一类差分不等式及其应用

建立一类二变量的和差分不等式,该不等式包含了一个一重和与两个二重和,二重和号内包含两个不同的没有假设单调性的未知函数的复合函数.使用单调化技术,利用了强单调的性质,给出了差分不等式中未知函数的估计.结果能使我们对相关文献中考虑的差分不等式中未知函数进行估计.进一步,用结果给出了一类差分方程解的估计.     

一类推广的具有时滞的Pachpatte离散不等式及其应用

不仅把Pachpatte的离散不等式推广成时滞不等式,而且把不等式中的常数项推广成连续的正函数.推广后的不等式不仅包含了更多项,且不要求函数的单调性.利用单调化技巧给出了不等式中未知函数的估计.最后用得到的结果研究时滞差分方程初值问题解的唯一性与有界性.     

一类非线性差分不等式中未知函数的估计及其应用

该文建立了一类非线性差分不等式.此不等式包含了非线性函数与未知函数的复合函数,是一个具有多重和的差分不等式.利用单调技巧、放大方法、积分中值定理、变量替换技巧、差分和求和技巧,给出了未知函数的上界估计.最后,用所得结果研究了差分方程解的估计.     

一类新的非线性和差分不等式及其应用

由于差分不等式是研究差分方程解的存在性、有界性、唯一性、稳定性等定性性质的重要工具,许多数学家不仅研究Gronwall类积分不等式的各种推广形式及其应用,而且研究差分不等式及其应用.该文建立了一类新的非线性和差分不等式,利用分析技巧给出了不等式中未知函数的上界估计.将得到的结果应用到时滞差分方程的边值问题,得到了差分方程解的估计.     

一类乘积形式的离散不等式及其应用

该文在文献[2]的基础上,研究了一类新的乘积形式的离散不等式.把参考文献中不等式右端第一个因子中包含的未知函数u推广成未知函数的幂函数u~2,运用变量替换技巧、放大技巧、微分中值定理、反函数技巧、常量与变量的辩证关系,给出了不等式中未知函数的估计.最后,阐述了所得的结果可以用来给出乘积形式差分方程解的绝对值的上界估计.     

一个推广的二变量时滞积分不等式及其应用

建立了一类二变量的时滞积分不等式,不等式包含一个一重积分和两个二重积分,二重积分内包含两个不同的没有假设单调性的未知函数的复合函数.使用单调化技术,给出积分不等式中未知函数的估计.结果能对相关文献中考虑的积分不等式中未知函数进行估计.进一步,结果给出了一类积分-微分方程解的估计.     

一类三变量非线性和差分不等式中未知函数的估计

Gronwall-Bellman型积分不等式的离散形式及其推广形式是研究和差分方程解的存在性、有界性和唯一性等定性性质的重要工具.研究了一类六重非线性和差分不等式,和号外含非常数因子,和项外包含了非常数项.利用差分算子的性质、求和技巧、变量替换技巧和积分中值定理等分析手段,给出了和差分不等式中未知函数的上界估计,推广了已有结果.最后举例说明所得结果可以用来研究三独立变量差分方程解的定性性质.     

一类含有最大值项的二元时滞积分不等式的推广

本文研究一类含有最大值项的二元时滞非线性积分不等式,放弃对函数的单调性和可分离性要求.通过对不等式中的函数的单调化,给出了未知函数解的估计,在较弱的条件下推广了一些已有的结果,进而将所得的结果应用到研究含有最大值项的偏微分方程解的有界性.     

时标上的推广的Pachpatte型不等式及其在边值问题中的应用

该文利用单调化技巧研究了时标上的推广的Pachpatte型不等式, 该不等式右端有一个非常数项和三个包含未知函数与没有假设单调性的非线性函数的复合函数的积分项, 不等式左端是未知函数与非线性函数的复合函数. 所得不等式不仅把Pachpatte型不等式的离散形式和连续形式统一起来, 而且推广了已有的时标上的相应不等式. 最后, 用得到的结果研究时标上边值问题解的估计.     

带有无穷求和的非线性离散不等式的推广及应用

本文研究一类带有多个非线性项和无穷求和的二元离散不等式,借助数学归纳法,给出这类不等式中未知函数的估计,所得结果推广了一些已有结果.最后,本文利用此结果得到一个差分方程解的上界.     

The interface between regions where u<0 andu > 0in the porous medium equation

We consider the porous medium equation with sign changes. In particular this equation describes the mixing of fresh and salt groundwater due to mechanical dispersion. The unknown function u, which denotes the velocity of the fluids, may take positive as well as negative values. Our main result is the following : under certain monotonicity hypotheses on the initial function, there exists a time T> 0 after which the regions where u < 0 and u > 0 are separated by an interface x = ζ(t) such that ζ is continuously differentiable on [T,∞]. The method of proof is based on a priori estimates for solutions of regularized problems and for their level lines     

Monotonicity criteria for difference schemes designed for hyperbolic equations

Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S.K. Godunov’s, A. Harten’s (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations.     

Complete monotonicity of a function involving the divided difference of digamma functions

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.     

From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions

In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated.     

Redheffer type bounds for Bessel and modified Bessel functions of the first kind

In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.     

A new method for interpolating in a convex subset of a Hilbert space

In this paper, interpolating curve or surface with linear inequality constraints is considered as a general convex optimization problem in a Reproducing Kernel Hilbert Space. The aim of the present paper is to propose an approximation method in a very general framework based on a discretized optimization problem in a finite-dimensional Hilbert space under the same set of constraints. We prove that the approximate solution converges uniformly to the optimal constrained interpolating function. Numerical examples are provided to illustrate this result in the case of boundedness and monotonicity constraints in one and two dimensions.     

社会福利函数独裁的特征

在这篇短文中,给出了关于社会福利函数F的半严格正向响应的概念,并且证明了如果备选对象至少有三个,则弱帕累托性质与半严格正向响应性质是独裁的充分必要条件.作为应用,我们给出了社会选择函数防止策略性操纵的一个等价描述,并对社会福利函数引进了防止局部策略性操纵的概念,得到了一个类似于Gibbard—Satterthwaite定理的结论.