fusce scelerisque dolor et ligula condimentum, ut fringilla orci blandit. Aliquam ut sagittis leo, in feugiat mauris. Donec ut lectus orci. Morbi imperdiet elementum venenatis. Morbi blandit pretium accumsan. Phasellus suscipit tincidunt ligula id cursus. Duis tincidunt vehicula mauris, sed malesuada ligula. Duis consectetur lorem in metus sollicitudin, vitae lobortis risus efficitur. In a pulvinar arcu. Curabitur mattis pretium pellentesque. Ut vitae ornare odio. Fusce mattis cursus tellus eu euismod. Cras at interdum risus. Vestibulum et mollis tellus. Vivamus hendrerit quam nec elit luctus, a faucibus purus finibus. Mauris sit amet augue velit. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Proin scelerisque ligula at est hendrerit efficitur. Proin elementum vestibulum ipsum, sit amet mollis ipsum interdum ac. Maecenas nec mi venenatis nulla consequat laoreet sit amet eu dolor. Cras hendrerit nisl eget ante tempus, id tincidunt tortor cursus. Phasellus orci turpis, convallis eu lacinia et, convallis et arcu. Ut ut venenatis ex. Curabitur eu dolor sit amet diam vestibulum sagittis convallis in eros. Praesent accumsan mi vitae diam tempus egestas. Vivamus sit amet tempor dui, et blandit odio. Sed sagittis eu lacus maximus interdum. Quisque laoreet volutpat rhoncus. Etiam bibendum sapien at magna pharetra commodo. Aenean eu tincidunt turpis. Aenean eros diam, mattis ut purus sed, consectetur pellentesque magna. Duis tempor dolor arcu, in dictum velit mattis non. In dignissim lectus velit, vel pharetra eros lacinia elementum. Donec varius risus ante, at tristique ex luctus vel. Donec laoreet libero at diam auctor elementum. Donec volutpat posuere luctus. Phasellus augue orci, pulvinar vel pharetra nec, imperdiet volutpat nulla. Maecenas cursus nibh lorem, ut pretium enim efficitur ut. Cras vel laoreet orci, vitae semper leo. In accumsan nisi magna, ut consequat velit facilisis nec. Phasellus faucibus vehicula auctor. Morbi eget luctus turpis, sit amet vestibulum nunc. Integer bibendum malesuada posuere. Morbi ligula augue, maximus sed convallis id, vehicula ac neque. Praesent diam mi, interdum sit amet volutpat ut, eleifend et leo. Nulla cursus ultricies libero, ut semper dolor tempor eu. Nam euismod nisi pellentesque orci tincidunt, sit amet dictum magna suscipit. Cras ac nulla urna. Maecenas vel mi ac nisi gravida cursus in id purus. In tincidunt ligula id felis tincidunt feugiat. Cras dapibus ullamcorper quam non rutrum. Cras a blandit mi, ut gravida erat. Nunc condimentum, diam sit amet dapibus congue, erat massa imperdiet dui, sit amet varius ligula lorem a nisi. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Cras nisl ex, dictum quis facilisis a, vulputate non eros. Nullam lacinia, dolor vel blandit imperdiet, ex dui laoreet dolor, non dignissim enim urna in quam. Sed placerat dolor vel nibh varius tristique. Fusce volutpat consequat tellus quis eleifend. Mauris condimentum dui mi, eget sollicitudin eros ultrices vitae. Praesent nulla metus, molestie id sapien a, ultrices mattis augue. Sed commodo vitae velit a pharetra. In dictum diam laoreet justo consequat laoreet. Morbi nec auctor lectus. Nullam iaculis arcu et rhoncus scelerisque. Quisque orci dolor, ornare a malesuada et, consectetur eu urna. Vestibulum aliquam, justo quis bibendum maximus, ante nisi auctor magna, id pellentesque nunc justo in sem. Donec ac lectus vel metus pellentesque ullamcorper id a est. Suspendisse elit metus, vestibulum id consectetur a, consequat a erat. Proin vel tortor nisi. Donec facilisis in neque vel pharetra. Nullam convallis efficitur tortor, quis aliquet augue volutpat et. Sed sit amet malesuada sem. Suspendisse enim felis, porttitor cursus venenatis non, maximus vitae est. Donec pharetra neque urna, ut aliquam libero tincidunt sit amet. Aenean ut enim nulla. Phasellus finibus viverra mi at molestie. Nullam in diam urna. Donec eget sapien tincidunt, lacinia eros a, tempus eros. Quisque efficitur porttitor lorem id porttitor. Ut vitae ex auctor, blandit magna ut, vulputate leo. Cras a tincidunt dolor, nec egestas felis. Quisque et lacus quis orci placerat pulvinar et nec ante. In imperdiet ultricies ante nec pellentesque. Nulla facilisi. Donec tincidunt ipsum et quam faucibus porta. Vivamus sagittis leo et leo viverra molestie. Sed tincidunt aliquet sem eu mollis. Proin imperdiet porttitor volutpat. Aenean ornare velit tellus, vulputate pellentesque neque convallis et. Etiam vestibulum ut libero nec cursus. Sed ornare semper lobortis. Sed feugiat enim in porttitor fermentum. Cras cursus elementum tortor. Etiam at congue ligula, ac tempor arcu. Proin nulla mauris, consequat non lobortis sed, fringilla condimentum urna. Fusce quis libero turpis. Integer vitae felis ac mi efficitur mattis a convallis quam. Nam bibendum est ut purus feugiat, vel ultrices ante porttitor. Nam molestie ante erat, vel tincidunt mi aliquam condimentum. In hac habitasse platea dictumst. Praesent efficitur mi sit amet efficitur molestie. Sed egestas mi purus, eget rhoncus leo vulputate vel. Mauris ut libero ut ante hendrerit viverra nec eget sapien. Aenean gravida libero vitae elementum bibendum. Fusce in ante et est convallis imperdiet nec vel nisi. Nunc vitae libero malesuada, efficitur magna a, suscipit neque. Nunc feugiat ante pretium nisi pellentesque, et finibus quam porta. Nulla ipsum turpis, ultricies eget nibh vitae, efficitur luctus leo. Sed consectetur arcu leo, eget tempor sapien aliquet sed. Praesent finibus leo a dignissim mattis. Aliquam nec imperdiet arcu, ut accumsan massa. Morbi sed luctus risus. Suspendisse potenti. Curabitur viverra tortor tempor elit lacinia hendrerit. Aenean semper justo ante, sit amet blandit enim blandit vel. Phasellus lectus felis, mattis at arcu nec, consectetur suscipit orci. Fusce pharetra fringilla imperdiet. Duis vel tristique massa. Pellentesque porttitor tempor ligula, vel euismod ipsum dictum ac. Curabitur ullamcorper dui risus, eget scelerisque libero accumsan eu. Nullam ut pellentesque arcu. Vivamus congue at risus a auctor. Fusce vulputate sem tortor, eget ultricies risus interdum non. Praesent fermentum justo mauris, eget consectetur ante accumsan id. Mauris in orci eu turpis placerat ultrices. Praesent pellentesque velit arcu, id egestas velit dignissim at. Nam feugiat lacus vel diam vehicula, vitae fermentum orci euismod. Proin egestas enim dui, quis rutrum leo rhoncus in. Nulla et quam sed nisi auctor laoreet. Nulla id porta mi. Aliquam aliquam neque quis ultricies pellentesque. Vestibulum consectetur felis nulla, eget feugiat purus pretium eget. Duis vulputate nunc sed leo commodo, vel vestibulum enim semper. Suspendisse ut ante ut neque consequat tincidunt. Sed et ullamcorper nunc. Vestibulum urna velit, tristique a elit in, euismod consectetur tortor. Suspendisse vel risus nulla. Sed ac tellus ac felis aliquam suscipit. Suspendisse ligula ante, scelerisque sed tellus a, accumsan accumsan lectus. Differential equation From Wikipedia, the free encyclopedia Not to be confused with Difference equation. This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (August 2009) Differential equations Navier–Stokes differential equations used to simulate airflow around an obstruction Navier–Stokes differential equations used to simulate airflow around an obstruction. Scope [show] Classification Types[show] Relation to processes[show] Solution General topics[show] Solution methods[show] People [show] v t e Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state temperature distribution. A differential equation is a mathematical equation that relates some function of one or more variables with its derivatives. Differential equations arise whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions — the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy. Contents [hide] 1 Example 2 Directions of study 3 Nomenclature 3.1 Ordinary and partial 3.2 Linear and non-linear 3.3 Examples 4 Related concepts 5 Connection to difference equations 6 Universality of mathematical description 7 Notable differential equations 7.1 Physics and engineering 7.2 Biology 7.3 Economics 8 See also 9 References 10 External links Example[edit] For example, in classical mechanics, the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly. An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the acceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity (and the velocity depends on time). Finding the velocity as a function of time involves solving a differential equation and verifying its validity. Directions of study[edit] The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods. Mathematicians also study weak solutions (relying on weak derivatives), which are types of solutions that do not have to be differentiable everywhere. This extension is often necessary for solutions to exist. The study of the stability of solutions of differential equations is known as stability theory. Nomenclature[edit] The theory of differential equations is well developed and the methods used to study them vary significantly with the type of the equation. Ordinary and partial[edit] An ordinary differential equation (ODE) is a differential equation in which the unknown function (also known as the dependent variable) is a function of a single independent variable. In the simplest form, the unknown function is a real or complex valued function, but more generally, it may be vector-valued or matrix-valued: this corresponds to considering a system of ordinary differential equations for a single function. Ordinary differential equations are further classified according to the order of the highest derivative of the dependent variable with respect to the independent variable appearing in the equation. The most important cases for applications are first-order and second-order differential equations. For example, Bessel's differential equation x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + (x^2 - \alpha^2)y = 0 (in which y is the dependent variable) is a second-order differential equation. In the classical literature a distinction is also made between differential equations explicitly solved with respect to the highest derivative and differential equations in an implicit form. Also important is the degree, or (highest) power, of the highest derivative(s) in the equation (cf. : degree of a polynomial). A differential equation is called a nonlinear differential equation if its degree is not one (a sufficient but unnecessary condition). A partial differential equation (PDE) is a differential equation in which the unknown function is a function of multiple independent variables and the equation involves its partial derivatives. The order is defined similarly to the case of ordinary differential equations, but further classification into elliptic, hyperbolic, and parabolic equations, especially for second-order linear equations, is of utmost importance. Some partial differential equations do not fall into any of these categories over the whole domain of the independent variables and they are said to be of mixed type. Linear and non-linear[edit] Both ordinary and partial differential equations are broadly classified as linear and nonlinear. A differential equation is linear if the unknown function and its derivatives appear to the power 1 (products of the unknown function and its derivatives are not allowed) and nonlinear otherwise. The characteristic property of linear equations is that their solutions form an affine subspace of an appropriate function space, which results in much more developed theory of linear differential equations. Homogeneous linear differential equations are a further subclass for which the space of solutions is a linear subspace i.e. the sum of any set of solutions or multiples of solutions is also a solution. The coefficients of the unknown function and its derivatives in a linear differential equation are allowed to be (known) functions of the independent variable or variables; if these coefficients are constants then one speaks of a constant coefficient linear differential equation. There are very few methods of solving nonlinear differential equations exactly; those that are known typically depend on the equation having particular symmetries. Nonlinear differential equations can exhibit very complicated behavior over extended time intervals, characteristic of chaos. Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory (cf. Navier–Stokes existence and smoothness). However, if the differential equation is a correctly formulated representation of a meaningful physical process, then one expects it to have a solution.[1] Linear differential equations frequently appear as approximations to nonlinear equations. These approximations are only valid under restricted conditions. For example, the harmonic oscillator equation is an approximation to the nonlinear pendulum equation that is valid for small amplitude oscillations (see below). Examples[edit] In the first group of examples, let u be an unknown function of x, and c and ω are known constants. Inhomogeneous first-order linear constant coefficient ordinary differential equation: \frac{du}{dx} = cu+x^2. Homogeneous second-order linear ordinary differential equation: \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. Homogeneous second-order linear constant coefficient ordinary differential equation describing the harmonic oscillator: \frac{d^2u}{dx^2} + \omega^2u = 0. Inhomogeneous first-order nonlinear ordinary differential equation: \frac{du}{dx} = u^2 + 4. Second-order nonlinear (due to sine function) ordinary differential equation describing the motion of a pendulum of length L: L\frac{d^2u}{dx^2} + g\sin u = 0. In the next group of examples, the unknown function u depends on two variables x and t or x and y. Homogeneous first-order linear partial differential equation: \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. Homogeneous second-order linear constant coefficient partial differential equation of elliptic type, the Laplace equation: \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. Third-order nonlinear partial differential equation, the Korteweg–de Vries equation: \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. Related concepts[edit] A delay differential equation (DDE) is an equation for a function of a single variable, usually called time, in which the derivative of the function at a certain time is given in terms of the values of the function at earlier times. A stochastic differential equation (SDE) is an equation in which the unknown quantity is a stochastic process and the equation involves some known stochastic processes, for example, the Wiener process in the case of diffusion equations. A differential algebraic equation (DAE) is a differential equation comprising differential and algebraic terms, given in implicit form. Connection to difference equations[edit] See also: Time scale calculus The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve approximation of the solution of a differential equation by the solution of a corresponding difference equation. Universality of mathematical description[edit] Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation. It turns out that many diffusion processes, while seemingly different, are described by the same equation; the Black–Scholes equation in finance is, for instance, related to the heat equation. Notable differential equations[edit] Physics and engineering[edit] Newton's Second Law in dynamics (mechanics) Euler–Lagrange equation in classical mechanics Hamilton's equations in classical mechanics Radioactive decay in nuclear physics Newton's law of cooling in thermodynamics The wave equation Maxwell's equations in electromagnetism The heat equation in thermodynamics Laplace's equation, which defines harmonic functions Poisson's equation Einstein's field equation in general relativity The Schrödinger equation in quantum mechanics The geodesic equation The Navier–Stokes equations in fluid dynamics The Diffusion equation in stochastic processes The Convection–diffusion equation in fluid dynamics The Cauchy–Riemann equations in complex analysis The Poisson–Boltzmann equation in molecular dynamics The shallow water equations Universal differential equation The Lorenz equations whose solutions exhibit chaotic flow. Biology[edit] Verhulst equation – biological population growth von Bertalanffy model – biological individual growth Lotka–Volterra equations – biological population dynamics Replicator dynamics – found in theoretical biology Hodgkin–Huxley model – neural action potentials Economics[edit] The Black–Scholes PDE Exogenous growth model Malthusian growth model The Vidale–Wolfe advertising model See also[edit] Complex differential equation Exact differential equation Integral equations Numerical methods Picard–Lindelöf theorem on existence and uniqueness of solutions Recurrence relation, also known as 'Difference Equation' References[edit] P. Abbott and H. Neill, Teach Yourself Calculus, 2003 pages 266-277 P. Blanchard, R. L. Devaney, G. R. Hall, Differential Equations, Thompson, 2006 E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955 E. L. Ince, Ordinary Differential Equations, Dover Publications, 1956 W. Johnson, A Treatise on Ordinary and Partial Differential Equations, John Wiley and Sons, 1913, in University of Michigan Historical Math Collection A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations (2nd edition), Chapman & Hall/CRC Press, Boca Raton, 2003. ISBN 1-58488-297-2. R. I. Porter, Further Elementary Analysis, 1978, chapter XIX Differential Equations Teschl, Gerald (2012). Ordinary Differential Equations and Dynamical Systems. Providence: American Mathematical Society. ISBN 978-0-8218-8328-0. D. Zwillinger, Handbook of Differential Equations (3rd edition), Academic Press, Boston, 1997. Jump up ^ Boyce, William E.; DiPrima, Richard C. (1967). Elementary Differential Equations and Boundary Value Problems (4th ed.). John Wiley & Sons. p. 3. External links[edit] Wikibooks has a book on the topic of: Ordinary Differential Equations Lectures on Differential Equations MIT Open CourseWare Videos Online Notes / Differential Equations Paul Dawkins, Lamar University Differential Equations, S.O.S. Mathematics Differential Equation Solver Java applet tool used to solve differential equations. Introduction to modeling via differential equations Introduction to modeling by means of differential equations, with critical remarks. Mathematical Assistant on Web Symbolic ODE tool, using Maxima Exact Solutions of Ordinary Differential Equations Collection of ODE and DAE models of physical systems MATLAB models Notes on Diffy Qs: Differential Equations for Engineers An introductory textbook on differential equations by Jiri Lebl of UIUC Khan Academy Video playlist on differential equations Topics covered in a first year course in differential equations. MathDiscuss Video playlist on differential equations [hide] v t e Areas of mathematics Areas Algebra (elementary linear multilinear abstract) Arithmetic / Number theory Calculus / Analysis Category theory Combinatorics Computation Control theory Differential equations / Dynamical systems Functional analysis Game theory Geometry (discrete algebraic differential finite) Graph theory Information theory Lie theory Mathematical logic Mathematical physics Mathematical statistics Numerical analysis Optimization Probability Representation theory Set theory Topology Trigonometry Divisions Pure Applied Discrete Computational CategoryCategory PortalMathematics portal / outline / topic lists Categories: Differential equations Quote Link to comment Share on other sites More sharing options...
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DreadFighter Posted August 22, 2014 Share Posted August 22, 2014 Waluigi's outfit includes a purple undershirt under black overalls, orange shoes, and a purple cap that covers his short, brown hair. He has a large, pink nose, a thin mustache which is straight (horizontal) and pointed up at the edge, and gray eyes, his eyes being surrounded by light blue rings. He also has long limbs and a skinny torso. The yellow symbol on his hat and gloves is a vertical mirror image of Luigi's "L" which forms a "Γ", just as Wario wears a "W" in contrast to Mario's "M". The "Γ" is actually the Greek letter Gamma, which is pronounced similarly to "G". Just like his partner, Waluigi is the extreme form of his rival. While Luigi is tall and skinny, Waluigi is taller and skinnier, just as Wario is short and obese in contrast to Mario. It has been stated that Wario routinely puts Waluigi on a rack to make him even taller. Luigi´s facial elements are also exaggerated in Waluigi. Waluigi has a very sharp jaw and a pointy chin. Waluigi's sharp, handlebar mustache is an exaggeration of Luigi's soft and fluffy mustache. Many biographies describing him in Mario sports games mention (and poke fun at) his odd facial elements, including his sharp jaw, pointy nose, and flat feet. Waluigi's clothing also breaks the palette-swap color scheme in place from Mario and Luigi. Mario and Luigi have the same colored pants, with their signature colors being opposites (red and green). With Wario and Waluigi, while the signature colors are still opposites (yellow and purple), their pants are not matching colors. Waluigi was designed to wear dark purple pants, rather than the lighter purple of Wario (in order to not be monochromatic), which breaks from the previous system of color-coding. On a side note, Waluigi has appeared wearing black pants at times. Waluigi's outfit is sometimes referenced by the Mario Bros.. In Paper Mario: The Thousand-Year Door, by wearing both the "L" Emblem (Luigi) and the "W" Emblem (Wario) together, Mario will wear a purple undershirt and black overalls. The same can be done in Super Smash Bros. Brawl by switching Luigi's costume color. Quote Link to comment Share on other sites More sharing options...
Julius Nepos Posted August 22, 2014 Share Posted August 22, 2014 This city, mistress of the whole earth and sea, which the Romans now inhabit, is said to have had as its earliest occupants the barbarian Sicels, a native race. As to the condition of the place before their time, whether it was occupied by others or uninhabited, none can certainly say. But some time later the Aborigines gained possession of it, having taken it from the occupants after a long war. 2 These people had previously lived on the mountains in unwalled villages and scattered groups; but when the Pelasgians,23 with whom some other Greeks had united, assisted them in the war against their neighbours, they drove the Sicels out of this place, walled in many towns, and contrived to subjugate all the country that lies between the two rivers, the Liris and the Tiber. These rivers spring from the foot of the Apennine mountains, the range by which all Italy is divided into two parts throughout its length, and at points about eight hundred stades from one another discharge themselves into the Tyrrhenian Sea, the Tiber to the north, near the city of Ostia, and the Liris to the south, as it flows by Minturnae, both these cities being Roman colonies. 3 And these people remained in this same place of abode, both never afterwards driven out by any others; but, although they continued to be one and the same people, their name was twice changed. Till the time of the Trojan war they preserved their ancient name p31of Aborigines; but under Latinus, their king, who reigned at the time of that war, they began to be called Latins, 4 and when Romulus founded the city named after himself sixteen generations after the taking of Troy, they took the name which they now bear. And in the course of time they contrived to raise themselves from the smallest nation to the greatest and from the most obscure to the most illustrious, not only by their humane reception of those who sought a home among them, but also by sharing the rights of citizenship with all who had been conquered by them in war after a brave resistance, by permitting all the slaves, too, who were manumitted among them to become citizens, and by disdaining no condition of men from whom the commonwealth might reap an advantage, but above everything else by their form of government, which they fashioned out of their many experiences, always extracting something useful from every occasion. 10 1 There are some who affirm that the Aborigines, from whom the Romans are originally descended, were natives of Italy, a stock which came into being spontaneously24 (I call Italy all that peninsula which is bounded by the Ionian Gulf25 and the Tyrrhenian Sea and, thirdly, by the Alps on the landward side); and these authors say that they were first called Aborigines because they were the founders of the p33families of their descendants, or, as we should call them, genearchai or prôtogonoi.26 2 Others claim that certain vagabonds without house or home, coming together out of many places, met one another there by chance and took up their abode in the fastnesses, living by robbery and grazing their herds. And these writers change their name, also, to one more suitable to their condition, calling them Aberrigenes,27 to show that they were wanderers; indeed, according to these, the race of the Aborigines would seem to be no different from those the ancients called Leleges; for this is the name they generally gave to the homeless and mixed peoples who had no fixed abode which they could call their country.28 3 Still others have a story to the effect that they were colonists sent out by those Ligurians who are neighbours of the Umbrians. For the Ligurians inhabit not only many parts of Italy but some parts of Gaul as well, but which of these lands is their native country is not known, since nothing certain is said of them further. 11 1 But the most learned of the Roman historians, among whom is Porcius Cato, who compiled with the greatest care the "origins"29 of the Italian cities, p35Gaius Sempronius30 and a great many others, say that they were Greeks, part of those who once dwelt in Achaia, and that they migrated many generations before the Trojan war. But they do not go on to indicate either the Greek tribe to which they belonged or the city from which they removed, or the date or the leader of the colony, or as the result of what turns of fortune they left their mother country; and although they are following a Greek legend, they have cited no Greek historian as their authority. It is uncertain, therefore, what the truth of the matter is. But if what they say is true, the Aborigines can be a colony of no other people but of those who are now called Arcadians; 2 for these were the first of all the Greeks to cross the Ionian Gulf, under the leadership of Oenotrus, the son of Lycaon, and to settle in Italy. This Oenotrus was the fifth from Aezeius and Phoroneus, who were the first kings in the Peloponnesus. For Niobê was the daughter of Phoroneus, and Pelasgus was the son of Niobê and Zeus, it is said; Lycaon was the son of Aezeius and Deïanira was the daughter of Lycaon; Deïanira and Pelasgus were the parents of another Lycaon, whose son Oenotrus was born seventeen generations before the Trojan expedition. This, then, was the time when the Greeks sent the colony into Italy. 3 Oenotrus left Greece because he was dissatisfied with his portion of his father's land; for, as Lycaon had twenty-two sons, it was necessary to divide Arcadia into as many shares. For this reason Oenotrus left the Peloponnesus, p37prepared a fleet, and crossed the Ionian Gulf with Peucetius, one of his brothers. They were accompanied by many of their own people — for this nation is said to have been very populous in early times — and by as many other Greeks as had less land than was sufficient for them. 4 Peucetius landed his people above the Iapygian Promontory, which was the first part of Italy they made, and settled there; and from him the inhabitants of this region were called Peucetians. But Oenotrus with the greater part of the expedition came into the other sea that washes the western regions along the coast of Italy; it was then called the Ausonian Sea, from the Ausonians who dwelt beside it, but after the Tyrrhenians became masters at sea its name was changed to that which it now bears. 12 1 And finding there much land suitable for pasturage and much for tillage, but for the most part unoccupied, and even that which was inhabited not thickly populated, he cleared some of it of the barbarians and built small towns contiguous to one another on the mountains, which was the customary manner of habitation in use among the ancients. And all the land he occupied, which was very extensive, was called Oenotria, and all the people under his command Oenotrians, which was the third name they had borne. For in the reign of Aezeius they were called Aezeians, when Lycaon succeeded to the rule, Lycaonians, and after Oenotrus p39led them into Italy they were for a while called Oenotrians. 2 What I say is supported by the testimony of Sophocles, the tragic poet, in his drama entitledTriptolemus; for he there represents Demeter as informing Triptolemus how large a tract of land he would have to travel over while sowing it with the seeds she had given him. For, after first referring to the eastern part of Italy, which reaches from the Iapygian Promontory to the Sicilian Strait, and then touching upon Sicily on the opposite side, she returns again to the western part of Italy and enumerates the most important nations that inhabit this coast, beginning with the settlement of the Oenotrians. But it is enough to quote merely the iambics in which he says: "And after this, — first, then, upon the right, Oenotria wide-outstretched and Tyrrhene Gulf, And next the Ligurian land shall welcome thee."31 3 And Antiochus of Syracuse,32 a very early historian, in his account of the settlement of Italy, when enumerating the most ancient inhabitants in the order in which each of them held possession of any part of it, says that the first who are reported to have inhabited that country are the Oenotrians. His words are these: "Antiochus, the son of Xenophanes, wrote this account of Italy, which comprises all that is most credible and certain out of p41the ancient tales; this country, which is now called Italy, was formerly possessed by the Oenotrians." Then he relates in what manner they were governed and says that in the course of time Italus came to be their king, after whom they were named Italians; that this man was succeeded by Morges, after whom they were called Morgetes, and that Sicelus, being received as a guest by Morges and setting up a kingdom for himself, divided the nation. After which he adds these words: "Thus those who had been Oenotrians became Sicels, Morgetes and Italians." 13 1 Now let me also show the origin of the Oenotrian race, offering as my witness another of the early historians, Pherecydes of Athens,33 who was a genealogist inferior to none. He thus expresses himself concerning the kings of Arcadia: "Of Pelasgus and Deïanira was born Lycaon; this man married Cyllenê, a Naiad nymph, after whom Mount Cyllenê is named." Then, having given an account of their children and of the places each of them inhabited, he mentions Oenotrus and Peucetius, in these words: "And Oenotrus, after whom are named the Oenotrians who live in Italy, and Peucetius, after whom are named the Peucetians who live on the Ionian Gulf." 2 Such, then, are the accounts given by the ancient poets and writers of legends concerning the places of abode and the origin of the Oenotrians; and on their authority p43I assume that if the Aborigines were in reality a Greek nation, according to the opinion of Cato, Sempronius and many others, they were descendants of these Oenotrians. For I find that the Pelasgians and Cretans and the other nations that lived in Italy came thither afterwards; nor can I discover that any other expedition more ancient than this came from Greece to the western parts of Europe. 3 I am of the opinion that the Oenotrians, besides making themselves masters of many other regions in Italy, some of which they found unoccupied and others but thinly inhabited, also seized a portion of the country of the Umbrians, and that they were called Aborigines from their dwelling on the mountains34 (for it is characteristic of the Arcadians to be fond of the mountains), in the same manner as at Athens some are called Hyperakriori,35 and others Paralioi.36 4 But if any are naturally slow in giving credit to accounts of ancient matters without due examination, let them be slow also in believing the Aborigines to be Ligurians, Umbrians, or any other barbarians, and let them suspend their judgment till they have heard what remains to be told and then determine which opinion out of all is the most probable. 14 1 Of the cities first inhabited by the Aborigines few remained in my day; the greatest part of them, having been laid waste both by wars and other calamities, are abandoned. These cities were in the Reatine territory, not far from the Apennine p45mountains, as Terentius Varro writes in his Antiquities,37 the nearest being one day's journey distant from Rome. I shall enumerate the most celebrated of them, following his account. 2 Palatium, twenty-five stades distant from Reate (a city that was still inhabited by Romans down to my time),38near the Quintian Way.39 Tribula, about sixty stades from Reate and standing upon a low hill. Suesbula, at the same distance from Tribula, near the Ceraunian Mountains. Suna, a famous city forty stades from Suesbula; in it there is a very ancient temple of Mars.3 Mefula, about thirty stades from Suna; its ruins and traces of its walls are pointed out. Orvinium, forty stades from Mefula, a city as famous and large as any in that region; for the foundations of its walls are still to be seen and some tombs of venerable antiquity, as well as the circuits of burying-places40 extending over lofty mounds; and p47there is also an ancient temple of Minerva built on the summit. 4 At the distance of eighty stades from Reate, as one goes along the Curian Way41 past Mount Coretus, stood Corsula, a town but recently destroyed. There is also pointed out an island, called Issa, surrounded by a lake; the Aborigines are said to have lived on this island without any artificial fortification, relying on the marshy waters of the lake instead of walls. Near Issa is Maruvium, situated on an arm of the same lake and distant forty stades from what they call the Septem Aquae. 5 Again, as one goes from Reate by the road towards the Listine district,42 there is Batia,43 thirty stades distant; then Tiora, called Matiene, at a distance of p49three hundred stades. In this city, they say, there was a very ancient oracle of Mars, the nature of which was similar to that of the oracle which legend says once existed at Dodona; only there a pigeon was said to prophesy, sitting on a sacred oak,44 whereas among the Aborigines a heaven-sent bird, which they call picus and the Greeks dryokolaptês,45 appearing on a pillar of wood, did the same. 6 Twenty-four stades from the afore-mentioned city46 stood Lista, the mother-city of the Aborigines, which at a still earlier time the Sabines had captured by a surprise attack, having set out against it from Amiternum by night. Those who survived the taking of the place, after being received by the Reatines, made many attempts to retake their former home, but being unable to do so, they consecrated the country to the gods, as if it were still their own, invoking curses against those who should enjoy the fruits of it. 15 1 Seventy stades from Reate stood Cutilia,47 a famous city, beside a mountain. Not far from it there is a lake, four hundred feet in diameter, filled by everflowing natural springs and, it is said, bottomless. This lake, as having something divine about p51it, the inhabitants of the country look upon as sacred to Victory; and surrounding it with a palisade, so that no one may approach the water, they keep it inviolate; except that at certain times each year those whose sacred office it is go to the little island in the lake and perform the sacrifices required by custom. 2 This island is about fifty feet in diameter and rises not more than a foot above the water; it is not fixed, and floats about in any direction, according to as the wind gently wafts it from one place to another. An herb grows on the island like the flowering rush and also certain small shrubs, a phenomenon which to those who are unacquainted with the works of Nature seems unaccountable and a marvel second to none.48 16 1 The Aborigines are said to have settled first in these places after they had driven out the Umbrians. And making excursions from there, they warred not only upon the barbarians in general but particularly upon the Sicels, their neighbours, in order to dispossess them of their lands. First, a sacred band of young men went forth, consisting of a few who were sent out by their parents to seek a livelihood, according to a custom which I know many barbarians and Greeks have followed.49 2 For whenever the population of any of their cities increased to such a degree that the produce of their p53lands no longer sufficed for them all, or the earth, injured by unseasonable changes of the weather, brought forth her fruits in less abundance than usual, or any other occurrence of like nature, either good or bad, introduced a necessity of lessening their numbers, they would dedicate to some god or other all the men born within a certain year, and providing them with arms, would send them out of their country. If, indeed, this was done by way of thanksgiving for populousness or for victory in war, they would first offer the usual sacrifices and then send forth their colonies under happy auspices; but if, having incurred the wrath of Heaven, they were seeking deliverance from the evils that beset them, they would perform much the same ceremony, but sorrowfully and begging forgiveness of the youths they were sending away. 3 And those who departed, feeling that henceforth they would have no share in the land of their fathers but must acquire another, looked upon any land that received them in friendship or that they conquered in war as their country. And the god to whom they had been dedicated when they were sent out seemed generally to assist them and to prosper the colonies beyond all human expectation. 4 In pursuance, therefore, of this custom some of the Aborigines also at that time, as their places were growing very populous (for they would not put any of their children to death, looking on this as one of the greatest of crimes), dedicated to some god or other the offspring of a certain year and when these children were grown to be men they sent them out of their country as colonists; and they, after leaving their own land, were p55continually plundering the Sicels. 5 And as soon as they became masters of any places in the enemy's country the rest of the Aborigines, also, who needed lands now attacked each of them their neighbours with greater security and built various cities, some of which are inhabited to this day — Antemnae, Tellenae, Ficulea, which is near the Corniculan mountains, as they are called, and Tibur, where a quarter of the city is even to this day called the Sicel quarter;50 and of all their neighbours they harassed the Sicels most. From these quarrels there arose a general war between the nations more important than any that had occurred previously in Italy, and it went on extending over a long period of time. 17 1 Afterwards some of the Pelasgians who inhabited Thessaly, as it is now called, being obliged to leave their country, settled among the Aborigines and jointly with them made war upon the Sicels. It is possible that the Aborigines received them partly in the hope of gaining their assistance, but I believe it was chiefly on account of their kinship; 2 for the Pelasgians, too, were a Greek nation originally from the Peloponnesus. They were unfortunate in many ways but particularly in wandering much and in having no fixed abode. For they first lived in the neighbourhood of the Achaean Argos, as it is now called, being natives of the country, according to most accounts. They received their name originally from Pelasgus, their king. 3 Pelasgus was the p57son of Zeus, it is said, and of Niobê the daughter of Phoroneus, who, as the legend goes, was the first mortal woman Zeus had knowledge of. In the sixth generation afterwards, leaving the Peloponnesus, they removed to the country which was then called Haemonia and now Thessaly. The leaders of the colony were Achaeus, Phthius and Pelasgus, the sons of Larisa and Poseidon. When they arrived in Haemonia they drove out the barbarian inhabitants and divided the country into three parts, calling them, after the names of their leaders, Phthiotis, Achaia and Pelasgiotis. After they had remained there five generations, during which they attained to the greatest prosperity while enjoying the produce of the most fertile plains in Thessaly, about the sixth generation they were driven out of it by the Curetes and Leleges, who are now called Aetolians and Locrians, and by many others who lived near Parnassus, their enemies being commanded by Deucalion, the son of Prometheus and Clymenê, the daughter of Oceanus. 18 1 And dispersing themselves in their flight, some went to Crete, others occupied some of the islands called the Cyclades, some settled in the region called Hestiaeotis near Olympus and Ossa, others crossed into Boeotia, Phocis and Euboea; and some, passing over into Asia, occupied many places on the coast along the Hellespont and many of the adjacent islands, particularly the one now called Lesbos, uniting with those who composed the first colony that was sent thither from Greece under p59Macar, the son of Crinacus.51 2 But the greater part of them, turning inland, took refuge among the inhabitants of Dodona, their kinsmen, against whom, as a sacred people, none would make war; and there they remained for a reasonable time. But when they perceived they were growing burdensome to their hosts, since the land could not support them all, they left it in obedience to an oracle that commanded them to sail to Italy, which was then called Saturnia. 3 And having prepared a great many ships they set out to cross the Ionian Gulf, endeavouring to reach the nearest parts of Italy. But as the wind was in the south and they were unacquainted with those regions, they were carried too far out to sea and landed at one of the mouths of the Po called the Spinetic mouth. In that very place they left their ships and such of their people as were least able to bear hardships, placing a guard over the ships, to the end that, if their affairs did not prosper, they might be sure of a retreat. 4 Those who were left behind there surrounded their camp with a wall and brought in plenty of provisions in their ships; and when their affairs seemed to prosper satisfactorily, they built a city and called it by the same name as the mouth of the river.52 These people attained to a greater degree of prosperity than any others who dwelt on the Ionian Gulf; for they had the mastery at sea for a long time, and p61out of their revenues from the sea they used to send tithes to the god at Delphi, which were among the most magnificent sent by any people.5 But later, when the barbarians in the neighbourhood made war upon them in great numbers, they deserted the city; and these barbarians in the course of time were driven out by the Romans. So perished that part of the Pelasgians that was left at Spina. 19 1 Those, however, who had turned inland crossed the mountainous part of Italy and came to the territory of the Umbrians who were neighbours to the Aborigines. (The Umbrians inhabited a great many other part of Italy also and were an exceeding great and ancient people.) At first the Pelasgians made themselves masters of the lands where they first settled and took some of the small towns belonging to the Umbrians. But when a great army came together against them, they were terrified at the number of their enemies and betook themselves to the country of the Aborigines. 2 And these, seeing fit to treat them as enemies, made haste to assemble out of the places nearest at hand, in order to drive them out of the country. But the Pelasgians luckily chanced to be encamped at that time near Cutilia, a city of the Aborigines hard by the sacred lake, and observing the little island circling round in it and learning from the captives they had taken in the fields the name of the inhabitants, they concluded that their oracle was now fulfilled. p633 For this oracle, which had been delivered to them in Dodona and which Lucius Mallius,53 no obscure man, says he himself saw engraved in ancient characters upon one of the tripods standing in the precinct of Zeus, was as follows: "Fare forth the Sicels' Saturnian land to seek, Aborigines' Cotylê,54 too, where floats an isle; With these men mingling, to Phoebus send a tithe, And heads to Cronus' son, and send to the sire a man."55 Quote Link to comment Share on other sites More sharing options...
Nobody Posted August 22, 2014 Share Posted August 22, 2014 (edited) never mind Edited August 22, 2014 by NOBODY Quote Link to comment Share on other sites More sharing options...
Nobody Posted August 22, 2014 Share Posted August 22, 2014 Btw, while trying to make a really big post, I got this Quote Link to comment Share on other sites More sharing options...
Magical Glace Posted August 22, 2014 Author Share Posted August 22, 2014 Btw, while trying to make a really big post, I got this This is amazing. Quote Link to comment Share on other sites More sharing options...
Elieson Posted August 22, 2014 Share Posted August 22, 2014 String Theory Overview Levels of magnification: 1. Macroscopic level: Matter 2. Molecular level 3. Atomic level: Protons, neutrons, and electrons 4. Subatomic level: Electron 5. Subatomic level: Quarks 6. String level The starting point for string theory is the idea that the point-like particles of elementary particle physics can also be modeled as one-dimensional objects called strings. According to string theory, strings can oscillate in many ways. On distance scales larger than the string radius, each oscillation mode gives rise to a different species of particle, with its mass, charge, and other properties determined by the string's dynamics. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. An analogy for strings' modes of vibration is a guitar string's production of multiple distinct musical notes.[clarification needed] In this analogy, different notes correspond to different particles. In string theory, one of the modes of oscillation of the string corresponds to a massless, spin-2 particle. Such a particle is called a graviton since it mediates a force which has the properties of gravity. Since string theory is believed to be a mathematically consistent quantum mechanical theory, the existence of this graviton state implies that string theory is a theory of quantum gravity. String theory includes both open strings, which have two distinct endpoints, and closed strings, which form a complete loop. The two types of string behave in slightly different ways, yielding different particle types. For example, all string theories have closed string graviton modes, but only open strings can correspond to the particles known as photons. Because the two ends of an open string can always meet and connect, forming a closed string, all string theories contain closed strings. The earliest string model, the bosonic string, incorporated only the class of particles known as bosons. This model describes, at low enough energies, a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge bosons such as the photon. However, this model has problems. What is most significant is that the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories; several kinds have been described, but all are now thought to be different limits of a theory called M-theory. Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it fully describes our universe, making it a theory of everything. One of the goals of current research in string theory is to find a solution of the theory that is quantitatively identical with the standard model, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. It is not yet known whether string theory has such a solution, nor is it known how much freedom the theory allows to choose the details. One of the challenges of string theory is that the full theory does not yet have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of perturbation theory, but it is not known in general how to define string theory nonperturbatively. It is also not clear as to whether there is any principle by which string theory selects its vacuum state, the spacetime configuration that determines the properties of our universe (see string theory landscape). Strings The motion of a point-like particle can be described by drawing a graph of its position with respect to time. The resulting picture depicts the worldline of the particle in spacetime. In an analogous way, one can draw a graph depicting the progress of a string as time passes. The string, which looks like a small line by itself, will sweep out a two-dimensional surface known as the worldsheet. The different string modes (giving rise to different particles, such as the photon or graviton) appear as waves on this surface. A closed string looks like a small loop, so its worldsheet will look like a pipe. An open string looks like a segment with two endpoints, so its worldsheet will look like a strip. In a more mathematical language, these are both Riemann surfaces, the strip having a boundary and the pipe none. Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory Strings can join and split. This is reflected by the form of their worldsheet, or more precisely, by its topology. For example, if a closed string splits, its worldsheet will look like a single pipe splitting into two pipes. This topology is often referred to as a pair of pants (see drawing at right). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes (one representing the incoming string, and the other representing the outgoing one). An open string doing the same thing will have a worldsheet that looks like an annulus connected to two strips. In quantum mechanics, one computes the probability for a point particle to propagate from one point to another by summing certain quantities called probability amplitudes. Each amplitude is associated with a different worldline of the particle. This process of summing amplitudes over all possible worldlines is called path integration. In string theory, one computes probabilities in a similar way, by summing quantities associated with the worldsheets joining an initial string configuration to a final configuration. It is in this sense that string theory extends quantum field theory, replacing point particles by strings. As in quantum field theory, the classical behavior of fields is determined by an action functional, which in string theory can be either the Nambu–Goto action or the Polyakov action. Branes Main articles: Brane and D-brane In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p, these are called p-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A p-brane sweeps out a (p+1)-dimensional volume in spacetime called its worldvolume. Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane. In string theory, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory. Branes are also frequently studied from a purely mathematical point of view since they are related to subjects such as homological mirror symmetry and noncommutative geometry. Mathematically, branes may be represented as objects of certain categories, such as the derived category of coherent sheaves on a Calabi–Yau manifold, or the Fukaya category. Dualities In physics, the term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. In addition to providing a candidate for a theory of everything, string theory provides many examples of dualities between different physical theories and can therefore be used as a tool for understanding the relationships between these theories. S-, T-, and U-duality Main articles: S-duality, T-duality and U-duality These are dualities between string theories which relate seemingly different quantities. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both classical and quantum physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality. M-theory Main article: M-theory Before the 1990s, string theorists believed there were five distinct superstring theories: type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today. It is now believed that this picture was incorrect and that the five superstring theories are related to one another by the dualities described above. The existence of these dualities suggests that the five string theories are in fact special cases of a more fundamental theory called M-theory. String theory details by type and number of spacetime dimensions Type Spacetime dimensions Details Bosonic 26 Only bosons, no fermions, meaning only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory. I 10 Supersymmetry between forces and matter, with both open and closed strings; no tachyon; gauge group is SO(32) IIA 10 Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are non-chiral IIB 10 Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are chiral HO 10 Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic, meaning right moving and left moving strings differ; gauge group is SO(32) HE 10 Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic; gauge group is E8×E8 Extra dimensions Number of dimensions An intriguing feature of string theory is that it predicts extra dimensions. In classical string theory the number of dimensions is not fixed by any consistency criterion. However, to make a consistent quantum theory, string theory is required to live in a spacetime of the so-called "critical dimension": we must have 26 spacetime dimensions for the bosonic string and 10 for the superstring. This is necessary to ensure the vanishing of the conformal anomaly of the worldsheet conformal field theory. Modern understanding indicates that there exist less trivial ways of satisfying this criterion. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions are related by dynamical transitions. The dimensions are more precisely different values of the "effective central charge", a count of degrees of freedom that reduces to dimensionality in weakly curved regimes. One such theory is the 11-dimensional M-theory, which requires spacetime to have eleven dimensions, as opposed to the usual three spatial dimensions and the fourth dimension of time. The original string theories from the 1980s describe special cases of M-theory where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is described by a complex number rather than a real number. The notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances. Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions manually and arbitrarily, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. In technical terms, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible. This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon that is predicted by string theory depends on the energy of the string mode that represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions, since for a larger number of dimensions there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions. When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). The subset of X is equal to the relation of photon fluctuations in a linear dimension. Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. Starting from any dimension greater than four, it is necessary to consider how these are reduced to four-dimensional spacetime. Compact dimensions Calabi–Yau manifold (3D projection) Two ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by present-day experiments. To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their holonomy. A 6-dimensional manifold must have SU(3) structure, a particular case (torsionless) of this being SU(3) holonomy, making it a Calabi–Yau space, and a 7-dimensional manifold must have G2 structure, with G2 holonomy again being a specific, simple, case. Such spaces have been studied in attempts to relate string theory to the 4-dimensional Standard Model, in part due to the computational simplicity afforded by the assumption of supersymmetry. More recently, progress has been made constructing more realistic compactifications without the degree of symmetry of Calabi–Yau or G2 manifolds. A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave–particle duality). Brane-world scenario Another possibility is that we are "stuck" in a 3+1 dimensional (three spatial dimensions plus one time dimension) subspace of the full universe. Properly localized matter and Yang–Mills gauge fields will typically exist if the sub-spacetime is an exceptional set of the larger universe. These "exceptional sets" are ubiquitous in Calabi–Yau n-folds and may be described as subspaces without local deformations, akin to a crease in a sheet of paper or a crack in a crystal, the neighborhood of which is markedly different from the exceptional subspace itself. However, until the work of Randall and Sundrum, it was not known that gravity can be properly localized to a sub-spacetime. In addition, spacetime may be stratified, containing strata of various dimensions, allowing us to inhabit the 3+1-dimensional stratum—such geometries occur naturally in Calabi–Yau compactifications. Such sub-spacetimes are D-branes, hence such models are known as brane-world scenarios. Effect of the hidden dimensions In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza's early work demonstrated that general relativity in five dimensions actually predicts the existence of electromagnetism. However, because of the nature of Calabi–Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four-dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions. Testability and experimental predictions Although a great deal of recent work has focused on using string theory to construct realistic models of particle physics, several major difficulties complicate efforts to test models based on string theory. The most significant is the extremely small size of the Planck length, which is expected to be close to the string length (the characteristic size of a string, where strings become easily distinguishable from particles). Another issue is the huge number of metastable vacua of string theory, which might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies. String harmonics One unique prediction of string theory is the existence of string harmonics. At sufficiently high energies, the string-like nature of particles would become obvious. There should be heavier copies of all particles, corresponding to higher vibrational harmonics of the string. It is not clear how high these energies are. In most conventional string models, they would be close to the Planck energy, which is 1014 times higher than the energies accessible in the newest particle accelerator, the LHC, making this prediction impossible to test with any particle accelerator in the near future. However, in models with large extra dimensions they could potentially be produced at the LHC, or at energies not far above its reach. Cosmology String theory as currently understood makes a series of predictions for the structure of the universe at the largest scales. Many phases in string theory have very large, positive vacuum energy. Regions of the universe that are in such a phase will inflate exponentially rapidly in a process known as eternal inflation. As such, the theory predicts that most of the universe is very rapidly expanding. However, these expanding phases are not stable, and can decay via the nucleation of bubbles of lower vacuum energy. Since our local region of the universe is not very rapidly expanding, string theory predicts we are inside such a bubble. The spatial curvature of the "universe" inside the bubbles that form by this process is negative, a testable prediction. Moreover, other bubbles will eventually form in the parent vacuum outside the bubble and collide with it. These collisions lead to potentially observable imprints on cosmology. However, it is possible that neither of these will be observed if the spatial curvature is too small and the collisions are too rare. Under certain circumstances, fundamental strings produced at or near the end of inflation can be "stretched" to astronomical proportions. These cosmic strings could be observed in various ways, for instance by their gravitational lensing effects. However, certain field theories also predict cosmic strings arising from topological defects in the field configuration. Supersymmetry Main article: Supersymmetry If confirmed experimentally, supersymmetry could also be considered circumstantial evidence, because all consistent string theories are supersymmetric. However, the absence of supersymmetric particles at energies accessible to the LHC would not necessarily disprove string theory, since the energy scale at which supersymmetry is broken could be well above the accelerator's range. AdS/CFT correspondence Main article: AdS/CFT correspondence The anti-de Sitter/conformal field theory (AdS/CFT) correspondence is a relationship which says that string theory is in certain cases equivalent to a quantum field theory. More precisely, one considers string or M-theory on an anti-de Sitter background. This means that the geometry of spacetime is obtained by perturbing a certain solution of Einstein's equation in the vacuum. In this setting, it is possible to define a notion of "boundary" of spacetime. The AdS/CFT correspondence states that this boundary can be regarded as the "spacetime" for a quantum field theory, and this field theory is equivalent to the bulk gravitational theory in the sense that there is a "dictionary" for translating calculations in one theory into calculations in the other. Examples of the correspondence The most famous example of the AdS/CFT correspondence states that Type IIB string theory on the product AdS5 × S5 is equivalent to N = 4 super Yang–Mills theory on the four-dimensional conformal boundary. Another realization of the correspondence states that M-theory on AdS4 × S7 is equivalent to the ABJM superconformal field theory in three dimensions. Yet another realization states that M-theory on AdS7 × S4is equivalent to the so-called (2,0)-theory in six dimensions. Applications to quantum chromodynamics Main article: AdS/QCD Since it relates string theory to ordinary quantum field theory, the AdS/CFT correspondence can be used as a theoretical tool for doing calculations in quantum field theory. For example, the correspondence has been used to study the quark–gluon plasma, an exotic state of matter produced in particle accelerators. The physics of the quark–gluon plasma is governed by quantum chromodynamics, the fundamental theory of the strong nuclear force, but this theory is mathematically intractable in problems involving the quark–gluon plasma. In order to understand certain properties of the quark–gluon plasma, theorists have therefore made use of the AdS/CFT correspondence. One version of this correspondence relates string theory to a certain supersymmetric gauge theory called N = 4 super Yang–Mills theory. The latter theory provides a good approximation to quantum chromodynamics. One can thus translate problems involving the quark–gluon plasma into problems in string theory which are more tractable. Using these methods, theorists have computed the shear viscosity of the quark–gluon plasma.[33] In 2008, these predictions were confirmed at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. Applications to condensed matter physics In addition, string theory methods have been applied to problems in condensed matter physics. Certain condensed matter systems are difficult to understand using the usual methods of quantum field theory, and the AdS/CFT correspondence may allow physicists to better understand these systems by describing them in the language of string theory. Some success has been achieved in using string theory methods to describe the transition of a superfluid to an insulator. Connections to mathematics In addition to influencing research in theoretical physics, string theory has stimulated a number of major developments in pure mathematics. Like many developing ideas in theoretical physics, string theory does not at present have a mathematically rigorous formulation in which all of its concepts can be defined precisely. As a result, physicists who study string theory are often guided by physical intuition to conjecture relationships between the seemingly different mathematical structures that are used to formalize different parts of the theory. These conjectures are later proved by mathematicians, and in this way, string theory has served as a source of new ideas in pure mathematics. Mirror symmetry Main article: Mirror symmetry (string theory) One of the ways in which string theory influenced mathematics was through the discovery of mirror symmetry. In string theory, the shape of the unobserved spatial dimensions is typically encoded in mathematical objects called Calabi–Yau manifolds. These are of interest in pure mathematics, and they can be used to construct realistic models of physics from string theory. In the late 1980s, it was noticed that given such a physical model, it is not possible to uniquely reconstruct a corresponding Calabi–Yau manifold. Instead, one finds that there are two Calabi–Yau manifolds that give rise to the same physics. These manifolds are said to be "mirror" to one another. The existence of this mirror symmetry relationship between different Calabi–Yau manifolds has significant mathematical consequences as it allows mathematicians to solve many problems in enumerative algebraic geometry. Today mathematicians are still working to develop a mathematical understanding of mirror symmetry based on physicists' intuition. Vertex operator algebras Main articles: Vertex operator algebra and Monstrous moonshine In addition to mirror symmetry, applications of string theory to pure mathematics include results in the theory of vertex operator algebras. For example, ideas from string theory were used by Richard Borcherds in 1992 to prove the monstrous moonshine conjecture relating the monster group (a construction arising in group theory, a branch of algebra) and modular functions (a class of functions which are important in number theory). History Question book-new.svg This section does not cite any references or sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2013) Main article: History of string theory Early results Some of the structures reintroduced by string theory arose for the first time much earlier as part of the program of classical unification started by Albert Einstein. The first person to add a fifth dimension to general relativity was German mathematician Theodor Kaluza in 1919, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. In 1926, the Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions. String theory was originally developed during the late 1960s and early 1970s as a never completely successful theory of hadrons, the subatomic particles like the proton and neutron that feel the strong interaction. In the 1960s, Geoffrey Chew and Steven Frautschi discovered that the mesons make families called Regge trajectories with masses related to spins in a way that was later understood by Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind to be the relationship expected from rotating strings. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix. The S-matrix approach was started by Werner Heisenberg in the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of quantum gravity. Working with experimental data, R. Dolen, D. Horn and C. Schmid[40] developed some sum rules for hadron exchange. When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the s-channel, the two particles annihilate to make temporary intermediate states that fall apart into the final state particles. In the t-channel, the particles exchange intermediate states by emission and absorption. In field theory, the two contributions add together, one giving a continuous background contribution, the other giving peaks at certain energies. In the data, it was clear that the peaks were stealing from the background—the authors interpreted this as saying that the t-channel contribution was dual to the s-channel one, meaning both described the whole amplitude and included the other. The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering amplitude that had the property of Dolen-Horn-Schmid duality, later renamed world-sheet duality. The amplitude needed poles where the particles appear, on straight line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line— the Gamma function— which was widely used in Regge theory. By manipulating combinations of Gamma functions, Veneziano was able to find a consistent scattering amplitude with poles on straight lines, with mostly positive residues, which obeyed duality and had the appropriate Regge scaling at high energy. The amplitude could fit near-beam scattering data as well as other Regge type fits, and had a suggestive integral representation that could be used for generalization. Over the next years, hundreds of physicists worked to complete the bootstrap program for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle that appears in the theory, an obvious self-consistency condition, the lightest particle must be a tachyon. Miguel Virasoro and Joel Shapiro found a different amplitude now understood to be that of closed strings, while Ziro Koba and Holger Nielsen generalized Veneziano's integral representation to multiparticle scattering. Veneziano and Sergio Fubini introduced an operator formalism for computing the scattering amplitudes that was a forerunner of world-sheet conformal theory, while Virasoro understood how to remove the poles with wrong-sign residues using a constraint on the states. Claud Lovelace calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. Charles Thorn, Peter Goddard and Richard Brower went on to prove that there are no wrong-sign propagating states in dimensions less than or equal to 26. In 1969, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind recognized that the theory could be given a description in space and time in terms of strings. The scattering amplitudes were derived systematically from the action principle by Peter Goddard, Jeffrey Goldstone, Claudio Rebbi, and Charles Thorn, giving a space-time picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the Virasoro conditions. In 1970, Pierre Ramond added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states. John Schwarz and André Neveu added another sector to the fermi theory a short time later. In the fermion theories, the critical dimension was 10. Stanley Mandelstam formulated a world sheet conformal theory for both the bose and fermi case, giving a two-dimensional field theoretic path-integral to generate the operator formalism. Michio Kaku and Keiji Kikkawa gave a different formulation of the bosonic string, as a string field theory, with infinitely many particle types and with fields taking values not on points, but on loops and curves. In 1974, Tamiaki Yoneya discovered that all the known string theories included a massless spin-two particle that obeyed the correct Ward identities to be a graviton. John Schwarz and Joel Scherk came to the same conclusion and made the bold leap to suggest that string theory was a theory of gravity, not a theory of hadrons. They reintroduced Kaluza–Klein theory as a way of making sense of the extra dimensions. At the same time, quantum chromodynamics was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the dustbin of history. String theory eventually made it out of the dustbin, but for the following decade all work on the theory was completely ignored. Still, the theory continued to develop at a steady pace thanks to the work of a handful of devotees. Ferdinando Gliozzi, Joel Scherk, and David Olive realized in 1976 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined. The resulting theory did not have a tachyon, and was proven to have space-time supersymmetry by John Schwarz and Michael Green in 1981. The same year, Alexander Polyakov gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. In 1979, Daniel Friedan showed that the equations of motions of string theory, which are generalizations of the Einstein equations of General Relativity, emerge from the Renormalization group equations for the two-dimensional field theory. Schwarz and Green discovered T-duality, and constructed two superstring theories—IIA and IIB related by T-duality, and type I theories with open strings. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices. First superstring revolution In the early 1980s, Edward Witten discovered that most theories of quantum gravity could not accommodate chiral fermions like the neutrino. This led him, in collaboration with Luis Alvarez-Gaumé to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé had missed, which restricted the gauge group of the type I string theory to be SO(32). In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution. During this period, David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm discovered heterotic strings. The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. Philip Candelas, Gary Horowitz, Andrew Strominger and Edward Witten found that the Calabi–Yau manifolds are the compactifications that preserve a realistic amount of supersymmetry, while Lance Dixon and others worked out the physical properties of orbifolds, distinctive geometrical singularities allowed in string theory. Cumrun Vafa generalized T-duality from circles to arbitrary manifolds, creating the mathematical field of mirror symmetry. Daniel Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field theory techniques. David Gross and Vipul Periwal discovered that string perturbation theory was divergent. Stephen Shenker showed it diverged much faster than in field theory suggesting that new non-perturbative objects were missing. In the 1990s, Joseph Polchinski discovered that the theory requires higher-dimensional objects, called D-branes and identified these with the black-hole solutions of supergravity. These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure. It quickly became clear that D-branes and other p-branes, not just strings, formed the matter content of the string theories, and the physical interpretation of the strings and branes was revealed—they are a type of black hole. Leonard Susskind had incorporated the holographic principle of Gerardus 't Hooft into string theory, identifying the long highly excited string states with ordinary thermal black hole states. As suggested by 't Hooft, the fluctuations of the black hole horizon, the world-sheet or world-volume theory, describes not only the degrees of freedom of the black hole, but all nearby objects too. Second superstring revolution Edward Witten In 1995, at the annual conference of string theorists at the University of Southern California (USC), Edward Witten gave a speech on string theory that in essence united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory. M-theory was also foreshadowed in the work of Paul Townsend at approximately the same time. The flurry of activity that began at this time is sometimes called the second superstring revolution. During this period, Tom Banks, Willy Fischler, Stephen Shenker and Leonard Susskind formulated matrix theory, a full holographic description of M-theory using IIA D0 branes. This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT correspondence. Andrew Strominger and Cumrun Vafa calculated the entropy of certain configurations of D-branes and found agreement with the semi-classical answer for extreme charged black holes. Petr Hořava and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Witten noted that the effective description of the physics of D-branes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and Nathan Seiberg had earlier discovered in terms of the location of the branes. In 1997, Juan Maldacena noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti-de Sitter space. He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that string theory on a near-horizon extreme-charged black-hole geometry, an anti-deSitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, the N = 4 supersymmetric Yang–Mills theory. This hypothesis, which is called the AdS/CFT correspondence, was further developed by Steven Gubser, Igor Klebanov and Alexander Polyakov, and by Edward Witten, and it is now well-accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational interaction. Through this relationship, string theory has been shown to be related to gauge theories like quantum chromodynamics and this has led to more quantitative understanding of the behavior of hadrons, bringing string theory back to its roots. Criticisms Some critics of string theory say that it is a failure as a theory of everything. Notable critics include Peter Woit, Lee Smolin, Philip Warren Anderson, Sheldon Glashow, Lawrence Krauss, Carlo Rovelli and Bert Schroer. Some common criticisms include: Very high energies needed to test quantum gravity. Lack of uniqueness of predictions due to the large number of solutions. Lack of background independence. High energies It is widely believed that any theory of quantum gravity would require extremely high energies to probe directly, higher by orders of magnitude than those that current experiments such as the Large Hadron Collider[53] can attain. This is because strings themselves are expected to be only slightly larger than the Planck length, which is twenty orders of magnitude smaller than the radius of a proton, and high energies are required to probe small length scales. Generally speaking, quantum gravity is difficult to test because gravity is much weaker than the other forces, and because quantum effects are controlled by Planck's constant h, a very small quantity. As a result, the effects of quantum gravity are extremely weak. Number of solutions String theory as it is currently understood has a huge number of solutions, called string vacua, and these vacua might be sufficiently diverse to accommodate almost any phenomena we might observe at lower energies. The vacuum structure of the theory, called the string theory landscape (or the anthropic portion of string theory vacua), is not well understood. String theory contains an infinite number of distinct meta-stable vacua, and perhaps 10520 of these or more correspond to a universe roughly similar to ours—with four dimensions, a high planck scale, gauge groups, and chiral fermions. Each of these corresponds to a different possible universe, with a different collection of particles and forces. What principle, if any, can be used to select among these vacua is an open issue. While there are no continuous parameters in the theory, there is a very large set of possible universes, which may be radically different from each other. It is also suggested that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent. Some physicists believe this is a good thing, because it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. The argument is that most universes contain values for physical constants that do not lead to habitable universes (at least for humans), and so we happen to live in the "friendliest" universe. This principle is already employed to explain the existence of life on earth as the result of a life-friendly orbit around the medium-sized sun among an infinite number of possible orbits (as well as a relatively stable location in the galaxy). Background independence See also: Background independence A separate and older criticism of string theory is that it is background-dependent—string theory describes perturbative expansions about fixed spacetime backgrounds which means that mathematical calculations in the theory rely on preselecting a background as a starting point. This is because, like many quantum field theories, much of string theory is still only formulated perturbatively, as a divergent series of approximations. Although the theory, defined as a perturbative expansion on a fixed background, is not background independent, it has some features that suggest non-perturbative approaches would be background-independent—topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background. Since there are dynamic corrections to the background spacetime in the perturbative theory, one would expect spacetime to be dynamic in the nonperturbative theory as well since they would have to predict the same spacetime. This criticism has been addressed to some extent by the AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter space asymptotics. Nevertheless, a non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking. Some hope that M-theory, or a non-perturbative treatment of string theory (such as "background independent open string field theory") will have a background-independent formulation. Quote Link to comment Share on other sites More sharing options...
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