一类拟线性奇异摄动方程组的空间对照结构

本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

一类线性奇异摄动最优控制问题的渐近解

研究了一类线性奇异摄动最优控制问题的空间对照结构,讨论了初始点固定,终端自由的情形.首先根据变分法得到了一阶最优性条件,其次运用退化最优控制问题的解证明了异宿轨道的存在性,从而结合奇异摄动理论证明了原问题空间对照结构解的存在性.进一步根据解的结构,利用边界层函数法构造了奇异摄动最优控制问题一致有效的形式渐近解.最后,通...     

在子区间上奇异摄动的一类边值问题解的渐近分析

研究了在子区间上奇异摄动的一类半线性二阶微分方程边值问题,用边界层函数法构造出问题的形式渐近解,借助微分不等式理论证明了渐近解的一致有效性.     

具有快慢层的非光滑奇异摄动问题的空间对照结构

该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

具有阶梯状空间对照结构的奇摄动

针对二阶半线性Dirichlet问题用边界层函数法构造了渐近解,给出了转移点的渐近表达式,并用微分不等式方法证明了阶梯状空间对照结构的存在性和进行了余项估计.     

二阶半线性奇摄动边值问题的渐近解

研究不满足法向双曲条件的二阶半线性非自治奇摄动Dirichlet边值问题.首先,利用边界层函数法,构造了问题在两个区间端点的代数边界层,获得了形式渐近解;接着,利用上下解方法,证明了解的存在性、渐近解的一致有效性以及渐近解与精确解之间的误差估计.研究表明:通过对奇异摄动参数进行适当的尺度变换,一定条件下可处理任意退化的二阶半线性非自治奇摄动边值问题.最后,通过一个典型例子验证了理论结果的正确性.     

几类近似达到Welch界码本的构造

具有低相关值的码本在分频多址(CDMA)通信系统,量子信息传输,编码理论,密码等多个领域有着重要的应用.目前,最佳的码本大多是由交换群上的差集合来构造的.近年来,人们考虑构造近似最佳的码本.本文利用高斯和,高斯周期,分圆类等数论工具,构造出了三类近似达到Welch界的近似最佳码本.     

带非线性无穷大边值条件的二阶半线性奇摄动问题

考虑关于带非线性无穷大边界值条件的二阶半线性奇摄动边值问题.基于边界层校正的思想,分别构造了左、右端点邻域的指数型及代数型的边界层校正函数,得到了问题的渐近解;根据微分不等式理论,获得了该问题解的存在性、渐近解的一致有效性以及渐近解的误差估计.还着重探讨了一定的稳定性条件下问题所能允许的边界值的奇异程度问题.通过一个典型的算例,验证了文中理论结果的正确性以及渐近解的高精度性.     

一类超线性k-Hessian方程耦合系统的径向解

研究一类带参数的奇异超线性k-Hessian系统Dirichlet问题解的存在性.基于Banach空间中的Krasnosel’skii型不动点定理,建立了非平凡径向解的存在性、多解性及不存在性结果.同时,讨论了解依赖于参数的渐近行为.     

渐近拟非扩张非自映射的收敛定理

在实线性赋范空间中引入了渐近拟非扩张非自映射概念.并在Banach空间中证明了渐近拟非扩张非自映射对的强收敛定理,所得结果推广和改进了相关文献的结论.     

Codebooks from almost difference sets

In direct spread CDMA systems, codebooks meeting the Welch bounds are used to distinguish among the signals of different users. Recently, constructions of codebooks with difference sets meeting Welch’s bound on the maximum cross-correlation amplitude were developed. In this paper, a generic construction of codebooks using almost difference sets is considered and several classes of codebooks nearly meeting the Welch bound are obtained. The parameters of the codebooks constructed in this paper are new.      

Cheap control of the time-invariant regulator

The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.     

Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations

The concept of almost-normed spaces is introduced. It is proved that the space of sufficiently smooth functions asymptotically approximating to polynomials (of degrees no higher than a given one) as their argument tends to infinity is an almost-normed space. It is demonstrated that this space is a complete metric space with respect to the metrics generated by the almost-norm introduced. The space of functions strongly asymptotically approximating to polynomials is defined, and its embedding into the space of functions asymptotically approximating to polynomials is proved. The results obtained give a new approach to studying boundary-value problems with asymptotic initial value data at singular points of ordinary differential equations.     

On the perturbation of semi-Fredholm relations with complemented ranges and null spaces

Multivalued semi-Fredholm type linear operators with complemented ranges and null spaces are introduced. Conditions are obtained under which the classes given are stable under compact, strictly singular and strictly cosingular additive perturbations.     

Singular Integral Operators with Fixed Singularities on Weighted Lebesgue Spaces

The paper is devoted to study of singular integral operators with fixed singularities at endpoints of contours on weighted Lebesgue spaces with general Muckenhoupt weights. Compactness of certain integral operators with fixed singularities is established. The membership of singular integral operators with fixed singularities to Banach algebras of singular integral operators on weighted Lebesgue spaces with slowly oscillating Muckenhoupt weights is proved on the basis of Balakrishnans formula from the theory of strongly continuous semi-groups of closed linear operators. Symbol calculus for such operators, Fredholm criteria and index formulas are obtained.     

Abstract singular evolution equations of “hyperbolic” type

This paper is concerned with the study of a large class of linear abstract evolution equations with singular coefficients under Kato's hyperbolicity assumptions. Existence and uniqueness results for strong and strict solutions are obtained in suitable weighted spaces.     

赋范线性空间中渐近伪压缩映象的不动点迭代逼近

研究了赋范线性空间中渐近非扩张映象和渐近伪压缩映象不动点的迭代逼近问题,所得结果改进和推广了已有的一些结果.     

Singular linear space and its applications

As a generalization of attenuated spaces, the concept of singular linear spaces was introduced in [K. Wang, J. Guo, F. Li, Association schemes based on attenuated spaces, European J. Combin. 31 (2010) 297–305]. This paper first gives two anzahl theorems in singular linear spaces, and then discusses their applications to the constructions of Deza digraphs, quasi-strongly regular graphs, lattices and authentication codes.     

The Dimensions of Spline Spaces and Their Singularity

In this paper, the dimensions of spaces $S^{\mu}_k(\Delta_n)(k\geq 2^n\mu +1)$ are obtained, where $(\Delta_n)$ is a general simplicial partition of a bounded region with piecewise linear boundary. It is also pointed that the singularity of spaces $S^{\mu}_k(\Delta_n)$ can not disappear when $n\geq 3$ no matter how large $k$ is. At the same time, a necessary and sufficient condition that Morgen and Scott's structure is singular is obtained.     

Backward Euler Scheme,Singular Hölder Norms,and Maximal Regularity for Parabolic Difference Equations

We show finite difference analogues of maximal regularity results for discretizations of abstract linear parabolic problems. The involved spaces are discrete versions of spaces of Hölder continuous functions, which can be singular in 0. The main tools are real interpolation and Da Prato–Grisvard's theory of the sum of linear operators.