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Separation of variables in one partial integrable case of Goryachev
Separation of variables partial integrable case of Goryachev
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2010/12/28
We show that the equations of motion in one partial integrable case of Goryachev in the rigid body dynamics can be separated by the appropriate change of variables,the new variables x, y being hyperel...
The Ising Susceptibility Scaling Function
Ising Susceptibility Scaling Function
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2011/3/4
We have dramatically extended the zero eld susceptibility series at both high and low temperature of the Ising model on the square, triangular and honeycomb lattices, and used these data to calculate...
The Unknotting Problem and Normal Surface Q-Theory
The Unknotting Problem Normal Surface Q-Theory
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2010/12/1
Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used.Suppose M is a triangulated, compact, irreducible, boundary-i...
Asymptotics of orthogonal polynomials and point perturbation on the unit circle
point masses bounded variation asymptotics of orthog-onal polynomials Kooman’s theorem
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2010/12/1
In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky co-efficients of p-type bounded variation. The goal is to investigate
the perturbati...
Characterizations of differentiability for h-convex functions in stratified groups
subdifferential stratified groups second order differentiability
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2010/12/14
Using the notion of h-subdifferential, we characterize both first and second order differentiability of h-convex functions in stratified groups. We show that Aleksandrov’s second order differentiabili...
Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times
University of California
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2010/12/6
Brown (1980, 1981) proved that the renewal function is concave if the inter-renewal istribution
is DFR (decreasing failure rate), and conjectured the converse. This note settles Brown’s conjecture wi...
Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition
Exceptional orthogonal polynomials QHJ formalism SWKB quantization condition
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2010/12/3
We study the quantum Hamilton-Jacobi structure of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials. The fact that the eigenfunctions have zeros an...
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
Laplacian eigenfunction nodal line Robin boundary
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2010/12/13
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary condi-tions has an interior nodal line. In the process, we adapt a bound of Donne...
A Pieri formula for Macdonald's spherical functions and polynomials
symmetric functions Hall-Littlewood polynomials Macdonald poly-nomials Pieri formulas root systems
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2010/12/10
We present explicit Pieri formulas for Macdonald’s spherical func-tions (or generalized Hall-Littlewood polynomials associated with root sys-tems) and their q-deformation the Macdonald polynomials. Fo...
A connection between HH3 and KdV with one source
Korteweg-de Vries Lax pair travelling wave
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2010/4/1
In the system made of Korteweg-de Vries with one source, we first show by applying the Painleve' test that the two components of the source must have the same potential. We then explain the natural in...
一类具有二个转向点的大参数奇摄动方程
奇摄动 外部解 内层 转向点
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2009/9/18
利用匹配方法研究了一类具有二个转向点的大参数奇摄动方程.得出了解在不同范围
内的渐近表示式.
Existence of positive solutions to semipositone singular Dirichlet boundary value problems
existence positive solution semipositone singular problem Dirichlet boundary conditions $\phi$-Laplacian
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2007/12/13
The paper presents the conditions which guarantee that for some positive value of $\mu$ there are positive solutions of the differential equation $(\phi(x'))'+\mu Q(t,x,x')=0$ satisfying the Dirichlet...
具II型Holling功能性反应强耦合椭圆系统共存问题
交叉扩散 自扩散 强耦合椭圆系统
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2007/12/12
本文研究带齐次Dirichlet 边界条件的强耦合椭圆系统,首先证明了当食饵和捕食者的扩散率足够大, 或者出生率足够小时,系统不存在共存现象, 并给出半平凡解存在的充分条件.然后利用Schauder不动点定理, 得到强耦合的椭圆问题至少有一个正解存在的充分条件.该条件说明只要捕食者的内部竞争强, 物种的交叉扩散相对弱,或者捕获率足够小,物种的交叉扩散相对弱,强耦合系统就至少有一个正解存在.
本文构造了紧连通流形上非退化扩散过程的一些耦合，并使用随机分析的方法证明这些耦合是成功的，进一步地，耦合时间一阶矩有限。最后，我们使用耦合方法研究了扩散过程依全变差范数的收敛速度。
马氏场的遍历性及耦合
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2007/12/12
给定一族具有相同的条件分布的马氏场,本文找出了它们一致弱遍历的充要条件.在此基础上,我们还证明了一类特殊的强马氏场能够一致成功耦合的充要条件是它们一致弱遍历.