一类圆锥曲线统一性质的逆向思考

文献[1]得出了圆锥曲线的一个统一性质,文献[2]在此基础上做了变式探究,受此启发,笔者对该问题进行逆向思考,得出了一些结论.     

与椭圆直径相关的几个性质

文[1]的作者对椭圆共轭直径作了有益的探究,得出了一组优美的性质.笔者通过探究,得出了椭圆共轭直径的另一组优美性质.同时,笔者对椭圆直径也作了一些探究,得出一组优美性质.供大家参考.为了叙述的方便,先引出文[1]的两个定义.定义1经过椭圆中心的弦叫做椭圆的直径.     

三角形网格的有效性分析

本文分析了利用三角形网格对π作统计估计的有效性,首先对任意三角形网格进行一般性的分析,得出了具体的表达式,又对等边三角形网格和等腰直角三角形网格两种特殊情形进行具体计算,得出了具体的数值.     

一般算子不动点定理及其在Strum-Liouville奇异边值问题中的应用

本文运用Zorn引理,得出了正则锥上的非紧非单调算子的不动点的存在性的结果,并用于讨论Strum-Liouville奇异边值问题,得出了有关解的存在性的全新的结论.     

泛Clifford分析中的Laurent展式和留数定理

该文由泛Clifford分析中在特异边界上的Cauchy积分式得出了具有孤立奇点的LR正则函数在其相应的Laurent域上的Laurent展式，并由此给出了留数的定义，得出了类似于经典函数理论的留数定理。     

关于不含k-C-圈的n阶γ-一致超图的若干结果

主要讨论了不含k-C-圈的n阶γ-一致超图,对不同的k, 分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

随机二叉搜索树的子树

本文讨论随机二叉搜索树上不同大小的子树和与给定某个二叉树同构的子树. 利用递归分布等式,　我们得出了它们各自数目的期望和方差\bd 最后, 用压缩法得出了它们的中心极限定理.     

关于不含k-C-圈的n阶r-一致超图的若干结果

主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

D-逻辑度量空间中的相容理论

在D-逻辑度量空间中提出了理论的D-开放度,得出一个理论的D-开放度与它的D-发散度取值相等;提出了理论的D-相容度,得出D-相容度在D-逻辑度量空间中能保持逻辑度量空间中的基本性质.     

一类“只需写出结果”题型的解题策略

<正>近些年来,在各省市的高考数学解答题中常常出现"只需写出结果"这样的限定只写出结果的设问方式,如果你正确地理解了相关概念,采取方法得当,可能很快就得出了"结果";反之,你可能采取的方法很麻烦,得出结果很费时(与很快得出"结果"相比相当于"减分"了),甚至得出错误的结果.因此,"只需写出结果"这种设问方式,是解答题的一种创新,丰富了解答题的考查方式.本文通过一些具体例子,     

Torsion points on families of products of elliptic curves

In a recent paper we proved a special case of a variant of Pink's Conjecture for a variety inside a semiabelian scheme: namely for any curve inside any scheme isogenous to a fibred product of two isogenous elliptic schemes. Here we go ahead with the programme of settling the conjecture for general abelian surface schemes by completing the proof for all non-simple surfaces. This involves some entirely new and crucial issues.     

Acceleration of Convergence of Static and Dynamic Iterations

A new technique for acceleration of convergence of static and dynamic iterations for systems of linear equations and systems of linear differential equations is proposed. This technique is based on splitting the matrix of the system in such a way that the resulting iteration matrix has a minimal spectral radius for linear systems and a minimal spectral radius for some value of a parameter in Laplace transform domain for linear differential systems.This revised version was published online in October 2005 with corrections to the Cover Date.     

Generalizations of a theorem of Rolewicz

The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz.     

Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems

The determination of solutions of the Jacobi partial differential equations (PDEs) for finite-dimensional Poisson systems is considered. In particular, a novel procedure for the construction of solution families is developed. Such a procedure is based on the use of time reparametrizations preserving the existence of a Poisson structure. As a result, a method which is valid for arbitrary values of the dimension and the rank of the Poisson structure under consideration is obtained. In this article two main families of time reparametrizations of this kind are characterized. In addition, these results lead to a novel application which is also developed, namely the global and constructive determination of the Darboux canonical form for Poisson systems of arbitrary dimension and rank two, thus improving the local result provided by Darboux' theorem for such a case.     

Categories of models of R-mingle

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.     

Estimates of rate of propagation of perturbations in quasilinear divergent degenerate parabolic equations of high order

A method is given for obtaining integral growth lemmas for solutions of boundary problems for a large class of quasilinear evolution equations. As a possible application a sharp estimate is obtained of the dependence of the support of a solution of a mixed problem and a Cauchy problem for a quasilinear divergent parabolic equation on time.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1451–1456, October, 1992.     

Superconvergence of mixed finite element semi-discretizations of two time-dependent problems

We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation for the error in the space discretization can be performed in the same way as for the underlying elliptic problem.     

Invariants of Characteristics of Some Systems of Partial Differential Equations

We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.     

Stability analysis of set trajectories for families of impulsive equations

In this paper, for a family of impulsive equations, a heterogeneous matrix-valued Lyapunov-like function is considered, the comparison principle is formulated, and stability conditions for the set of stationary solutions are established. In addition, for a class of impulsive equations with uncertain parameters the monotone iterative technique for constructing a set of solutions is adapted.     

The impact of cost uncertainty on the location of a distribution center

The location of a distribution center (DC) is a key consideration for the design of supply chain networks. When deciding on it, firms usually allow for transportation costs, but not supplier prices. We consider simultaneously the location of a DC and the choice of suppliers offering different, possibly random, prices for a single product. A buying firm attempts to minimize the sum of the price charged by a chosen supplier, and inbound and outbound transportation costs. No costs are incurred for switching suppliers. We first derive a closed-form optimal location for the case of a demand-populated unit line between two suppliers offering deterministic prices. We then let one of the two suppliers offer a random price. If the price follows a symmetric and unimodal distribution, the optimal location is closer to the supplier with a lower mean price. We also show the dominance of high variability: the buyer can decrease the total cost more for higher price variability for any location. The dominance result holds for normal, uniform, and gamma distributions. We propose an extended model with more than two suppliers on a plane and show that the dominance result still holds. From numerical examples for a line and a plane, we observe that an optimal location gets closer to the center of gravity of demands as the variability of any supplier’s price increases.