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Smoothness of Certain Functions in Two Kinds of Risk Models with a Barrier Dividend Strategy

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 661-668页

作者： Wei Wang Jing-min He Rong Wu School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China College of Science Tianjin University of TechnologyTianjin 300191China

In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend *** using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk *** the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk ***-differential equations satisfied by them are derived.

关键词： Piecewise deterministic Markov process weak infinitesimal generator barrier strategy

Existence of the Eigenvalues for the Cone Degenerate p-Laplacian

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Chinese Annals of Mathematics,Series B 2021年第2期42卷 217-236页

作者： Hua CHEN Yawei WEI School of Mathematics and Statistics Wuhan UniversityWuhan 430072China School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China

The present paper is concerned with the eigenvalue problem for cone degenerate p-Laplacian. First the authors introduce the corresponding weighted Sobolev spaces with important inequalities and embedding properties. Then by adapting LusternikSchnirelman theory, they prove the existence of infinity many eigenvalues and eigenfunctions. Finally, the asymptotic behavior of the eigenvalues is given.

关键词： Quasi-linear Degenerate operator Variational methods

A Fast Symmetric Alternating Direction Method of Multipliers

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Numerical Mathematics(Theory,Methods and Applications) 2020年第1期13卷 200-219页

作者： Gang Luo Qingzhi Yang School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China School of Mathematics and Statistics Kashi UniversityKashi 844006China

In recent years,alternating direction method of multipliers(ADMM)and its variants are popular for the extensive use in image processing and statistical learning.A variant of ADMM:symmetric ADMM,which updates the Lagrange mul-tiplier twice in one iteration,is always faster whenever it *** this paper,combined with Nesterov’s accelerating strategy,an accelerated symmetric ADMM is *** prove its O(1/k^(2))convergence rate under strongly convex *** the general situation,an accelerated method with a restart rule is *** preliminary numerical experiments show the efficiency of our algorithms.

关键词： Nesterov’s accelerating strategy alternating direction method of multipliers sym-metric ADMM separable linear constrained optimization

Extremal P_(8)-Free/P_(9)-Free Planar Graphs

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Journal of the Operations Research Society of China 2023年第3期11卷 451-457页

作者： Yong-Xin Lan Yong-Tang Shi School of Science Hebei University of TechnologyTianjin300401China Center for Combinatorics and lpmc Nankai UniversityTianjin300071China

An H-free graph is a graph not containing the given graph H as a *** is well known that the Turán number ex(n,H)is the maximum number of edges in an H-free graph on n *** on this definition,we define ex_(P)(n,H)to restrict the graph classes to planar graphs,that is,ex_(P)(n,H)=max{|E(G)|:G∈G,where G is a family of all H-free planar graphs on n ***,we have ex_(P)(n,H)=3n−6 if the graph H is not a planar *** study is initiated by Dowden(J Graph Theory 83:213–230,2016),who obtained some results when H is considered as C_(4)or C_(5).In this paper,we determine the values of ex_(P)(n,Pk)with k∈{8,9},where Pk is a path with k vertices.

关键词： Turán number Extremal graph Planar graph

PROPERTIES OF THE POSITIVE SOLUTIONS OF FRACTIONAL P&Q-LAPLACE EQUATIONS WITH A SIGN-CHANGING POTENTIAL

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Acta Mathematica Scientia 2024年第6期44卷 2422-2442页

作者： Yubo DUAN Yawei WEI School of Mathematical Sciences Nankai UniversityTianjin 300071China School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China

In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing *** model is inspired by the De Giorgi *** are two main results in this ***,in the bounded domain,we use the moving plane method to show that the solution is radially ***,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.

关键词： fractional p&q-Laplacian moving plane method sliding method

Nontrivial Solutions of Superquadratic Hamiltonian Systems with Lagrangian Boundary Conditionsand the L-index Theory

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Chinese Annals of Mathematics,Series B 2008年第6期29卷 597-610页

作者： Chong LI Chungen LIU School of Mathematical Sciences Nankai University Tianjin 300071 China School of Mathematical Sciences and lpmc Nankai University Tianjin 300071 China

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z）＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.

关键词： L-index Nontrivial solution Hamiltonian systems Lagrangian boundary conditions Superquadratic condition

Global structure of spectra of periodic non-Hermitian Jacobi operators

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Science China Mathematics 2024年第12期67卷 2753-2770页

作者： Hui Lu Jiangong You School of Mathematics Nanjing Audit UniversityNanjing 211815China Chern Institute of Mathematics and lpmc Nankai UniversityTianjin 300071China

We give global structure of spectra of periodic non-Hermitian Jacobi operators by the discriminant and its stationary points. We also give necessary and sufficient conditions for real spectra and single interval spectra.

关键词： periodic Jacobi operator non-Hermitian operator global structure real spectra

Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy

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Frontiers of Mathematics in China 2014年第5期9卷 1073-1088页

作者： Yuhua LU Rong WU School of Mathematics Sciences Qufu Normal University Qufu 273165 China School of Mathematics Sciences and lpmc Nankai University Tianjin 300071 China

We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.

关键词： Expected discounted dividends ruin time integro-differentialequation Laplace transform barrier strategy

Upper bounds for eigenvalues of Cauchy-Hankel tensors

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Frontiers of Mathematics in China 2021年第4期16卷 1023-1041页

作者： Wei MEI Qingzhi YANG School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China School of Mathematics and Statistics Kashi UniversityKashi 844006China

We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel *** is proved that an m-order infinite dimensional Canchy-Hankel tensor defines a bounded and positively(m-1)-homogeneous operat... 详细信息

关键词： Cauchy-Hankel tensor eigenvalues upper bound M-positive definite