Complexity results for multicriterial and parametric network flows using a pathological graph of Zadeh

For two classes of network flow problems a worst-case analysis is given depending on the number of vertices of a pathological graph of Zadeh. Firstly, an exponential number of breakpoints in the optimal value function of the maximal flow problem in generalized networks with parametric capacities is demonstrated. Secondly, it is shown that the bicriterial min-cost flow has, in the worst case. an exponential number of efficient extreme point solutions in the objective space.

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Zusammenfassung Für zwei Klassen von Netzwerkflußproblemen wird eine worst-case Analyse in Abhängigkeit von der Anzahl der Knoten eines pathologischen Graphen von Zadeh vorgenommen. Demnach besitzt das Maximalflußproblem in verallgemeinerten Netzwerken mit parametrischen Kapazitätsbeschränkungen eine exponentielle Anzahl von Knickstellen in der Optimalwertfunktion. und kostenminimale Flüsse haben bereits für zwei Kriterien eine exponentielle Zahl von effizienten Eckpunkten im Bildbereich.

     

Pole-type singularities and the numerical conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly-connected domain Ω onto a circular annulus, and let $\text{H(z)=}\text{f′(z)}\text{f(z)}\text{?}\text{1}\text{z}$. In this paper we consider the problem of determining the main singularities of the function H in compl($\text{Ω∪?Ω}$). Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping.     

Epi-convergent discretization of the generalized Bolza problem in dynamic optimization

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general results in this direction. Research of B. S. Mordukhovich was partially supported by the USA National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the Australian Research Council under grant DP-0451168. Research of T. Pennanen was supported by the Finnish Academy of Sciences under contract No. 3385.     

应用双面电极的PLZT横向电光调制器电场的精确解

使用保角变换方法导出了横向电光调制器中双面电极结构的电场和电容的解析表达式，给出了用于ＰＬＺＴ电光陶瓷介质中二次电光效应分析的电场分布的物理图像。通过计算对比表明，双面电极结构电极边级区域由于过剩双折射引起的强度调制非均匀性较单面电极有所改善。     

g-非扩张型FUZZY映象序列的公共FUZZY混合不动点

提出fuzzy映象序列的公共fuzzy混合不动点的概念，研究了g-非扩张型fuzzy映象序列的公共fuzzy混合不动点定理，我们所得的定理改进和推广了近期相关的重要结果．     

A new method for a class of nonlinear variational inequalities with fuzzy mappings

In this paper, we construct a new iterative algorithm of solution for a new class of nonlinear variational inequalities with fuzzy mappings and give some convergence analysis of iterative sequences generated by algorithm.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Multivalued convexity and optimization: A unified approach to inequality and equality constraints

Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes.     

Generalized curve approach to elementary particles

The theory developed in Ref. 1 is applied in a simplified form to a relativistic one-particle universe, and boundary symmetry conditions are imposed. The existence, for the particle, of a series of resonance states and a series of gauge states is derived. For the proton and the electron, a selection of such states accounts for the elementary particles observed to date.Dedicated to L. CesariThis research was sponsored by the United States Army under Contracts Nos. DAAG29-75-C-0024 and DAAG29-80-C-0041.This work was carried out at IMPA while the first author was visiting there in November 1981.