A version of Hill's lemma for Cosserat continuum

On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.

On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

Hill’s方程的Magnus积分

基于Magnus积分方法,针对Hamilton系统下卫星编队绕飞轨道误差问题,对二阶Hill’s方程进行了降阶变换和数值模拟。通过引进新状态变量将二阶动力学系统表示为一阶动力学系统,从而保留了原二阶动力学系统的典则性质。采用Magnus积分方法求解一阶系统方程,与传统四阶Runge-Kutta方法相比,该方法计算简单,精度高。文中采用该方法分析了两种绕飞半径的轨道误差问题,分析结果表明该方法具有良好的精度和稳定性。

梯度增强Cosserat连续体的广义Hill定理

基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元(RVE)。依据此广义Hill定理,对梯度增强Cosserat连续体表征元提出了满足Hill-Mandel能量等价条件和平均场理论的强形式及弱形式边界条件。

New versions of Barbalat's lemma with applications

This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.

基于广义Hille引理及扰动想法之下的一种非参数回归方法

近几十年来,非参数回归的研究方兴未艾.针对Fan(1992,1993,2003)局部核函数法的2个缺陷,该文基于广Hille引理及扰动思想提出了一种新的回归方法,新的回归估计量具有逐点一致性及最优渐进均方误差.该文还利用CV技术及ISE标准对该回归估计的光滑参数进行最优筛选,模拟结果表明:与Fan(1992,1993,2003)中的方法相比,在大样本下该文所提出回归方法有更佳估计效果.

The Extension of Robinson's Sequential Lemma and Its Application

A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.

A Darcy-Law Based Model for Heat and Moisture Transfer in a Hill Cave

A hill can be regarded as an environmental carrier of heat.Water,rocks and the internal moisture naturally pre-sent in such environment constitute a natural heat accumulator.In the present study,the heat and moisture trans-fer characteristics in a representative hill cave have been simulated via a method relying on the Darcy’s law.The simulations have been conducted for both steady and unsteady conditions to discern the influence of permeability and geometric parameters on the thermal and moisture transfer processes.The reliability of the simulation has been verified through comparison of the numerical results with the annual observation data.As revealed by the numericalfindings,the internal temperature of the hill accumulator is proportional to the permeability,outside surface temperature,overground height,underground constant temperature layer depth,and underground tem-perature of the hill,and it is inversely proportional to the horizontal size of the hill.Moreover,in the considered case,the order of magnitude of the permeability of the hill is contained in the range 10-15–10-13,and displays a certain sensitivity to the rainwater seepage.

A microstructure-based analysis of cyclic plasticity of pearlitic steels with Hill's self-consistent scheme incorporating general anisotropic Eshelby tensor

A pearlitic steel is composed of numerous pearlitic colonies with random orientations, and each colony consists of many parallel lamellas of ferrite and cementite. The constitutive behavior of this kind of materials may involve both inherent anisotropy and plastic deformation induced anisotropy. A description of the cyclic plasticity for this kind of dual-phase materials is proposed by use of a microstructure-based constitutive model for a pearlitic colony, and the Hill＇s self-consistent scheme incorporating anisotropic Eshelby tensor for ellipsoidal inclusions. The corresponding numerical algorithm is developed. The responses of pearlitic steel BS 11 and single-phase hard-drawn copper subjected to asymmetrically cyclic loading are analyzed. The analytical results agree very well with experimental ones. Compared with the results using isotropic Eshelby tensor, it is shown that the isotropic approximation can provide acceptable overall responses in a much simpler way.

Constant Power Model in Arm Rotation—A New Approach to Hill’s Equation

The purpose of this study was to further develop the constant power model of a previous study and to provide the final solution of Hill’s force-velocity equation. Forearm and whole arm rotations of three different subjects were performed downwards (elbow and shoulder extension) and upwards (elbow and shoulder flexion) with maximum velocity. These arm rotations were recorded with a special camera system and the theoretically derived model of constant maximum power was fitted to the experimentally measured data. The moment of inertia of the arm sectors was calculated using immersion technique for determining accurate values of friction coefficients of elbow and whole arm rotations. The experiments of the present study verified the conclusions of a previous study in which theoretically derived equation with constant maximum power was in agreement with experimentally measured results. The results of the present study were compared with the mechanics of Hill’s model and a further development of Hill’s force-velocity relationship was derived: Hill’s model was transformed into a constant maximum power model consisting of three different components of power. It was concluded that there are three different states of motion: 1) the state of low speed, maximal acceleration without external load which applies to the hypothesis of constant moment;2) the state of high speed, maximal power without external load which applies to the hypothesis of constant power and 3) the state of maximal power with external load which applies to Hill’s equation. This is a new approach to Hill’s equation.

基于遗传粒子群算法的超混沌S盒设计

针对目前基于混沌系统所构造的S盒难以拥有良好密码学性能的问题,提出一种基于超混沌系统及遗传粒子群优化算法的S盒设计方案.在一维混沌映射基础上,引入正余弦函数以及指数因子,构造一个二维超混沌系统,从系统分叉图、相图、Lyapunov指数图进行性能分析,该混沌系统在参数范围内有着连续的超混沌区间,混沌行为复杂.通过改变混沌系统的初值、参数以及迭代次数可以动态生成S盒,随后结合粒子群优化算法和遗传算法提出一种针对S盒的遗传粒子群优化算法,将混沌系统生成的S盒作为初始种群,利用粒子群算法改进遗传算法中的交叉操作,同时结合爬山算法提出一种新的变异策略.为验证所生成S盒性能,对S盒的双射特性、非线性度、严格雪崩准则、差分均匀性及输出比特间独立性进行仿真测试,仿真结果表明:所提出的优化算法能够生成非线性度、差分均匀性、输出比特间独立性方面表现良好的S盒.

Wiener's lemma:localization and various approaches

Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.

Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma

We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem with the well-known from combinatorial topology Sperner’s lemma. We also notice that our geometric approach is strongly based on the associated vector field.

Arnold Tongues for Discrete Hill’s Equation

In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called Discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.

Fuzzy Zorn’s lemma with applications

We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn’s lemma,we got the following results:(1)Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2)Every nonzero ring contained a fuzzy maximal ideal.(3)Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma,we proved the fuzzy Tychonoff Theorem.

Symbols In HEMINGWAY'S “Hills Like White Elephants” Story commentary

HEMINGWAY’s story,“Hills Like White Elephants”,is about lovingrelationships between an American man and a girl.As lovers,they are in-timate,with the girl in the state of pregnancy.The story is told from the objective point of view.It takes place duringa 40-minute wait between trains.What lies behind them is indicated by thelabels on their bags.What lies ahead of them implies entire force and dir-ection of the story.It is at the station that a decision will be made

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

Small Modular Solutions to Fermat’s Last Theorem

The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.

Identities on q-Harmonic Numbers

With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.