THE WEAK BENSON PROPER EFFICIENT SUBGRADIENT AND THE OPTIMALITY CONDITIONS OF SET-VALUED OPTIMIZATION

1 IntroductionIt is wel1 known that Hahn-Banach theo1.em is one of the basic theorems in functionaIanalysis. It has been extended to vector function, under efficiency by Shi[1] and Wang[2]in ordered vector spacest alld, under strong cone efficiency to set-valued maPping by Chenand Wang(3l. Receatly, Mengt4] and LiI5] has extended it to set--valued mapping with weakefficiency. Generally speaking, weak efficiency has too wide a scope for the decider to obtain afinal choice, so several prope…     

CHARACTERIZATIONS OF PROPER EFFICIENT SOLUTIONS IN TERMS OF SADDLE POINTS AND DUALITY

In this paper we characterize the proper efficient solution of a mul-tiobjective programming problem(P)in terms of the saddle point criterion of anew problem(S)and establish a pair of dual problems(S_α)and(D_α)in order todecide the proper efficient solution by the strong duality.We also give methodof characterization in terms of the saddle point criterion of(P).Finally,we provethat every efficient solution of the matrix linear programming problem is a properefficient solution.     

ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE

Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.     

PROPER EFFICIENT SOLUTIONS AND PROPER SADDLE POINTS

This paper offers a characterization method for the proper efficient solution ofthe multiobjective programming problem in terms of the proper saddle point and proves anecessary and sufficient condition for the equivalence between the proper efficient solutionand the associated proper saddle point by using the duality of a pair of problems.     

THE SYMMETRY GROUPS OF NONLINEARITY CRITERIA

It is already known that there are several nonlinearity criteria such as algebraic degree, nonlinearity,distance to linear structures, correlation immune, propagationcriterion, differential uniformity,which are used to check whether a cryptographic functionis weak or not. In this paper we will discuss these criteria from a valuation point of view,and consider the largest transformation group which leave a criterion invariant, which isnamed its symmetry group. It can serve as a way of comparing the stability of nonlinearitycriteria under the action of invertible transformations.     

Integration of spatial attractions between and within pixels for sub-pixel mapping

As a promising technique to enhance the spatial resolution of remote sensing imagery,sub-pixel mapping is processed based on the spatial dependence theory with the assumption that the land cover is spatially dependent both within pixels and between them.The spatial attraction is used as a tool to describe the dependence.First,the spatial attractions between pixels,subpixel/pixel spatial attraction model (SPSAM),are described by the modified SPSAM (MSPSAM) that estimates the attractions according to the distribution of sub-pixels within neighboring pixels.Then a mixed spatial attraction model (MSAM) for sub-pixel mapping is proposed that integrates the spatial attractions both within pixels and between them.According to the expression of the MSAM maximumising the spatial attraction,the genetic algorithm is employed to search the optimum solution and generate the sub-pixel mapping results.Experiments show that compared with SPSAM,MSPSAM and pixel swapping algorithm modified by initialization from SPSAM (MPS),MSAM can provide higher accuracy and more rational sub-pixel mapping results.     

The Class of the Generalized αk-Major Efficient Solutions for Multi-objective Programming

1 IntroductionConsider the following multi--objective programming:V -- minf(x) Cl)x e xwhere XcrR" is a constrained set, and f: R"-R"(m22) is the vector objective function.A non--dominated solution for (1 ) is usually called the Pareto efficient solution. HuL1jintroduced the concepts of major efficient solutions and major optimal solutions, thenpresented the concepts of a--major efficient so1utions and a--major optimal solutions. Ma[2Jgave a genera1ization of the major optimal solutions, a…     

Bidirectional Texture Mapping

Texture mapping is an important technique for high -quality image generation in computer graphics. In this paper, the shortcoming of the traditional texture mapping approaches is analysed and a general bidirectional texture mapping method is proposed. Based on the bidirectional mapping, an algorithm for mapping an image to an arbitrary polygon in 3D space is given.     

MAXIMUM PRINCIPLE FOR THE OPTIMAL CONTROL OF AN ABLATION-TRANSPIRATION COOLING SYSTEM

This paper is concerned with an optimal control problem of an ablationtranspiration cooling control system with Stefan-Signorini boundary condition. The existence of weak solution of the system is considered. The Dubovitskii and Milyutin approach is adopted in the investigation of the Pontryagin‘s maximum principle of the system. The optimality necessary condition is presented for the problem with fixed final horizon and phase constraints.     

CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE

In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.     

THE PROPER PARAMETRIZATION OF A SPECIAL CLASS OF RATIONAL PARAMETRIC EQUATIONS

We give a proper reparametrization theorem for a set of rational parametric equationswhich is proper for all but one of its parameters.We also give an algorithm to determine whether aset of rational parametric equations belongs to this class,and if it does,we reparametrize it such thatthe new parametric equations are proper.     

Extended research on software hybrid testing combining reliability and directed testing

The software reliability testing has many disadvantages in practice,such as high complexity of constructing operational profiles and poor fault detection efficiency.Oppositely,the directed testing with a high fault detection rate is incapable of estimating reliability quantificationally.To solve this problem,a hybrid testing combining reliability and directed testing as well as a reliability model based on the order statistic(OS) model were presented by Mitchell.An extended research on Mitchell’s work is proposed.Firstly,the most proper distribution of the fault’s failure rate which tends to be lognormal is suggested,and a detailed form of the OS model based on lognormal and the corresponding parameter estimation method are proposed,respectively.Secondly,an implementing framework for the hybrid testing is proposed.Finally,the hybrid testing and the OS model are applied on a real website system.The experimental results indicate:the hybrid testing has more efficient fault detection power and lower testing cost than the reliability testing;compared with three traditional software reliability growth models,the OS model has a best or pretty estimation or prediction power for each data set;and for the failure data set collected from hybrid testing,the OS model also achieves an acceptable estimation result.     

Dynamic WTA optimization model of air defense operation of warships'''' formation

1.INTRODUCTIONThe WTA(weapon-target allocation)problemof airdefense operation is to find a proper assignment ofweapons to targets with the objective of mini mizingthe expected operational loss of the warship forma-tion.It is an i mportant task for the commanders tomake a proper WTAto defend own warships.Opti-mization of WTA problemis the key content of airdefense operational command and control.Variousmethods for solving opti mization problems have beenreportedinthe Refs.[2]~[6]and ge…     

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

ON MANAGERIAL DECISION PROBLEM OF THE AUCTION SITES

This paper studies one managerial decision problem of the auction sites： how to combine penalties with commissions？ It is shown that when there exists secondary auction market, the auction whose penalty is a linear function of the seller＇s commission will be more efficient than the auction with only commissions but no penalties. It has also been proven that using this strategy can maximize the expected revenue for the seller, the auction site and their total expected revenues.     

Modular flexible “Tetris” microsatellite platform based on sandwich assembly mode

In this paper, a flexible modular “Tetris” microsatellite platform is studied to implement the rapid integration and assembly of microsatellites. The proposed microsatellite platform is fulfilled based on a sandwich assembly mode which consists of the isomorphic module structure and the standard mechanical-electric-data-thermal interfaces. The advantages of the sandwich assembly mode include flexible reconfiguration and efficient assembly. The prototype of the sandwich assembly mode is built for...     

Importance measure of system reliability upgrade for multi-state consecutive k-out-of-n systems

Importance measures in reliability systems are used to identify weak components in contributing to a proper function of the system. Traditional importance measures mainly concerned the changing value of the system reliability caused by the change of the reliability of the component, and seldom considered the joint effect of the probability distribution, improvement rate of the object component. This paper studies the rate of the system reliability upgrading with an improvement of the component reliability for the multi-state consecutive k-out-of-n system. To verify the multi-state consecutive k-out-of-n system reliability upgrading by improving one component based on its improvement rate, an increasing potential importance (IPI) and its physical meaning are described at first. Secondly, the relationship between the IPI and Birnbaum importance measures are discussed. And the IPI for some different improvement actions of the component is further discussed. Thirdly, the characteristics of the IPI are analyzed. Finally, an application to an oil pipeline system is given.     

Necessary conditions for efficient solution of vector optimization problems

In this paper,by using Ljusternik’s theorem and the open mapping theorem of convex process,the author gives necessary conditions for the efficient solution to the vector optimization problems without requiring that the ordering cone in the objective space has a nonempty interior.     

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.     

THE EQUILIBRIA OF THE SIZE STRUCTURED POPULATION MODEL

In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz‘s theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.