奇异半线性热方程初值问题解的存在性与Blow-up问题

本文讨论如下奇异半线性热方程的初值问题其中γ＞1，σ＞O，f（x）连续有界非负但不恒为零．我们讨论了问题（1），（2）非负局部经典解的存在性和非负整体解的不存在问题，得到当0＜σ＜1且时，（1），（2）没有非负整体解．当σ＝1且时，（1），（2）没有非负整体解，当σ＞1时（1），（2）没有非负整体解．     

一阶急式微分方程周期边值问题(英文)

本文我们描述了一个构造性方法．在存在一个上解β及下解α且α≤β情形下,得到两个单调序列一致收敛于如下周期边值问题．ｘ′（ｔ）＝ｆ（ｔ,ｘ（ｔ）,ｘ′（ｔ））,ｔ∈［０,Ｔ］ｘ（０）＝ｘ（Ｔ）,｛的极值解     

一类半线性热方程整体解的存在性与非存在性

本文研究半线性热方程的初值问题u_t－△u＝u~γ＋cu,（γ＞1）;u（x,0）=（x）非负整体L~P解的存在性与非存在性．首先证明,若C＞0,则不存在非负整体解．而后,对C＜0情形给出了解的整体存在与非存在的充分条件,特别证明了,若P＞（γ一1）或,则当。充分小时存在非负整体L~P解.最后,对系数C和初值（x）得到无穷多个门槛结果．     

Lienard方程的比较原理

本文证明了一个比较原理，使方程ｘ″＋ｆ（ｘ）ｘ′＋ｇ（ｘ）＝０周期解存在性定理可以用判断方程ｘ″＋ｈ（ｘ，ｘ′）ｘ′＋ｇ（ｘ）＝０的周期解存在性。     

具非齐次线性部分的高阶非线性抛物型方程组的初值问题

本文讨论线性部分为非齐次的高阶非线性抛物型偏微分方程组整体经典解的存在性，得到了这类问题对小初值而言存在整体经典解的一些充分条件．     

Nagumo条件下三阶两点边值问题解的存在性

讨论Nagumo条件下非线性常微分方程三阶两点边值问题{y″′=t,y,′,y″）,t∈[0,1],y（0）=y′（0）=y′（1）=0解的存在性，其中f：[0，1]×R^3→R为连续函数．     

半线性热方程整体解的存在性与非存在性

本文研究半线性热方程的初值问题ｕｔ－Δｕ＝ｕγ（γ＞１），ｕ（ｘ，０）＝φ（ｘ）的非负古典解与Ｌｐ解的整体存在性、非存在性与ｂｌｏｗ－ｕｐ．首先，利用归一化的高斯函数得到了一些新的解的非整体存在的充分条件，这些条件对古典解与Ｌｐ解是普遍适用的；然后又讨论了某些非负整体解的存在性．本文不但得到了一些新的结果，而且还简化和统一了某些已知结果的证明．     

五维空间中半线性波动方程整体解的存在性定理

本文研究五维空间中半线性波动方程u_tt-△u=G（u）整体解的存在性,其中G（u）～|u|^p并且p>（3+(17)^1/2)/4.利用经典的迭代方法证明了:如果初始值很小并且紧支的,径向对称方程有一个经典整体解.     

一类具分布时滞的高阶泛函微分方程的周期解存在性问题

利用Fourier级数理论。伯努利数理论和重合度理论研究了一类具分布时滞的高阶泛函微分方程x^（m）（t）＋f（x^（m-1）（t）＋g（∫-r^0x（t＋s）da（s））=p^（t）的周期解问题，得到了周期解存在的一些新结果．     

退化拟共形映射的整体同胚与二维奇异积分方程

设Ｄ是一个边界Г∈C_a¹（０＜a≤１）的有界单连通域,复函数ｑ（ｚ）∈C_a¹,|ｑ（ｚ）|≤１,等式只能在Г上成立,且在Г上等式ｑ（ｚ（ｔ）)ｚ′（ｔ）/ｚ′（ｔ）+1|_z∈Г＝０最多在有限个点上成立．本文给出了复伸张ｑ（ｚ）满足上述条件时的退化拟共形映射的整体同胚解及以ｑ（ｚ）为系数的一类二维奇异积分方程的解．     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.