单调函数的列表判别法

本文讨论了单调函数和函数的最小列表,在此基础上提出单调函数、单调递增函数和单调递减函的列表判别方法,并举例说明了判别过程。     

正三角形上本征函数的对称性

由D3群一维表示,得到了正三角形上满足Dirichlet边界条件拉普拉斯算子的本征值和本征函数,并讨论了本征函数的对称性.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Fermilab top mass and modified Fritzsch mass matrices

Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context of latest data regardingm _t ^phys , |V _ub|, |V _cb|, |V _td| and |V _ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm _t ^phys in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V _cb| ≊0.040 and |V _ub/V_cb| = 0.08±0.02 and |V _td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement with other recent calculations.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

自反Banach空间中一类广义集值强非线性变分不等式问题

在自反Banach空间中引进并研究一类具有集值映射的广义强非线性变分不等式问题,并且证明了这类变分不等式解的存在性定理。结果修正、改进和推广了文献Cho Y.J等人的主要结果。     

Pseudo-monotone complementarity problems in Hilbert space

In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.This research was partially supported by the National Science Foundation Grant DMS-89-13089, Department of Energy Grant DE-FG03-87-ER-25028, and Office of Naval Research Grant N00014-89-J-1659. The authors would like to express their sincere thanks to Professor S. Schaible, School of Administration, University of California, Riverside, for his helpful suggestions and comments. They also thank the referees for their comments and suggestions that improved this paper substantially.     

THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.     

Extending hysteresis operators to spaces of piecewise continuous functions

We consider continuous-time hysteresis operators, defined to be causal and rate independent operators mapping input signals to output signals . We show how a hysteresis operator defined on the set of continuous piecewise monotone functions can be naturally extended to piecewise continuous piecewise monotone functions. We prove that the extension is also a hysteresis operator and that a number of important properties of the original operator are inherited by the extension. Moreover, we define the concept of a discrete-time hysteresis operator and we show that discretizing continuous-time hysteresis operators using standard sampling and hold operations leads to discrete-time hysteresis operators. We apply the concepts and results described above in the context of sampled-data feedback control of linear systems with input hysteresis.