Integral sets of quasilinear pulse systems

Sufficient conditions for the existence of integral sets of weakly nonlinear systems of differential equations with pulse effect on a surface are presented. The asymptotic behavior of solutions originating on integral sets and in the vicinity of these sets is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 5–11, January, 1992.     

Über Picardmengen ganzer Funktionen

Following Lehto we call a set E in the complex plane a Picard set for integral functions, if every non-rational integral function omits at most one finite value in the complement (with respect to the plane) of E. The existence of non-trivial Picard sets was proved by Lehto [3]. The aim of this paper is to give a new criterion for denumberable point sets E to be Picard sets for integral functions. In some way the criterion given by theorem 1 is an extension of the result on Picard sets for integral functions given by Toppila [5] and improves the criterion given by the author in [6].     

Integral sets of a class of discontinuous dynamical systems

The existence of integral sets of a certain class of systems of differential equations, driven by pulses at discrete instants of time, is investigated.Translated from Ukrainskii Matemticheskii Zhurnal, Vol. 44, No. 5, pp. 589–595, May, 1992.     

Stieltjes integral equations in partially ordered sets

Stieltjes integral equations are considered in partially ordered sets of real valued functions, and connections are made using integral inequalities to the existence and uniqueness problems of hereditary systems which are not Lipschitz.     

Generalized-periodic motions of nonautonomous systems

The definition and existence criterion are given for the generalized-periodic motions of a certain wide class of systems. The class contains all the systems that can be characterized by the classical periodic operator of displacement, the systems generated by the Volterra integral equations, and some others. A relationship is established between generalized-periodic motions and integral invariant sets.     

序有界模糊n-方体数集的上确界与下确界

本文中,我们讨论了在定义模糊n-方体数值映射的某种类型的积分时要用到的序有界模糊n-方体数集的上确界与下确界的问题。我们证明了序有界模糊n-方体数集的上、下确界的存在性,并给出了它们的表示。     

可达到和可逼近总极小点的存在性和最优性

针对积分总极值，讨论并拓展了丰满集和丰满函数的概念，研究了拟上丰满和伪上丰满函数的总极值问题. 在总极值的变差积分最优性条件下，证明了拟上丰满函数的可达到极小点和伪上丰满函数的可逼近极小点的存在性.     

Classical perturbation theory and resonances in some rigid body systems

We consider the system of a rigid body in a weak gravitational field on the zero level set of the area integral and study its Poincaré sets in integrable and nonintegrable cases. For the integrable cases of Kovalevskaya and Goryachev–Chaplygin we investigate the structure of the Poincaré sets analytically and for nonintegrable cases we study these sets by means of symbolic calculations. Based on these results, we also prove the existence of periodic solutions in the perturbed nonintegrable system. The Chaplygin integrable case of Kirchhoff’s equations is also briefly considered, for which it is shown that its Poincaré sets are similar to the ones of the Kovalevskaya case.     

Some results about integration on regular stratified sets

Summary In this paper we prove the existence of the integral of differential forms with cornpact support on stratified subsets of Rⁿ with locally finite volume and toe give some sufficient conditions to have Stokes' formula on regular stratified sets.     

Application of Wiener-Hopf technique to linear nonhomogeneous integral equations for a new representation of Chandrasekhar's H-function in radiative transfer, its existence and uniqueness

In this paper, the linear nonhomogeneous integral equation of H-functions is considered to find a new form of H-function as its solution. The Wiener-Hopf technique is used to express a known function into two functions with different zones of analyticity. The linear nonhomogeneous integral equation is thereafter expressed into two different sets of functions having the different zones of regularity. The modified form of Liouville's theorem is thereafter used, Cauchy's integral formulae are used to determine functional representation over the cut region in a complex plane. The new form of H-function is derived both for conservative and nonconservative cases. The existence of solution of linear nonhomogeneous integral equations and its uniqueness are shown. For numerical calculation of this new H-function, a set of useful formulae are derived both for conservative and nonconservative cases.     

Existence and compactness of solutions to impulsive differential equations with nonlocal conditions

The new type of nonlinear integral inequalities of Volterra–Fredholm type for discontinuous functions is investigated. Then, by using these inequalities and Schaefer fixed‐point theorem, we present new existence results for impulsive semilinear differential equations with nonlocal conditions. Moreover, the compactness of solution sets can be shown in some certain conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

控制系统中的分形

本文将整数维与分形的Hausdorff测度引入并应用于控制系统,同时也介绍了准自相似集这个新概念,证明了这种集合的存在性与唯一性.并将计算自相似集维数的公式推广到准自相似集,在此基础上,说明了控制系统的可达集可以具有分数维.表明在分析非线性系统可控性与可观性时,分形几何学也将是一种有意义的工具.     

On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces

The main purpose of this paper is to deal with almost automorphic and asymptotically almost automorphic solutions of the initial value problem as well as the nonlinear Volterra integral equation in Banach spaces. We obtain a collection of existence results of such solutions to these equations. We investigate also a topological structure of such solution sets. Moreover, we prove Aronszajn-type theorems for solutions of the initial value problem as well as the nonlinear Volterra integral equation, defined on the whole real line.     

一类含时间奇异性的二阶非线性Dirichlet问题的正解

通过使用Hammastein积分方程和锥上的不动点定理对于一类含时间奇异性的二阶非线性Dirich．1et问题建立了三个局部存在定理．主要结论表明只要非线性项的主要部分在某些有界集合上的高度是适当的此问题具有n个正解,其中竹是一个任意的自然数．     

The Upper and Lower Solutions Method for Stochastic Inclusions with Discontinuous Multivalued Mappings

Abstract

In this article, we consider a stochastic integral inclusion driven by semimartingale with discontinuous multivalued right hand side. We discuss the existence of strong solutions using lower and upper solutions method and a fixed point theorem for ordered sets. The presented studies extend some recent results both for deterministic differential inclusions and stochastic differential equations for increasing operators.     

Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

On local Whittaker models for the Jacobi group of degree one

The lowest dimensional Jacobi groupG ^J sets a link between the theory of Siegel modular forms of degree two and the elliptic modular forms of integral and half integral weight. This note is meant to help finding a way to associateL-functions to automorphic representations of the groupG ^J by using the approach via Whittaker models of these representations. Thus, here the question of existence and unicity of these models is discussed. This question may be reduced to a closer study of the Schrödinger and Weil representation of the Heisenberg resp. the metaplectic group and thus to the application of some results by Waldspurger.     

积分凸性及其应用

该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集，下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.     

The Meir–Keeler fixed point theorem in incomplete modular spaces with application

In this paper, we present a new generalized modular version of the Meir–Keeler fixed point theorem endowed with an orthogonal relation. Our results improve the results of (Eshaghi Gordji et al., On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 2017). Finally, this result is applied to the existence and uniqueness of solutions to perturbed integral equations in modular function spaces.     

Maximal integral point sets in affine planes over finite fields

Motivated by integral point sets in the Euclidean plane, we consider integral point sets in affine planes over finite fields. An integral point set is a set of points in the affine plane over a finite field F_q, where the formally defined squared Euclidean distance of every pair of points is a square in F_q. It turns out that integral point sets over F_q can also be characterized as affine point sets determining certain prescribed directions, which gives a relation to the work of Blokhuis. Furthermore, in one important sub-case, integral point sets can be restated as cliques in Paley graphs of square order.In this article we give new results on the automorphisms of integral point sets and classify maximal integral point sets over F_q for q≤47. Furthermore, we give two series of maximal integral point sets and prove their maximality.