HOLOMORPHIC INTERGATED MILD C-EXISTENCE FAMILIES

0IntroductionIn[1],deLaubenfelsdefilledexpollelltiitllyboullded11olonlorphicC-existeuccfalllilies,holomorpllicC-senhgroupsand11olonlorpllicilltegratedselnigroups.Healsodiscussedtheirrelationships,alldgavesomeHille-YOsidatypecollditiollsforalloperatortogenerateallyofthesefamiliesofoperatorsin[1].ZllengalldLetdefinedexpollelltiallyboulldedllololllorphiconceilltegratedC-semigroups,andpreselltedageueratiolltlleorelllill[2J.Moregelleral71-tilllesintegratedmildC-existencefamilieswereintroducedby…     

Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System

A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration. The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.     

Families of stable manifolds for one-dimensional parabolic equations

We prove that to any invariant subset of the dynamical system generated by a one-dimensional quasilinear parabolic equation there corresponds an invariant family of stable manifolds of finite codimension. Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 11–23, July, 1996.     

Bahadur deficiency of likelihood ratio tests in exponential families

For many testing problems several different tests may have optimal exact Bahadur slope. The introduction of Bahadur deficiency provides further information about the performance of such tests. Roughly speaking a sequence of tests is deficient in the sense of Bahadur of order (h_n) at a fixed alternative θ if the additional number of observations necessary to obtain the same power as the optimal test at θ is of order (h_n) as the level of significance tends to zero. In this paper it is shown that in typical testing problems in multivariate exponential families the LR test is deficient in the sense of Bahadur of order (log n).     

The Unbalance of Set Systems

The unbalance of an intersecting family is defined as , where is the maximum degree of i.e. the maximum of over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most when n ≥ 6k ³ and we determine all families achieving this bound.     

A note on three-parameter families and generalized convex functions

The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363–371] is extended to the two-dimensional case. Using three-parameter families, we define generalized convex (midconvex, M-convex) functions and show some continuity properties of them.     

基于双光子光折变效应的非相干耦合灰光伏孤子族

为了研究开路条件下双光子光伏光折变材料中的灰光伏孤子族,建立了光伏孤子族的动态演化方程,给出了非相干耦合灰光伏孤子族的数值解.采用数值模拟的方法,求解孤子族的数值表达式.结果表明:这种孤子族是由多束偏振方向和波长都相同的互不相干光束耦合形成的.当孤子族只有两个分量时,灰光伏孤子族可以退化成灰-灰光伏孤子对;当孤子的灰度...     

Some properties and characterizations for generalized multivariate Pareto distributions

In this paper, several distributional properties and characterization theorems of the generalized multivariate Pareto distributions are studied. It is found that the multivariate Pareto distributions have many mixture properties. They are mixed either by geometric, Weibull, or exponential variables. The multivariate Pareto, MP^(k)(I), MP^(k)(II), and MP^(k)(IV) families have closure property under finite sample minima. The MP^(k)(III) family is closed under both geometric minima and geometric maxima. Through the geometric minima procedure, one characterization theorem for MP^(k)(III) distribution is developed. Moreover, the MP^(k)(III) distribution is proved as the limit multivariate distribution under repeated geometric minimization. Also, a characterization theorem for the homogeneous MP^(k)(IV) distribution via the weighted minima among the ordered coordinates is developed. Finally, the MP^(k)(II) family is shown to have the truncation invariant property.