The PI index of product graphs

The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C₄ nanotubes and nanotori are computed.     

Necessary and sufficient conditions for linear suboptimality in constrained optimization

This article is devoted to the study of some extremality and optimality notions that are different from conventional concepts of optimal solutions to optimization-related problems. These notions reflect certain amounts of linear subextremality for set systems and linear suboptimality for feasible solutions to multiobjective and scalar optimization problems. In contrast to standard notions of optimality, it is possible to derive necessary and sufficient conditions for linear subextremality and suboptimality in general nonconvex settings, which is done in this article via robust generalized differential constructions of variational analysis in finite-dimensional and infinite-dimensional spaces.      

产品多方面差异下双寡头定位定价模型

建立在同类产品存在多方面差异条件下双寡头企业两阶段动态定位定价博弈模型,在市场中存在不同类型消费者时,求出了使企业利润最大化的子博弈精炼纳什均衡,并深入分析了消费者对两家企业平均偏好效用差(ΔU)和企业的运输成本率(t)对企业定位定价策略的影响.     

A Numerical Approach of the sentinel method for distributed parameter systems

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.      

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

Isoperimetric estimates in products

In a product M ₁ × M ₂ of Riemannian manifolds, the least perimeter required to enclose given volume among general regions is at least 1/√ 2 times that among regions of product form, assuming that the isoperimetric profiles of M ₁ and M ₂ are concave. This result sharpens earlier work of Grigor'yan, generalizes results of Bollobás and Leader and of Barthe, and yields a lower bound on the Cheeger isoperimetric constant of a product.     

Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

剩余格与FI代数的可嵌入性

给出剩余格可嵌入于全序剩余格的乘积的充要条件。还给出定义在格上的FI代数可嵌入于全序FI代数的乘积的充要条件。     

Numerical differentiation from a viewpoint of regularization theory

In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical differentiation regularized by the iterated Tikhonov method. These methods are shown to be effective for the differentiation of noisy functions, and the order-optimal convergence results for them are proved.

     

Positioning of new brands in an experiment

This paper deals with an experimental investigation of positioning new brands. For this purpose, a management game was carried out with students. The brands introduced in the cause of the game were analysed in respect to their positions in a two-dimensional feature space. We try to find out which of the two strategies, niche policy and imitation, is more frequently used in complex decision situations and if there is a difference in profits. Furthermore, we want to find out, whether differences of prices and advertising exist in our experiment depending on the positioning strategy used.