On zero-degree stochastic geometric programs

The Mellin transform is used to encode randomness in the constraint and objective function coefficients using the substituted dual function. This enables one to obtain statistical moments and the probability distribution of the optimal objective valueZ*. Advantage is taken of the form of the dual function and the limiting property of the lognormal distribution to prove that the probability distribution ofZ* approximates the lognormal distribution, independent of the distribution of the parameters. This is of importance because those probability distributions are seldom known; even if they are, a derivation of the distribution ofZ* is apt to be elusive. Further, the larger the number of stochastic parameters in the geometric program, the more closely, in general, does the distribution ofZ* approximate the lognormal distribution. Illustrative examples are provided.Credit is due to Keith R. Weiss who developed the examples. The Office of Naval Research supported the work under Contract No. N000-14-75-C-0254.     

On the non-starlikeness of solutions to the starlike interior wake problem

We study examples of the starlike interior ``wake problem" for which no starlike solution exists relative to the natural star center of the problem. These examples show that the main result of D.E. Tepper in ``A mathematical model for a wake' (Michigan Math. J. 31 (1984), 161-165) is not correct.

     

Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_s, N_t and M_s, M_t, respectively, are given. The torques N_s, N_t (the angular momentums M_s, M_t), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.     

BRST Invariant Theory of a Generalized 1 + 1 Dimensional Nonlinear Sigma Model with Topological Term

We give a generalized Lagrangian density of 1 + 1 Dimensional O(3) nonlinear σ model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear σ model, give the example of not introducing the lost constraint = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter β originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field. PACS numbers: 11.10.Lm; 11.30.Ly     

The strong conical hull intersection property for convex programming

The strong conical hull intersection property (CHIP) is a geometric property of a collection of finitely many closed convex intersecting sets. This basic property, which was introduced by Deutsch et al. in 1997, is one of the central ingredients in the study of constrained interpolation and best approximation. In this paper we establish that the strong CHIP of intersecting sets of constraints is the key characterizing property for optimality and strong duality of convex programming problems. We first show that a sharpened strong CHIP is necessary and sufficient for a complete Lagrange multiplier characterization of optimality for the convex programming model problem where C is a closed convex subset of a Banach space X, S is a closed convex cone which does not necessarily have non-empty interior, Y is a Banach space, is a continuous convex function and g:X→Y is a continuous S-convex function. We also show that the strong CHIP completely characterizes the strong duality for partially finite convex programs, where Y is finite dimensional and g(x)=−Ax+b and S is a polyhedral convex cone. Global sufficient conditions which are strictly weaker than the Slater type conditions are given for the strong CHIP and for the sharpened strong CHIP. The author is grateful to the referees for their constructive comments and valuable suggestions which have contributed to the final preparation of the paper.     

度量空间上的切集在凸集上的表示

讨论了度量空间上切集的定义和一些性质．并且给出了一阶和二阶切集在凸集上的表示．     

A new construction for skew multivariate distributions

This paper considers a new approach to develop a very general class of skew multivariate distributions. The approach is based on a linear combination of an elliptically distributed random variable with a linear constraint. Using this approach two different classes of multivariate distributions are constructed based on original distribution. These new classes include different types of skew normal (type A and type B) and other skew elliptical distributions, exist in the literature. We also derive the moment generating function, marginal and conditional density of our proposed classes of distributions. Straightforward explanations are applied to demonstrate the relationships among previous approaches by others with our proposed class of skew distributions.     

Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts

Gerber-Shiu analysis with the generalized penalty function proposed by Cheung et al. (in press-a) is considered in the Sparre Andersen risk model with a K_n family distribution for the interclaim time. A defective renewal equation and its solution for the present Gerber-Shiu function are derived, and their forms are natural for analysis which jointly involves the time of ruin and the surplus immediately prior to ruin. The results are then used to find explicit expressions for various defective joint and marginal densities, including those involving the claim causing ruin and the last interclaim time before ruin. The case with mixed Erlang claim amounts is considered in some detail.