On the Existence of Positive Solutions for Hemivariational Inequalities Driven by the p-Laplacian

We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens.     

New proof of the Hörmander multiplier theorem on compact manifolds without boundary

On compact manifolds without boundary, the gradient estimates for unit band spectral projection operators are proved for a second order elliptic differential operator . A new proof of the Hörmander Multiplier Theorem (first proved by A. Seeger and C.D. Sogge in 1989) is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.

     

中厚扁壳断裂问题的特征根及特征函数

证明了含任意切口、任意切口边界的多材料中厚扁壳问题的特征根等于相应的平面切口问题和平板弯曲切口问题两部分的特征根组合。进而证明了中厚扁壳切口问题的特征根等于相应反平面切口问题和平面切口问题的组合。中厚扁壳切口问题的特征根及其对应的0级特征函数均可直接按相应的两类基本问题（反平面切口问题和平面切口问题）进行求解。     

基于截断区域特征函数展开法的金属管材电涡流检测线圈阻抗解析模型

针对金属管材电涡流检测线圈阻抗的理论计算问题,通过施加磁绝缘边界条件, 应用分离变量法和Cheng矩阵法建立了内穿式和外穿式线圈阻抗解析模型.因模型含有与虚宗量Bessel函数有关的积分, 通过研究函数特性,提出基于高斯积分算法的数值计算方法.以铜管管壁减薄为例进行仿真研究,并与Dodd模型、 有限元模型进行了对比.比较表明,三种方法的仿真结果基本一致,验证了所建立模型的正确性.与传统的Dodd模型、 有限元模型相比,所建立的模型具有效率高、精度调整方便等优点.     

厄米算符本征函数完备性的一般证明

从一组完备的本征函数开始,以表象原理为前提,建立一个唯象的公式,利用反证法证明了力学量算符的完备性,即这一组完备的本征函数可以投影到力学量算符的本征函数空间中.从而给出了力学量算符本征函数完备性的一般证明.     

Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectic eigenfunction expansion method.     

Bilinear Identities and Squared Eigenfunction Symmetries of the BCr-KP Hierarchy

The BC_r-KP hierarchy is an important sub hierarchy of the KP hierarchy, which includes the BKP and CKP hierarchies as the special cases. Some properties of the BC_r-KP hierarchy and its constrained case are investigated in this paper, including bilinear identities and squared eigenfunction symmetries. We firstly discuss the bilinear identities of the BC_r-KP hierarchy, and then generalize them into the constrained case. Next, we investigate the squared eigenfunction symmetries for the BC_r-KP hierarchy and its constrained case, and also the connections with the additional symmetries. It is found that the constrained BC_r-KP hierarchy can be defined by identifying the time flow with the squared eigenfunction symmetries.     

Exact Eigenfunctions of N-body System with Quadratic Pair Potential

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.     

Solutions of the SchrödingerEquation forPT-Symmetric Coupled Quintic Potentialsin Two Dimensions

This paper deals with the solutions of time independent Schrödinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.     

Non-hypergeometric Type of Polynomialsand Solutions of Schrödinger Equation with Position-Dependent Mass

Using the coordinate transformation method, we study the polynomial solutions of the Schrödinger equation with position-dependentmass (PDM). The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The issues related to normalization of the wavefunctions and Hermiticity of the Hamiltonian are also analyzed.