MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.

Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

在局部地凸的 Hausdorff 拓扑的向量空格，有珍视集合的地图的向量优化的强烈有效的解决方案被讨论。第一，集合的强烈有效的点被介绍。第二，在下面将近 cone-subconvexlike 珍视集合的地图，为向量优化的 scalarization 的定理被获得。最后， optimality 强烈有效的答案调节因为有概括不平等限制和平等限制的向量优化被获得。

Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces

这份报纸在局部地凸的 Hausdorff 拓扑的向量空格为向量优化处理锥有效的解决方案集合的 connectedness。锥有效的答案集合的 connectedness 为在选择的一个紧缩的凸的集合上印射的连续一对一的 cone-quasiconvex 定义的 multiobjective 编程被证明。在证明期间，概括僵绳定理起一个关键作用。

Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.

An Efficient Accurate Direct Solution of Poisson's Equation for Computation of Meteorological Parameters

Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.

GLOBAL WEAK SOLUTIONS TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL

In this paper,we study a quantum kinetic-fluid model in a three-dimensional torus.This model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity.We establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form p(ρ)=ργ+pc(ρ),whereγ>1 is the adiabatic coefficient and pc(ρ)satisfies■for k≥4 and some constant c>0.

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM)system for quantum fluids with a linear density dependent viscosity in a 3D torus.By introducing the cold pressure Pc,we prove the global existence of weak solutions with the pressure P+Pc,where P=Aργwithγ≥1.Our main result extends the one in[13]on the quantum Navier-Stokes equations to the CNSLLM system.

Efficient Authentication Scheme for UAV-Assisted Mobile Edge Computing

Preserving privacy is imperative in the new unmanned aerial vehicle(UAV)-assisted mobile edge computing(MEC)architecture to ensure that sensitive information is protected and kept secure throughout the communication.Simultaneously,efficiency must be considered while developing such a privacy-preserving scheme because the devices involved in these architectures are resource constrained.This study proposes a lightweight and efficient authentication scheme for theUAV-assistedMECenvironment.The proposed scheme is a hardware-based password-less authentication mechanism that is based on the fact that temporal and memory-related efficiency can be significantly improved while maintaining the data security by adopting a hardwarebased solution with a simple implementation.The proposed scheme works in four stages:system initialization,EU registration,EU authentication,and session establishment.It is implemented as a single hardware chip comprising registers and XOR gates,and it can run the entire process in one clock cycle.Consequently,the proposed scheme has significantly higher efficiency in terms of runtime and memory consumption compared to other prevalent methods in the area.Simulations are conducted to evaluate the proposed authentication algorithm.The results show that the scheme has an average execution time of 0.986 ms and consumes average memory of 34 KB.The hardware execution time is approximately 0.39 ns,which is a significantly less than the prevalent schemes,whose execution times range in milliseconds.Furthermore,the security of the proposed scheme is examined,and it is resistant to brute-force attacks.Around 1.158×10^(77) trials are required to overcome the system’s security,which is not feasible using fastest available processors.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

弱光下锑基太阳电池的光谱响应与性能优化

锑基薄膜太阳电池因其制备方法简单,原材料丰富,光电性能稳定等优点而得到了快速发展。其中锑基吸光层材料(硫化锑、硫硒化锑、硒化锑)具有高吸收系数特点,因而在室内或者水下等弱光条件下具有相当大的应用潜力。通过构造两种衰减光谱以研究新型锑基薄膜太阳电池在弱光下的光电响应。首先通过厚度调节硒化锑太阳电池的吸光能力,发现当吸光层厚度较薄时,电池的光电转换效率存在较大差值;而当吸光层厚度过厚时,电池性能又因载流子复合的增大而降低。在吸光层厚度处于合适的0.4~1.2μm之间时,硒化锑太阳电池在长波衰减光谱和短波衰减光谱下都能获得高于16%的转换效率。然后通过硒含量调节锑基太阳电池的光谱吸收范围,发现长波衰减光谱下,锑基太阳电池的器件性能显著高于标准光谱,并且在20%~40%硒含量下能够获得最佳的转换效率。而在短波衰减光谱下,锑基太阳电池的最佳性能出现在硒含量为60%的情况下。因而在弱光条件下,锑基太阳电池的最佳硒含量需要通过具体的光谱特性确定。最后研究了两种衰减光谱下,硫化锑/硒化锑双结叠层太阳电池的光谱响应特性。发现在短波衰减光谱下,叠层太阳电池效率会随着总厚度的增加而增加。而在长波衰减光谱下,叠层太阳电池的最佳性能能够一直保持在较高水平。当叠层电池总厚度为2μm,且硫化锑顶电池厚度在0.5~1.2μm之间时,器件在两种衰减光谱下都能够实现光谱能量在两个子电池中的合理分配,使得叠层电池效率能够保持在20%以上。通过该研究对锑基太阳电池器件结构的合理设计,能够保证单结和双结器件在不同弱光条件下的高性能输出,为高环境适应性的锑基薄膜太阳电池的研发提供技术支持。