Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controlled initial conditions

We introduce the notions of equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables for solutions with partly controlled initial conditions. We obtain sufficient conditions for the equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables of solutions with partly controlled initial conditions. We introduce the notions of equiboundedness and uniform boundedness with respect to part of the variables for solutions of systems with partly controlled initial conditions. We obtain sufficient conditions for the equiboundedness and uniform boundedness with respect to part of the variables of solutions with partly controlled initial conditions.     

On subtractive varieties II: General properties

As a sequel to [23] we investigate ideal properties focusing on subtractive varieties. After having listed a few basic results, we give several characterizations of the commutator of ideals and prove, for example, that it commutes with finite direct products. We deal with the ideal extension property (IEP) and with related commutator properties, showing for instance that IEP implies that the commutator commutes with restriction to subalgebras. Then we characterize varieties with distributive ideal lattices and relate this property with (a form of) equationally definable principal ideals and with IEP. Then, at the other extreme, we deal with Abelian and Hamiltonian properties (of ideals and congruences), giving for example a purely ideal theoretic characterization of varieties of Abelian groups with linear operations. To finish with, we present a few examples aiming at vindicating our work.Presented by A. F. Pixley.     

Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.     

模糊正则文法的逼近性

为了扩大现有研究的应用范围,基于max-min型模糊正则文法引入了max-*型模糊正则文法(其中*为特定t-模)的概念,讨论了max-*型模糊正则文法可以通过max-min型模糊正则文法在任意给定的逼近精度来逼近.研究表明,当t-模*满足一定的条件时,max-*型模糊正则文法与max-min型模糊正则文法在生成模糊语言能力方面是等价的.     

Differential equations on manifolds with edge singularities in spaces with asymptotics

The present paper deals with differential equations with edge degeneration in spaces with asymptotics. We give the definition of an edge space with asymptotics, prove the continuity of operators with edge degeneration in the scale of these spaces, present statements of problems with edge operators, and state conditions providing their Fredholm property.     

Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.     

On the weighted trees with given degree sequence and positive weight set

We determine the (unique) weighted tree with the largest spectral radius with respect to the adjacency and Laplacian matrix in the set of all weighted trees with a given degree sequence and positive weight set. Moreover, we also derive the weighted trees with the largest spectral radius with respect to the matrices mentioned above in the sets of all weighted trees with a given maximum degree or pendant vertex number and so on.     

带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

The first Dirichlet eigenvalue of bicyclic graphs

In this paper, we have investigated some properties of the first Dirichlet eigen-value of a bicyclic graph with boundary condition. These results can be used to characterize the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicyclic graphs with a given graphic bicyclic degree sequence with minor conditions. Moreover, the extremal bicyclic graphs with the smallest first Dirichlet eigenvalue among all the bicycle graphs with fixed k interior vertices of degree at least 3 are obtained.     

变厚度圆薄板非对称非线性弯曲问题

首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化,其结果和物理概念完全吻合·     

Mathematical Programming with System of Equilibrium Constraints

In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.     

On the spectral radius of unicyclic graphs with prescribed degree sequence

We consider the set of unicyclic graphs with prescribed degree sequence. In this set we determine the (unique) graph with the largest spectral radius (or index) with respect to the adjacency matrix. In addition, we give a conjecture about the (unique) graph with the largest index in the set of connected graphs with prescribed degree sequence.     

Irreducible Apollonian Configurations and Packings

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles.     

M/G/1一般减量服务单重休假排队系统的随机分解

本文讨论了M/G/1型一般减量服务单重休假排队模型,运用结构分析法得到稳态队长和服务时间的随机分解的母函数和拉式变换,并给出稳态分布成立的条件及其概率含义．     

Hitting Times in Markov Chains with Restart and their Application to Network Centrality

Motivated by applications in telecommunications, computer science and physics, we consider a discrete-time Markov process with restart. At each step the process either with a positive probability restarts from a given distribution, or with the complementary probability continues according to a Markov transition kernel. The main contribution of the present work is that we obtain an explicit expression for the expectation of the hitting time (to a given target set) of the process with restart. The formula is convenient when considering the problem of optimization of the expected hitting time with respect to the restart probability. We illustrate our results with two examples in uncountable and countable state spaces and with an application to network centrality.     

Lyapunov direct method in the analysis of Lagrange instability with respect to part of the variables

We obtain a sufficient condition using two Lyapunov functions for the Lagrange instability with respect to part of the variables. We also obtain another sufficient condition for the Lagrange instability with respect to part of the variables; this condition uses one Lyapunov function and is an analog of the Chetaev theorem on the instability with respect to part of the variables. If the considered part of the variables coincides with the set of all variables, then the sufficient criterion with one Lyapunov function is a corollary of the sufficient criterion with two Lyapunov functions.     

Queues with group arrivals and exhaustive service discipline

Queues with compound Poisson arrivals, phase-type service and exhaustive service discipline are studied. An algorithmic method is developed to compute the steady-state probability distribution of the number of customers in the system with unlimited or limited queue capacities. Examples with different model parameters are given to show the computational efficiency of the method. In the Appendix, the stochastic decomposition property for the queues with single arrivals and with exhaustive service discipline is extended to queues with group arrivals.     

Homeomorphs and amallamorphs of the Petersen graph

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family of P amallamorphs with 9 parameters, three families with 7 parameters, seven families with 6 parameters and many families with fewer parameters are obtained.     

Temps de vie des solutions d'un problème de Cauchy non linéaire

We solve the global Cauchy problem, with small initial data, in the space of the holomorphic functions with respect to t and Gevrey class with respect to x. We establish the existence and the stability of the solution to Cauchy problem with nul initial data without hyperbolicity hypothesis. In the stationary case, we give estimates of life span of the solutions with respect to size of the initial data.     

Linearly-implicit two-step methods and their implementation in Nordsieck form

We consider the Nordsieck representation of well-known linearly-implicit two-step methods in order to facilitate stepsize changes. These methods are treated as implicit schemes with one Newton step with a special predictor. A new predictor with better accuracy is discussed. Methods with 4–7 stages are tested and compared with RODAS. The numerical results show the potential of the Nordsieck implementation of the methods.