关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

关于Logistic模型的倍周期收敛现象

运用实验和归纳的方法 ,讨论了如何利用 Mathematic数学软件观察 Logistic模型的倍周期收敛现象以及对初值的依赖性 ,并从理论上解释了倍周期收敛现象     

Stability of a class of transformations of distribution-valued processes and stochastic evolution equations

Stability of a class of linear transformations of distribution-valued stochastic processes is studied. Two types of applications to convergence of solutions of stochastic evolution equations are given. One of them, for the case of continuous limits, simplifies the tightness problem considerably due to a recent result of Aldous.Centro de Investigación y de Estudios Avanzados.     

Discrete groups actions and corresponding modules

We address the problem of interrelations between the properties of an action of a discrete group on a compact Hausdorff space and the algebraic and analytical properties of the module of all continuous functions over the algebra of invariant continuous functions . The present paper is a continuation of our joint paper with M. Frank and V. Manuilov. Here we prove some statements inverse to the ones obtained in that paper: we deduce properties of actions from properties of modules. In particular, it is proved that if for a uniformly continuous action the module is finitely generated projective over , then the cardinality of orbits of the action is finite and fixed. Sufficient conditions for existence of natural conditional expectations are obtained.

     

Evaluation of elastic modulus of cantilever beam by TA-ESPI

The paper proposes an evaluation technique for the elastic modulus of a cantilever beam by vibration analysis based on time average electronic speckle pattern interferometry (TA-ESPI) and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of a thin film are the Nano indentation test, Buldge test, Micro-tensile test, and so on. They each have strength and weakness in the preparation of the test specimen and the analysis of experimental results. ESPI is a type of laser speckle interferometry technique offering non-contact, high-resolution and whole-field measurement. The technique is a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI can be used to find the resonance frequency for each vibration mode shape. And the elastic modules of a test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique can be used to find the elastic modulus of a material requiring simple preparation process and analysis.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

Algebraic and Geometric Properties of Matrix Solutions of Nonlinear Wave Equations

We improve the construction of exact matrix solutions for nonlinear wave equations by using unitary anti-Hermitian and anticommuting matrices. We prove the theorem that constructs the matrix functions u _n satisfying the nonlinear wave equation for a set of special potentials. In this case, the graph of complex solution u ₁ has a soliton-like form with a finite number of coils. Exponential representation of matrix solutions u _n is associated with continuous rotations that can be used for describing intrinsic rotations and state changes of elementary particles. We also prove the theorem on the decomposition of continuous rotation (described by solution u ₂) onto three simultaneous rotations about coordinate vectors. Each of the three constructed matrix solutions u ₃ is also decomposed into the triplet of elementary matrix solutions.     

Explicit Exact Solutions for Some Nonlinear Partial Differential Equations with Nonlinear Terms of Any Order

In this paper, by introducing some appropriate transformation and with the help of symbolic computation, we study exact travelling wave solutions for the high-order modified Boussinesq equation, a single nonlinear reaction-diffusion equation and a generalized nonlinear Schrödinger equation with nonlinear terms of any order by use of the extended-tanh method. Thus, some new exact travelling-wave solutions, which contain kink-shaped solitons, bell-shaped solitons, periodic solutions, combined formal solitons, rational solutions and singular solitons for these equations, are obtained.