具有相同边界的单圈图的Faber-Krahn型不等式}

通过研究具有相同``体积'的图类中具有最小的第一Dirichlet特征值的图的性质, 刻画了具有给定边界点数的单圈图中具有Faber-Krahn性质的图.     

具有逆断面的纯正群的构造

本文用具有半格断面的带和Clifford半群给出具有逆断面的纯正群的一个构造定理.     

算子RS和SR的局部谱性质

对算子RS和SR的局部谱性质进行了比较系统的研究,得到如下结果:RS具有(C)属性当且仅当SR具有(C)属性;RS具有有限升当且仅当SR具有有限升;RS具有(β)_ε属性当且仅当SR具有(2)_ε属性;RS和SR具有相同的非零Kato谱.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

具有控制结构的向量均衡问题与解集的性质

提出一种具有控制结构的向量均衡问题与向量映射的新的伪单调性概念,得到具有控制结构的向量均衡问题解的存在性及其解集的紧凸性．作为应用,得到具有控制结构的向量变分不等式与互补问题的解．     

一类具有对称性和插值性的紧支撑尺度函数

具有对称性和插值性的多进尺度函数的滤波器也具有相应的对称性和插值 性,本文研究具有具有对称性和插值性的滤波器构造问题.     

线性系统的极限跟踪性

给出了Rⁿ上的线性同构和线性流具有极限跟踪性的特征：线性同构具有极限跟踪性当且仅当其对应的矩阵为双曲的;线性流具有极限跟踪性当且仅当其对应矩阵的所有特征根均具有非零实部.     

数据驱动的具有周期Holling功能反应的云杉蚜虫模型的学习

从数据中推断微分方程模型是具有挑战性又重要的课题.本文对云杉蚜虫的实际数据进行分析,通过稀疏回归算法学习构建具有周期Holling功能反应的微分方程模型,模型能很好的与实际数据吻合并能预测云杉蚜虫的周期爆发行为.本工作对探索云杉蚜虫的动力学行为具有指导意义.     

“正“”误”例说类比思想的运用

类比是根据两个(或两类)对象之间具有(不具有)某些相同或相似的性质,而且其中一个(或一类)还具有(或不具有)另一性质,由此推出另一个(或另一类)对象也具有(或不具有)这一性质,类比法是研究数学问题的重要方法,也是掌握知识的好方法,正如玻利亚所言:"类比是     

一类食饵具有投放率和捕食者具有捕获率的非自治捕食系统的全局分析

研究了一类具有Beddington-DeAngelis类功能反应以及捕食者具有捕获率和食饵具有投放率的非自治系统,用微分方程稳定性理论及构造Liapunov函数获得系统持续生存和全局稳定的充分条件.     

Variation formulas of solutions and optimal control problems for differential equations with retarded argument

The authors prove a theorem on the continuous dependence of solutions of nonlinear systems of differential equations with variable delay on the perturbations of initial data (initial instant, initial function, and initial value of the trajectory) and the right-hand side in the case where these perturbations are small in the Euclidean and integral topology, respectively. The variation formulas of solutions of a differential equation with discontinuous and continuous initial condition are deduced; as compared with those known earlier, these formulas take into account the variation of the initial instant and the discontinuity and continuity of the initial data. A necessary condition for criticality of mappings defined on a finitely locally convex set is obtained. The quasiconvexity of filters in studying optimal problems with delays in controls is proved. Necessary optimality conditions and existence theorems are proved for optimal problems with variable delays in phase coordinates and controls having a nonfixed initial instant, a discontinuous and a continuous initial condition, and functional and boundary conditions of general form. Necessary optimality conditions are obtained for optimal problems with variable structure and delays. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 25, Optimal Control, 2005.     

具有初始层间压力的层合圆筒的热冲击研究

采用一种解析方法求解具有初始层间压力的双层层合圆筒内的动态热应力的瞬态响应·　首先,将由自紧装配双层层合圆筒引起的初始层间压力考虑作为热弹性动力学方程的初始条件·　其次,利用一个简便的数学变换方法求解具有初始应力场的单层圆筒的热弹性动力学解,然后利用层合圆筒的边界条件和连接条件,得到具有初始层间压力的双层层合圆筒的热冲击解·     

The substitution theorem for semilinear stochastic partial differential equations

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinite-dimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating initial conditions.     

A depletion of assets model of organizational learning*

This research investigates how population heterogeneity with respect to initial assets affects the rate of failure (or change) of organizations and social relationships. Organizations and social relationships are assumed to be endowed with initial assets which buffer against initial risks of failure. Failure is seen as the outcome of a process in which the assets are depleted and finally become exhausted. The core idea is that the assets of a unit become depleted through learning experiences which incur search costs and setbacks. Two settings are explored: A constant rate of depletion, and a declining rate of depletion of assets. The study explores additionally how the distribution of initial assets affects the failure rate of the population. It is found that the type of distribution of initial assets has a strong impact on the time dependence of the failure rate. A Normal distribution of initial assets leads to positive time dependence if the depletion rate is constant, and to negative time dependence if the depletion rate declines. The results show that population heterogeneity with respect to initial assets has effects on the time dependence of failure rates which are quite different from the popular case of population heterogeneity with respect to fit.     

LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES

We are concerned with local existence and uniqueness of solutions for a general model of viscous and heat-conductive gases with low regularity assumptions on the initial data (the velocity and the temperature may be discontinuous). Local well-posedness is showed to hold in spaces which are critical with respect to the scaling of the equations, provided that the initial density is close enough to a positive constant. When initial data are a trifle more regular, local well-posedness holds for any initial density bounded away from zero. This former result lies on new estimates for linear heat equations with a non constant diffusion coefficient.     

Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations

We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the solution is specified at an initial moment of time). We then show how our method applies in fluid mechanics. More specifically, we present a complete solution to the problem of long waves run-up in inclined bays of arbitrary shape with nonzero initial velocity.     

Sharp critical thresholds for a class of nonlocal traffic flow models

We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams.     

Global strong solution to the three-dimensional density-dependent incompressible magnetohydrodynamic flows

An initial-boundary value problem is considered for the density-dependent incompressible viscous magnetohydrodynamic flow in a three-dimensional bounded domain. The homogeneous Dirichlet boundary condition is prescribed on the velocity, and the perfectly conducting wall condition is prescribed on the magnetic field. For the initial density away from vacuum, the existence and uniqueness are established for the local strong solution with large initial data as well as for the global strong solution with small initial data. Furthermore, the weak-strong uniqueness of solutions is also proved, which shows that the weak solution is equal to the strong solution with certain initial data.     

Cauchy–Gelfand problem and the inverse problem for a first-order quasilinear equation

Gelfand’s problem on the large time asymptotics of the solution of the Cauchy problem for a first-order quasilinear equation with initial conditions of the Riemann type is considered. Exact asymptotics in the Cauchy–Gelfand problem are obtained and the initial data parameters responsible for the localization of shock waves are described on the basis of the vanishing viscosity method with uniform estimates without the a priori monotonicity assumption for the initial data.     

Spatial behaviour of solutions of the three-phase-lag heat equation

In this paper we study the spatial behaviour of solutions for the three-phase-lag heat equation on a semi-infinite cylinder. The theory of three-phase-lag heat conduction leads to a hyperbolic partial differential equation with a fourth-order derivative with respect to time. First, we investigate the spatial evolution of solutions of an initial boundary-value problem with zero boundary conditions on the lateral surface of the cylinder. Under a boundedness restriction on the initial data, an energy estimate is obtained. An upper bound for the amplitude term in this estimate in terms of the initial and boundary data is also established. For the case of zero initial conditions, a more explicit estimate is obtained which shows that solutions decay exponentially along certain spatial-time lines. A class of non-standard problems is also considered for which the temperature and its first two time derivatives at a fixed time T₀ are assumed proportional to their initial values. These results are relevant in the context of the Saint-Venant Principle for heat conduction problems.