Tensor roots of isomorphisms and weak limits of transformations

We prove that two transformations S and T are isomorphic if their Cartesian squares are isomorphic, under the assumption that the sequence of powers of T converges weakly to a polynomial.     

Generalized limits and representations of attraction sets in problems with constraints of asymptotic character

Doklady Mathematics -     

Equivalence and existence of weak Pareto optima for multiobjective optimization problems with cone constraints

In this work, a differentiable multiobjective optimization problem with generalized cone constraints is considered, and the equivalence of weak Pareto solutions for the problem and for its η-approximated problem is established under suitable conditions. Two existence theorems for weak Pareto solutions for this kind of multiobjective optimization problem are proved by using a Karush–Kuhn–Tucker type optimality condition and the F-KKM theorem.     

Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints

The relocation problem addressed in this paper is to determine a reconstruction sequence for a set of old buildings, under a limited budget, such that there is adequate temporary space to house the residents decanted during rehabilitation. It can be regarded as a resource-constrained scheduling problem where there is a set of jobs to be processed on a single machine. Each job demands a number of resources for processing and returns probably a different number of resources on its completion. Given a number of initial resources, the problem seeks to determine if there is a feasible sequence for the successful processing of all the jobs. Two generalizations of the relocation problem in the context of single machine scheduling with due date constraints are studied in this paper. The first problem is to minimize the weighted number of tardy jobs under a common due date. We show that it is NP-hard even when all the jobs have the same tardy weight and the same resource requirement. A dynamic programming algorithm with pseudo-polynomial computational time is proposed for the general case. In the second problem, the objective is to minimize the maximum tardiness when each job is associated with an individual due date. We prove that it is strongly NP-hard. We also propose a pseudo-polynomial time dynamic programming algorithm for the case where the number of possible due dates is predetermined.     

A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and supersolutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C⁰-space-like hypersurfaces in a Lorentzian manifold. As one application, a Lorentzian warped product splitting theorem is given. © 1998 John Wiley & Sons, Inc.     

Constructions of maximum distance separable symbol-pair codes using cyclic and constacyclic codes

Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible error-correction capability. Employing cyclic and constacyclic codes, we construct three new classes of MDS symbol-pair codes with minimum pair-distance five or six. Moreover, we find a necessary and sufficient condition which ensures a class of cyclic codes to be MDS symbol-pair codes. This condition is related to certain property of a special kind of linear fractional transformations. A detailed analysis on these linear fractional transformations leads to an algorithm, which produces many MDS symbol-pair codes with minimum pair-distance seven.     

Modeling and analyzing the performance of aviation security systems using baggage value performance measures

Aviation security is an important concern of national interest.Baggage screening security devices and operations at airportstations throughout the United States address this concern.Determining how and where to assign (deploy) such devices canbe quite challenging. Moreover, even after such systems arein place, it can be difficult to measure their effectiveness.Uncovered flight segment (UFS) and uncovered passenger segment(UPS) performance measures provide a useful framework for measuringthe effectiveness of a baggage screening security device deploymentto a given station. However, the optimization models associatedwith these measures do not consider baggage screening strategiesthat permit partial screening of flights. To allow for suchstrategies, as well as to identify baggage screening securitysystem models where the decision to screen each individual selecteebag is made individually (rather than collectively by flight),this paper introduces performance measures in which each selecteebag is assigned an individual value. In particular, the flightsegment baggage value (FSBV) assigns a value to each selecteebag based upon the proportion of the flight segment that thebag covers. The passenger segment baggage value (PSBV) assignsa value to each selectee bag based on the proportion of thepassenger segments that the bag covers. For each of these measures,an associated decision problem and integer programming modelare introduced. In addition, several results are presented detailingboth optimization techniques for the models associated witheach measure and the relationships between the baggage valuemeasures and other baggage screening security system measures.A real-world example using actual flight data from the officialairline guide is presented to illustrate an application of thesemodels and results.     

Optimization of laminated composite plates for maximum fundamental frequency using Elitist-Genetic algorithm and finite strip method

In the present paper, fundamental frequency optimization of symmetrically laminated composite plates is studied using the combination of Elitist-Genetic algorithm (E-GA) and finite strip method (FSM). The design variables are the number of layers, the fiber orientation angles, edge conditions and plate length/width ratios. The classical laminated plate theory is used to calculate the natural frequencies and the fitness function is computed with a semi-analytical finite strip method which has been developed on the basis of full energy methods. To improve the speed of the optimization process, the elitist strategy is used in the Genetic algorithm. The performance of the E-GA is also compared with the simple genetic algorithm and shows the good efficiency of the E-GA algorithm. A multi-objective optimization strategy for optimal stacking sequence of laminated box structure is also presented, with respect to the first natural frequency and critical buckling load, using the weighted summation method to demonstrate the effectiveness of the E-GA. Results are corroborated by comparing with other optimum solutions available in the literature, wherever possible.