分享到:

关于STURM-LIOUVILLE方程的一些概率结果(英文)

We stu衡the reduced Sturm一Liouville equationf“+Zqf一0,where q 15 a continuousfunetion,in[0,l].The boundaw data are the values off‘at 0 and 1 .The solution 15 re-Presented by probabilistie quantities involving theF即nman一Kae fonetional and the local timesat 0 andl,of the(renected)Brownian motion.In the final result(28)a new kind of stop-Ping ti毗15 used. Le:{x,,t李。}be山e Brownian motion。n,t hel访。.Let口be。ont访uous。n:hef访itei...  (本文共5页) 阅读全文>>

《Chinese Annals of Mathematics,Series B》2017年01期
Chinese Annals of Mathematics,Series B

One-Dimensional Symmetry and Liouville Type Results for the Fourth Order Allen-Cahn Equation in R~N

(Dedicated to Ha¨?m Brezis with deep admiration)1 Introduction and Main ResultsWe consider the equationwithγ0,which is a fourth order model arising in many bistable physical,chemical or biological systems.Whenγ=0 in(1.1),we recognize the well-known Allen-Cahn equationalso called the scalar Ginzburg-Landau equation or the Fitz Hugh-Nagumo equation.When the solution u is positive and the right-hand side is of the type ...  (本文共24页) 阅读全文>>

《Chinese Annals of Mathematics,Series B》2016年04期
Chinese Annals of Mathematics,Series B

Symmetric Periodic Orbits and Uniruled Real Liouville Domains

1 IntroductionFor closed symplectic manifolds,Hu,Li and Ruan[8]have defined the notion of symplecticaluniruledness by requiring the existence of a non-zero Gromov-Witten invariant of genus zerowith a point constraint(see[8]).It was pointed out by Li[9],that it is not meaningful to naivelymimic the definition of algebraic geometry,since he showed that for a simply-connected,closedsymplectic manifold,there always exist...  (本文共18页) 阅读全文>>

《应用数学》2014年01期
应用数学

一类不连续奇异Strum-Liouville算子的渐近估计(英文)

1.IntroductionThe discontinuous Sturm-Liouville problems are interested for their applications inphysics.The various physics applications of this kind of problems are found in many litera-tures.For example,some boundary-value problems with transmission conditions can arise inheat and mass transfer problems[1],in vibrating string problems when the string loaded addi-tionally with point masses[2],and in diffraction pro...  (本文共11页) 阅读全文>>

《Communications in Theoretical Physics》2013年11期
Communications in Theoretical Physics

General Rotating Black Hole with Four Charges and Liouville Theory

1 IntroductionThe relevance of Liouville theory to black hole physicshas been found some time ago.[1 2]In particular,Solo-dukhin studied the dimensional reduction of gravitationaltheory to two-dimensional(2D)dilaton gravity on the t rplane.[3]Through the careful analysis of the near-horizonregime,he resorted to some conformal transformation tofind the Liouville-like action.The black hole entropy canbe obtained from t...  (本文共4页) 阅读全文>>

《石河子大学学报(自然科学版)》2009年03期
石河子大学学报(自然科学版)

广义二型Liouville分布不存在正相依结构的再证明

1问题的提出在社会、经济、技术等许多领域的数据分析中,成分数据(compositional data)是一种应用较为广泛的数据类型,可以被用来反映投资结构、居民消费结构、岩石的化学成分结构等诸如此类的问题。成分数据是指其n个分量的取值满足约束条件:∑nk=1xk=1,xk≥0的任意n维向量X=(x1,x2,…,xn)。为刻画和拟合成分数据,D irichle分布、Liouville及广义Liouville分布是可供选择、考虑的参数分布类。一个众所周知的事实是D irichle分布类具有非正的协方差结构,自然带有正相依或混合协方差结构的成分数据不能用D irichle分布来描述。Rayens and Srinivasan[1]用A itchison[2]引入的完全子成分独立(complete subcomposional independ-ence)和Doksum[3]引入的随机成分向量的完全中立性(complete neutra...  (本文共3页) 阅读全文>>