Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.     

A unifying theory of exactness of linear penalty functions II: parametric penalty functions

In this article, we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions, and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parametric penalty functions, and derive necessary and sufficient conditions for a parametric penalty function to not have any stationary points outside the set of feasible points of the constrained optimization problem under consideration. In the second part of the paper, we apply the general theory of exact parametric penalty functions to a class of parametric penalty functions introduced by Huyer and Neumaier, and to smoothing approximations of nonsmooth exact penalty functions. The general approach adopted in this article allowed us to unify and significantly sharpen many existing results on parametric penalty functions.     

On the first eigenvalue of the mean finsler-laplacian

In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.     

一类非线性椭圆方程的刘维尔型定理

设（Mⁿ,g）是一个n维非紧的完备黎曼流行.本文考虑有正解的非线性椭圆方程△_fu+au log u=0的刘维尔型定理,其中a是一个非零常数.利用Bochner公式和极大值原理,获得了以上方程在Bakry-Emery里奇曲率有下界时正解的Li-Yau型梯度估计和某些有关的刘维尔理论,推广了文献[7]的结果.     

城镇职工养老保险随机模型研究

构建了包含个人、企业、政府等市场参与者相互制衡的城镇职工养老保险随机模型,该模型涉及了储蓄、工作期消费、个人养老金账户、工资、退休后消费共5个随机变量;利用ITo引理证明了随机微分方程解的存在性,唯一性,利用2010-2014年中国有关宏观数据,对5个变量进行了动态模拟,并对部分参数变动对模型的影响进行分析,得出了储蓄替代率和人口出生率与两期消费正相关,两者的小范围变动不会影响两期消费的趋势等结论.     

Hypergeometric approach to Apéry-like series

By reformulating four hypergeometric series formulae, we derive 36 Apéry-like series expressions for the Riemann zeta function, including a couple of identities conjectured by Sun [New series for some special values of L-functions. Nanjing Univ J Math. 2015;32(2): 189–218].     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

On the two classes of high‐order convergent methods of approximate inverse preconditioners for solving linear systems

Two classes of methods for approximate matrix inversion with convergence orders p =3?2^k +1 (Class 1) and p =5?2^k ?1 (Class 2), k ≥1 an integer, are given based on matrix multiplication and matrix addition. These methods perform less number of matrix multiplications compared to the known hyperpower method or p th‐order method for the same orders and can be used to construct approximate inverse preconditioners for solving linear systems. Convergence, error, and stability analyses of the proposed classes of methods are provided. Theoretical results are justified with numerical results obtained by using the proposed methods of orders p =7,13 from Class 1 and the methods with orders p =9,19 from Class 2 to obtain polynomial preconditioners for preconditioning the biconjugate gradient (BICG) method for solving well‐ and ill‐posed problems. From the literature, methods with orders p =8,16 belonging to a family developed by the effective representation of the p th‐order method for orders p =2^k , k is integer k ≥1, and other recently given high‐order convergent methods of orders p =6,7,8,12 for approximate matrix inversion are also used to construct polynomial preconditioners for preconditioning the BICG method to solve the considered problems. Numerical comparisons are given to show the applicability, stability, and computational complexity of the proposed methods by paying attention to the asymptotic convergence rates. It is shown that the BICG method converges very quickly when applied to solve the preconditioned system. Therefore, the cost of constructing these preconditioners is amortized if the preconditioner is to be reused over several systems of same coefficient matrix with different right sides.     

The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.