The Steinberg formula for orbit groups

The aim of this note is to give a direct proof of the fact that the Steinberg formula holds for the Vaserstein symbol and the universal weak Mennicke symbol. We also give an alternate proof of the fact that the Steinberg formula holds for the Vaserstein symbol.     

The linear flows in the space of Krichever–Lax matrices over an algebraic curve

Krichever (Commun Math Phys 229(2):229–269, 2002) invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation (Hitchin, Duke Math J 54(1):91–114, 1987). We study a necessary and sufficient condition for the linearity of flows on the space of Krichever–Lax matrices in a Lax representation in terms of cohomological classes using the similar technique and analysis from the work by Griffiths (Am J Math 107(6):1445–1484, 1985).      

Notes on particular symmetric polynomials with applications

This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the power sum symmetric polynomials. The applications includes a simple proof of El-Mikkawy conjecture in [M.E.A. El-Mikkawy, Appl. Math. Comput. 146 (2003) 759-769] and a very easy proof of the Newton-Girard formula. In addition, a generalization of Stirling numbers is obtained.     

以"N2分子的结构与性质"为例谈元素化学课堂教学的设计

以"N_2分子的结构与性质"为例说明元素化学课堂教学中的具体做法,教师引导学生复习化学键理论解释氮气分子结构与其化学性质之间的关系,组织学生以分组方式讨论光化学污染、工业合成氨等实际生产生活问题中的化学原理,由教师主讲化学模拟固氮的研究思路,而鼓励学生以报告形式展示热化学、电化学等氮活化科研课题的进展情况。     

Channeling chaotic transport in a wave-particle experiment

A numerical and experimental study of a control method aimed at channeling chaos by building barriers in phase space is performed on a paradigm for wave-particle interaction, i.e., a traveling wave tube. Control of chaotic diffusion is achieved by adding small apt modifications to the system with a low additional cost of energy. This modification is realized experimentally through additional waves with small amplitudes. Robustness of the method is investigated both numerically and experimentally. An erratum to this article is available at .     

Uniform Kazhdan constant for some families of linear groups

Let R be a ring generated by l elements with stable range r. Assume that the group EL_d(R) has Kazhdan constant ₀>0 for some dr+1. We prove that there exist (₀,l)>0 and , s.t. for every nd, EL_n(R) has a generating set of order k and a Kazhdan constant larger than . As a consequence, we obtain for where n3, a Kazhdan constant which is independent of n w.r.t. generating set of a fixed size.     

关于Smarandache 函数S(n)的一个猜想

对任意正整数n,著名的Smarandache 函数S(n)定义为最小的正整数m,使得n|m!.即就是S(n)=min{m∶n|m!,m∈N}.本文的主要目的是利用初等方法研究一个包含函数S(n)的猜想,并部分的得到解决.     

HeⅡ中元激发和色散关系的计算机模拟研究

液体HeⅡ的色散关系涉及到元激发的类型以及它们之间的相互作用,对液体4He物理性质的解释和实际应用都是至关重要的,因此从理论和实验两个方面展开对它的研究一直是液体4He研究的热点之一.本文采用计算机模拟的方法对液体HeⅡ的元激发和色散关系进行了比较深入的研究,给出了在一定温度范围内色散关系的统一解析表达,并在此基础上计算出自由能以及熵随温度的变化关系,模拟结果与实验数据吻合得很好.     

An Independence Result on Weak Second Order Bounded Arithmetic

We show that length initial submodels of S¹₂ can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division.     

Organotransition-metal chemistry: past development and future outlook

The course of the development of organometallic chemistry is reviewed from the author's personal viewpoint. The impact of the discoveries of ferrocene and the Ziegler catalyst on the later development of organotransition-metal chemistry is discussed. Through evolution of fundamental concepts, such as the insertion of olefins and carbon monoxide into metal—carbon bonds, oxidative addition and reductive elimination, and attack of nucleophiles on coordinated ligands, together with reactivities of carbene and metallacyclic complexes, various important processes have been developed. The diversity of transition-metal complexes and their unique reactivities not found in usual organic compounds warrant further developments in the various forefronts related to organometallic chemistry with almost limitless possibilities in applications as well as in fundamental studies.