Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

The Ramanujan Journal - In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of...     

静高压下Al80Mn14Si6合金准晶相形成的研究

 本文首次研究了Al₈₀Mn₁₄Si₆合金在静高压下准晶相得形成。利用静高压熔态淬火方法，在压力2.8和3.1 GPa下得到淬火的Al-Mn-Si样品。电子和X射线衍射实验表明，高压淬火样品中含有准晶二十面体相和非晶相。X射线衍射实验还表明，高压淬火样品经350 ℃退火一小时基本上没有发生变化；而经过500 ℃退火一小时后，准晶相晶化为α-Al₇₃Si₁₀Mn₁₇相。另外，电子衍射实验表明，高压淬火后样品中还存在其它中间亚稳相。本文还讨论了静高压熔态淬火方法的适用性。     

ON THE ORDER PROPERTIES OF DIGITAL CURVES IN THE PAN-EUCLIDEAN GEOMETRY

How to increase the speed in drawing and recognizing curves has always been a major concern. From the Breshenham Algorithm and DDA Algorithm in the sixties to the double-step and quadruple-step line generation iu the eighties, curves were all dragon point by point. The algorithm in this paper fully utilizes machine commands to accelerate the generation of lines and curves. We introduce and prove for the first time characterization theorems of the segment code order of digital lines and curyes. These theorems give new methods in the recognition and the measure of smoothness of lines and curves.     

Constructions for Permutation Codes in Powerline Communications

A permutation array (or code) of length n and distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x, y ∈ Γ is at least d. One motivation for coding with permutations is powerline communication. After summarizing known results, it is shown here that certain families of polynomials over finite fields give rise to permutation arrays. Additionally, several new computational constructions are given, often making use of automorphism groups. Finally, a recursive construction for permutation arrays is presented, using and motivating the more general notion of codes with constant weight composition.     

A variant of the Reynolds operator

Let be a linearly reductive group over a field , and let be a -algebra with a rational action of . Given rational --modules and , we define for the induced -action on Hom a generalized Reynolds operator, which exists even if the action on Hom is not rational. Given an -module homomorphism , it produces, in a natural way, an -module homomorphism which is -equivariant. We use this generalized Reynolds operator to study properties of rational - modules. In particular, we prove that if is invariantly generated (i.e. ), then is a projective (resp. flat) -module provided that is a projective (resp. flat) -module. We also give a criterion whether an -projective (or -flat) rational --module is extended from an -module.

     

THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.     

Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of adaptive synchronization between two nearly identical chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on Lyapunov stability theory, a novel adaptive synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. The controller is simple and systemic, no parameters of the slave system are included in the controller, and, for some specific error systems, the controller can be simplified ulteriorly. New chaotic and a new hyper-chaotic systems with uncertain parameters are taken as the examples to show the effectiveness of the proposed adaptive synchronization method.     

激光喷丸改善TC6钛合金组织和力学性能

为了使激光冲击强化技术能较好地应用于TC6钛合金的发动机叶片,对TC6钛合金进行试验研究。通过X射线衍射仪、透射电子显微镜等测试技术分析了不同参数下TC6钛合金的微观组织变化,用显微硬度计和残余应力测试仪分别表征表层硬度和残余应力变化,并测试材料冲击后的振动高周疲劳性能。试验结果表明:激光冲击材料后表面组织得到明显细化,随着冲击次数的增加,先后出现了高密度位错、位错胞、亚晶和纳米晶。性能方面,表面硬度在冲击一次即可提高19%,硬度影响深度达到700 m;与此同时表面残余应力最高达到-608.5 MPa,在500 m深度上仍具有-100 MPa左右的应力存在。经三次冲击后,标准疲劳试片的疲劳极限提高近20%。     

ERM learning with unbounded sampling

The learning approach of empirical risk minimization (ERM) is taken for the regression problem in the least square framework. A standard assumption for the error analysis in the literature is the uniform boundedness of the output sampling process. In this paper we abandon this boundedness assumption and conduct error analysis for the ERM learning algorithm with unbounded sampling processes satisfying an increment condition for the moments of the output. The key novelty of our analysis is a covering number argument for estimating the sample error.     

Complete noncompact manifolds with harmonic curvature

Let (M ⁿ , g) be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that (M ⁿ , g) is a space form if it has sufficiently small L ^n/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for (M ⁿ , g) with positive scalar curvature.