Necessary Condition for a Strong Relative Minimum for Singular Optimal Control

A necessary condition is developed for a strong relative minimum for a first-order singular optimal control. It is shown that the strong condition is identical with the existing weak condition, namely, the generalized Legendre-Clebsch condition. It is conjectured that the strong condition for a second-order singular control will be the same as the corresponding weak condition.     

KKT系统结构条件数与条件数的比较

本文讨论Karush-Kuhn_Tucker(KKT)系统的条件数．首先利用单参数展开方法建立了Byers型不等式,然后讨论结构条件数与条件数的定性比较,结果表明,在极端情形,条件数与结构条件数之比可以任意大．     

A new constraint qualification condition

We introduce a new constraint qualification condition in mathematical programming which encompasses the Mangasarian-Fromovitz's condition and the constant rank condition of Janin. Contrarily to the Mangasarian-Fromovitz's condition, our condition is still satisfied when one translates equalities as double inequalities. It relies on the fact that linearization stability is easier to check with equalities than with inequalities.     

Characterizations by Automorphism Groups of Some Rank 3 Buildings, III. Moufang-Like Conditions

In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type Ã2 satisfying the root-Moufang condition are Bruhat–Tits buildings. Also, every rank 3 affine building satisfying the p-adic Moufang condition is a Bruhat-Tits building. We motivate the introduction of the new conditions by showing that all Bruhat– Tits Ã2-buildings satisfy the root-Moufang condition, and that the Ã2-buildings over a p-adic field also satisfy the p-adic Moufang condition. Another application of the p-adic Moufang condition is given in Part IV of this paper.     

用条件(Pw)刻画的幺半群

本文引入了条件（P_w）,讨论了条件（P_w）与条件（P）、条件（P_E）之间的关系,刻画了幺半群上S-系的平坦性.     

一类拟线性椭圆方程组非平凡解的存在性

首先证明了一个抽象的紧性定理,然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De．Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件,并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性,最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De．Figueiredo(2002)的条件弱．     

A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

We establish a sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. The sufficient condition relates to a sufficient condition for the weak stability of the fluid networks that correspond to the queueing networks under consideration. In addition, we establish a necessary condition for the network to have a continuous diffusion limit; the necessary condition is to require a reflection matrix (of dimension equal to the number of stations) to be completely-S. When applied to some examples, including generalized Jackson networks, single station multiclass queues, first-buffer-first-served re-entrant lines, a two-station Dai–Wang network and a three-station Dumas network, the sufficient condition coincides with the necessary condition.     

论连续体有限变形的位移协调条件

有限变形的协凋条件在文献中常以Riemann-Christoffel张量等于零表达.水文应用Cesaro方法和作者的非线性应变-转动张量分解定理证明上述条件仅是必要的,尚不充分保证位移场的单值性与连续;文中导出新的一般有限变形的位移协调条件.当应变与转动微小时,它化为Saint-Venant方程.     

关于模糊拟阵的独立子集套和独立集函数

本文的研究方法主要是将模糊拟阵问题转化为普通拟阵问题来研究的方法。本文首先建立独立子集套概念,并使用这个概念和独立集函数概念构建了闭模糊拟阵的充要条件和模糊独立集的充要条件;然后,本文仔细分析了模糊基的性质,找到了一个使用独立子集套和独立集函数来描述的模糊基的充要条件;最后,利用模糊基的这个充要条件提出并证明了闭正规模糊拟阵的充要条件。     

A criterion for checking if a convex set belongs to the union of a finite number of convex sets

A necessary and sufficient condition for the inclusion of a convex compact set in the union of a finite number of convex sets is proved. This condition obtained using the convex analysis techniques is a condition on the maximin of a given function. Using the dynamic programming, checking this condition is reduced to evaluating a set of functions and checking a condition for their values. The reduced form of the criterion is more convenient from the computational point of view.     

On the Palais–Smale condition

We present a new sufficient assumption weaker than the classical Ambrosetti–Rabinowitz condition which guarantees the boundedness of (PS) sequences. Moreover, we relax the standard subcritical polynomial growth condition ensuring the compactness of a bounded (PS) sequences. We also revise the Costa–Magalhaes condition [8] to obtain Cerami condition. As a consequence, some existence results derived by minimax methods were proved. Finally, we establish the existence of positive solution under the subcritical polynomial growth condition, while the strong superlinear condition is only required along an unbounded sequence. In other words, a certain degraded oscillation is allowed.     

A new necessary condition for optimality of systems with time delay

A new necessary condition for optimality of nonsingular control problems with time delay is developed. This condition accounts for the interaction of the different delays in the control vector. A necessary condition for optimality of singular control problems with time delay is also obtained as a corollary of the new condition.     

On global quadratic growth condition for min-max optimization problems with quadratic functions

Second-order sufficient condition and quadratic growth condition play important roles both in sensitivity and stability analysis and in numerical analysis for optimization problems. In this article, we concentrate on the global quadratic growth condition and study its relations with global second-order sufficient conditions for min-max optimization problems with quadratic functions. In general, the global second-order sufficient condition implies the global quadratic growth condition. In the case of two quadratic functions involved, we have the equivalence of the two conditions.     

Topological and metrical conditions for Collet-Eckmann unimodal maps

1. IntroductionColletEchazann maps (i.e. every ColletEckmann maP has positive lower LyaPunovexponent at the critical value) play a very important role in the study of one dimensionaldynamical systems. They have very good metricaI and ergodic properties[ll2], for example,every COllet-Eckmann map admits an absolutely cootinuous invariani m.asur.[1].In I3,4] Benedicks and Carleson proved that Collet-Eckmann maps are abundant in theso-caJled quadratic family which is a typical family of one …     

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.     

The strong open set condition in the random case

To describe some fractal properties of a self-similar set or measure, such as the Hausdorff dimension and the multifractal spectrum, it is useful that it satisfy the strong open set condition, which means there is an open set satisfying the open set condition and, additionally, a part of the self-similar set must meet the open set. It is known that in the non-random case the strong open set condition and the open set condition are equivalent. This paper treats the random case. If the open set condition is assumed, we show that there is a random open set satisfying the strong open set condition. Further, we give an application to multifractal analysis of the random self-similar fractal.

     

Comparison between exact thermal boundary condition and harmonic mean conductivity condition at the solid–fluid interface for finite thickness shrouded non-isothermal fin array

A numerical study is made comparing the exact thermal boundary condition and a harmonic mean conductivity condition at the solid–fluid interface for a finite thickness shrouded non-isothermal fin array. Results highlight that there exists a significant deviation of pressure drop across the length of the fin for the exact thermal boundary condition, which is as high as 20% as compared to that obtained using the harmonic mean conductivity condition. The exact thermal boundary condition forecasts relatively more non-isothermal fin as compared to a harmonic mean conductivity condition. The greater the fin spacing the larger the non-isothermal behavior of the fin and it also depends upon Grashof number as well as inlet fluid velocity. The larger the Grashof number the greater is the non-isothermal behavior of fin. The greater the inlet velocity, the larger is the non-isothermal behavior of fin. Bulk fluid temperature is over predicted by as much as 13% by the harmonic mean conductivity condition for larger fin spacing with highest Grashof number coupled with larger velocity. This deviation is only 6% for smaller fin spacing. Overall Nusselt number is over predicted for the harmonic mean conductivity condition as compared to exact thermal boundary condition. This over prediction is limited to about 8%.     

关于条件极值充分条件的重新推导和证明

李文学用拉格朗日函数提出求条件极值的充分条件,但他的证明却是错误的.本文不用拉格朗日函数,而是直接通过消去一个变量将条件极值转化成无条件极值,重新推导出充分性条件.推导的过程也是条件极值充分条件的证明过程.     

A Note on the Type of Local von Neumann Algebras in Quantum Field Theory over Curved Space-time

It is shown that there are relations between the Connes invariant for local v. Neumann algebras belonging to different curved space-times provided these local algebras are connected by a certain asymptotic condition. This asymptotic condition is implied by a scaling limit condition as well as by a condition of connectedness by large translations.     

BCQ条件和广义限制域最佳一致逼近的特征

研究了广义限制域的最佳一致逼近问题,在允许有有限个节点的情况下,引入次强内点条件的概念,并将优化理论中的BCQ条件等概念应用到本文所研究的问题中,刻划了次强内点条件、BCQ条件和最佳一致逼近的特征之间的关系.