- published: 04 Jun 2014
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In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley) and uses a specified, usually finite, set of generators for the group. It is a central tool in combinatorial and geometric group theory.
Suppose that is a group and is a generating set. The Cayley graph is a colored directed graph constructed as follows:
In geometric group theory, the set is usually assumed to be finite, symmetric (i.e. ) and not containing the identity element of the group. In this case, the uncolored Cayley graph is an ordinary graph: its edges are not oriented and it does not contain loops (single-element cycles).
Hausdorff dimension is a concept in mathematics introduced in 1918 by mathematician Felix Hausdorff, and it serves as a measure of the local size of a set of numbers (i.e., a "space"), taking into account the distance between each of its members (i.e., the "points" in the "space"). Applying its mathematical formalisms provides that the Hausdorff dimension of a single point is zero, of a line is 1, and of a square is 2, of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is a counting number (integer) agreeing with a dimension corresponding to its topology. However, formalisms have also been developed that allow calculation of the dimension of other less simple objects, where, based solely on its properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.
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Geometric Structures on 3-manifolds Topic: Free group Cayley graph and measure decompositions Speaker: Yong Hou Date:Tuesday, February 23 I will talk about convex-cocompact representations of finitely generated free group FgFg into PSL(2,ℂ)PSL(2,C). First I will talk about Schottky criterion. There are many ways of characterizes Schottky group. In particular, convex hull entropy criterion, Hausdorff dimension criterion. In addition we can also construct measure decomposition on Cayley graph, which is a generalization of the Culler-Shalen decomposition, gives criterion on primitive sets. And, I will discuss primitive curves in hyperbolic Handlebody that are Schottky. This is joint work with Jim Anderson. For more videos, visit http://video.ias.edu
Dit is zo cute :D en hij zei dat hij nederland leuk vindt :D Jeej. B.A.P. is echt awesome... ik wil nog steeds een BAP mv vertalen zit te denken om Power of Crash te vertalen... nou nederland,... tenminste ik xD houd ook van jou :D
【Chinese Title】卧薪尝胆 (Wo Xin Chang Dan) 【Genre】Ancient / Historical 【Country/Region】China 【Issue Date】2007-01-10 【Number of Episodes】41 【Director】侯咏 (Hou Yong) 【Starring】 【陈道明~勾践】Chen Dao Ming as Goujian 【胡军~夫差】Hu Jun as Fuchai 【左小青~雅鱼】Zuo Xiao Qing as Yayu 【贾一平~范蠡】Jia Yi Ping as Fan Li 【安以轩~西施】Ann or An Yi Xuan as Xishi 【王冰~伍子胥】Wang Bing as Wu Zixu 【郑天庸~文种】Zheng Tian Yong as Wen Zhong 【丁勇岱~伯噽】Ding Yong Dai as Bopi ----------------------------------------------------------------------------------------------- • Playlist for The Great Revival: http://www.youtube.com/playlist?list=PLYRGCE_sj_lE1Ii96dtuBXYjf-Nv152mi ------------------------------------------------------------ • Turn on captions (CC button) to show the English subtitles • Change caption settings to adjust font size, style, co...
開了口 故事就從這個夏天開始 || SONY質感新男聲 Eric周興哲 || 第一首發表夏悸好評抒情曲 [ 以後別做朋友 ] Eric周興哲官方FB 做我朋友→https://www.facebook.com/ericchou0622 * 林心如監製、楊一展、許瑋甯主演強勢華劇<16個夏天>片尾曲 超越2400萬收視人次共同催生見證 最強好男聲 / 好口碑首選獻聲 * SONY MUSIC品牌年度力捧創作型才子新人 * 三金音樂神手 - 陳建騏領軍製作:熟稔的音樂性X青澀的情感面 創新交織首席大提琴家范宗沛 | 茱莉亞音樂學院的古典小提琴家蘇子茵 | 電影/劇場配樂佳人 羅恩妮 * 琴歌才子第一首琴感式創作,獻給承擔與不承擔的那些穹蒼之愛 給觸不到的戀人們 聽完這首歌 我們都不准哭... Eric周興哲的歌陪你渡日 以後別做朋友,是問號?還是驚歎號! 答案 也許就在這個夏天見分曉... <16個夏天>電視原聲帶|錯過與遺憾珍藏盤 ♠精裝實體通路 博客來►►http://goo.gl/ywkvpS 五大►►http://goo.gl/bR0npX 佳佳►►http://goo.gl/XayGKM 誠品►►http://goo.gl/nvKPQB 玫瑰大眾►►http://goo.gl/mGJpzC 山海山►►http://goo.gl/FAvwEC ♠數位下載 ◎iTunes►►http://goo.gl/2X2Hyw ◎KKBOX►►http://goo.gl/WpR6MG ◎myMusic►►http://goo.gl/Y19tui ◎Omusic►►http://goo.gl/pFyXl7 ◎Spotify►►http://goo.gl/nP9afL ♠鈴聲下載 ◎中華►►http://goo.gl/XttgH...
Topic: Hausdorff dimension of Kleinian group uniformization of Riemann surface and conformal rigidity Speaker: Yong Hou Date:Tuesday, November 24 For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimension spectrum. I'll discuss and pose some questions which also in particular will imply a conjecture due to Bers. More videos at http://video.ias.edu
Video de la canción Xin Wo / 新窝 de S.H.E y Fahrenheit. Letra: 感受不易形容 就算會有一點唐突也要說 請搬進我心窩 如果你不幸福再离家出走 我心窩做你的新窩 也許坪數不太夠 甚至會擁擠到 只裝得下你我 請快准備行李 丟掉用不到的傷心舊回憶 腦海中相本日記 從此更新只有彼此專屬甜蜜 抱枕就丟掉 有肩膀就夠 最后用關心問候 捆綁我們的手完工 只要在你身邊 我就省掉思念 時間只用來眷戀 我要在你身邊 盡情浪費喜悅 也許一待就永遠 管它金窩銀窩 怎樣都比不過彼此的心窩 打包一箱溫柔 今后多多指教就相互寬容 你心窩做我的新窩 暖气不需要使用 我已經溫暖到 融化所有冷漠 請快准備行李 丟掉用不到的傷心舊回憶 腦海中相本日記 從此更新只有彼此專屬甜蜜 抱枕就丟掉 有肩膀就夠 最后用關心問候 捆綁我們的手完工 只要在你身邊 我就省掉思念 時間只用來眷戀 我要在你身邊 盡情浪費喜悅 也許一待就永遠 Pin yin: Xin Wo S.H.E feat. Fahrenheit (Jiro Wang & Aaron Yan): Gan shou bu yi xing rong Jiu suan hui you yi dian tang tu ye yao shuo Qing ban jing wo de xin wo Ru guo bu xin fu zai li jia chu zou Wo xin wo zuo ni de xin wo Ye xu ping shuo xia tai guo Shen zhi hui yong ji dao Zhi zhuang de xia ni wo (Calvin Chen and Wu Chun): Qing kuai zhun bei xing li Dui diao ...
Downwards, downwards
Life's spiraling descent
Downwards, downwards
Life's spiraling descent
All love is lost
Premature and unreasoning
Premature and unreasoning
Perversely chained without any values
Perversely chained without any values
Wretched, degraded
Wretched, degraded
Take it all on the chin
To forever hold my peace
To forever hold my peace
The reins turned noose, pull taunt as I fall
The reins turned noose, pull taunt as I fall
The figment is more painful than fact
And I'm the one to hang
Just for being me, for being me
The murky clouds wash, solace comforts not
And I'm the one to hang
Just for being me, just for being me
Black numbing blanket smothers attrition