Affine Weyl group symmetries of Frobenius Painlevé equations

In this paper, we introduce a Frobenius Painlevé IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painlevé IV equation. Then, we construct the Lax pair of the Frobenius Painlevé IV equation. Furthermore, we recall the Frobenius modified KP hierarchy and the Frobenius KP hierarchy by bilinear equations, then we show how to get Frobenius Painlevé IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painlevé IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painlevé II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painlevé II equation.     

Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions

We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely near-monotonicity, and show that there always exists a solution to the risk-sensitive Hamilton–Jacobi–Bellman (HJB) equation, and that any minimizer in the Hamiltonian is optimal in the class of stationary Markov controls. Under the additional hypothesis that the coefficients of the diffusion are bounded, and satisfy a condition that limits (even though it still allows) transient behavior, we show that any minimizer in the Hamiltonian is optimal in the class of all admissible controls. In addition, we present a sufficient condition, under which the solution of the HJB is unique (up to a multiplicative constant), and establish the usual verification result. We also present some new results concerning the multiplicative Poisson equation for elliptic operators in ${\mathbb{R}}^d$.     

A note on the Hamilton–Waterloo problem with C8-factors and Cm-factors

In this paper, we almost completely solve the Hamilton–Waterloo problem with $C_8$-factors and $C_m$-factors where the number of vertices is a multiple of $8m$.     

The Local Spectral Properties of Extended Hamilton Operators

In this paper, we introduce the class of extended Hamilton operators and study various properties of this class. We examine the decomposability of extended Hamilton operators. In addition,we prove that an extended Hamilton operator with property(δ) is subscalar. Finally, we consider Weyl type theorems of this class.     

Existence of an optimal control for a coupled FBSDE with a non degenerate diffusion coefficient

We consider a controlled system driven by a coupled forward–backward stochastic differential equation with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation, at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to construct a sequence of approximating controlled systems for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition.     

Quadrilaterals,extremal quasiconformal extensions and Hamilton sequences

The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.     

渐近线性二阶Hamilton系统解的存在性和多重性

在实际问题中存在着Neumann边值情形.为实际需要,运用指标理论和Morse理论研究了渐近线性二阶Hamilton系统在这种情形下解的存在性和多重性问题。     

Hamilton ?-cycles in uniform hypergraphs

We say that a k-uniform hypergraph C is an ?-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of consecutive edges (in the natural ordering of the edges) intersects in precisely ? vertices. We prove that if 1??<k and k−? does not divide k then any k-uniform hypergraph on n vertices with minimum degree at least contains a Hamilton ?-cycle. This confirms a conjecture of Hàn and Schacht. Together with results of Rödl, Ruciński and Szemerédi, our result asymptotically determines the minimum degree which forces an ?-cycle for any ? with 1??<k.     

方差保费准则下的最优脉冲控制

本文研究保险公司在有再保险控制下的最优脉冲分红问题. 对保险公司的理赔损失, 假定有两家再保险公司参与分保, 且保险公司与两家再保险公司采取不同参数下的方差保费准则. 进一步, 假定保险公司有股东红利分配, 且每次分红有固定交易费和比例税收, 即脉冲分红. 在扩散逼近模型下, 本文应用随机动态规划方法研究破产前的最大期望折现分红, 给出值函数的解析表达式, 进而获得最优再保险策略和分红策略的具体形式.