Ekeland’s principle for vector equilibrium problems

In this paper, the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vector-valued function is considered, and some of its properties are presented. Via the vector Ekeland’s principle, existence results for vector equilibria are proved in both compact and noncompact domains.     

Cosmological Consequences of Scale-Related Comoving Masses for Cosmic Pressure, Mass, and Vacuum Energy Density

According to ideas of Mach, Whitrow, Dirac, or Hoyle, inertial masses of particles should not be a genuine, predetermined quantity; rather they should represent a relational quantity which by its value somehow reflects the deposition and constellation of all other objects in their cosmic environment. In this paper we want to pick up suggestions given by Thirring and by Hoyle of how, due to requirements of the equivalence of rotations and of general relativistic conformal scale invariance, the particle masses of cosmic objects should vary with the cosmic length scale. We study cosmological consequences of comoving cosmic masses which co-evolve by mass with the expansion of the universe. The vanishing of the covariant divergence of the cosmic energy-momentum tensor under the new prerequisite that matter density only falls off with the reciproke of the squared cosmic scale S(t) then leads to the astonishing result that cosmic pressuredoes not fall off adiabatically but rather falls off in a quasi-isothermal behaviour, varying with S(t) as matter density does. Hence, as a new cosmological fact, it arises that, even in the late phases of cosmic expansion, pressure cannot be neglected what concerns its gravitational action on the cosmic dynamics. We then show that under these conditions the cosmological equations can, however, only be solved if, in addition to matter, also pressure and energy density of the cosmic vacuum are included in the calculation. An unaccelerated expansion with a Hubble parameter falling off with S(t)⁻¹ is obtained for a vacuum energy density decay according to S(t)⁻² with a well-tuned proportion of matter and vacuum pressures. As it appears from these results, a universe with particle masses increasing with the cosmic sale S(t) is in fact physically conceivable in an energetically consistent manner, if vacuum energy at the expansion of the universe is converted into mass density of real matter with no net energy loss occuring. This universe in addition also happens to be an economical one which has and keeps a vanishing total energy.     

基于FPGA技术的通信原理课程实验教学研究

根据目前通信原理课程实验教学的现状,提出并利用FPGA及QuartusII软件设计通信原理课程实验系统,给出了实施方案.该系统结合了传统实验方法和计算机仿真技术的优点,在教学中效果明显提高.     

Quantum Dot and Antidot Infrared Photodetectors: Iterative Methods for Solving the Laplace Equation in Domains with Involved Geometry

We propose iteration methods for solving the Dirichlet problem in domains with involved geometry. Such problems arise in relation to the problem of optimizing quantum dot and antidot infrared detectors. We estimate the deviation of an approximate solution from the exact solution.     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

On the maximum principle for complete second-order elliptic operators in general domains

This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain.     

弹性梁静态方程的可解性

给出滑动支撑的弹性梁静态方程可解的一组两参数非共振条件.     

Nonparametric estimation and adaptive control in a class of finite Markov decision chains

We consider a class of Markov decision processes withfinite state and action spaces which, essentially, is determined by the following condition: The state space isirreducible under the action of any stationary policy. However, except by this restriction, the transition law iscompletely unknown to the controller. In this context, we find a set of policies under which thefrequency estimators of the transition law are strongly consistent and then, this result is applied to constructadaptive asymptotically discount-optimal policies.Dedicated to Professor Truman O. Lewis, on the occasion of his sixtieth birthdayThis research was supported in part by the Third World Academy of Sciences (TWAS) under Grant TWAS RG MP 898-152, and in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant A128CCOEO550 (MT-2).     

Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.