李三系的Frattini子系

李三系是从黎曼对称空间产生的三元运算的代数系统,近年来备受数学家们的重视.针对李三系的Frattini子系和基本李三系的问题进行了研究,给出了Frattini子系和基本李三系的一些性质,并证明了李三系的非嵌入定理,同时得到了幂零李三系是基本李三系的一个充要条件.     

Small embedding characterizations for large cardinals

We show that many large cardinal notions can be characterized in terms of the existence of certain elementary embeddings between transitive set-sized structures, that map their critical point to the large cardinal in question. As an application, we use such embeddings to provide new proofs of results of Christoph Weiß on the consistency strength of certain generalized tree properties. These new proofs eliminate problems contained in the original proofs provided by Weiß.     

Enumeration of limit cycles in noncylindrical cellular automata

Recently a method has been developed by Jen to enumerate limit cycles in cellular automata (CA) with periodic boundary conditions. This involves operations on a connectivity matrix whose elements are related to the invariance of a site in a particular neighborhood to application of the CA rule. We extend this method to the case of fixed boundary conditions, of interest in simulations. In this case, translational invariance is lost, and the enumeration procedure is much more tedious than with periodic boundary conditions. We show examples for a fixed-point, a period-two, and a period-three enumeration in considerable detail, and give results-in agreement with simulations—for the number of fixed points and period-two cycles in selected two-state, nearest-neighbor CA rules.     

Some results on extending and sharpening the Weierstrass product inequalities

In this paper, we establish two extensions of Weierstrass's inequality involving symmetric functions by means of the theory of majorization, and give an interesting sharpness of Weierstrass's inequality by using the arithmetic-geometric mean inequality. Furthermore, we apply these results to improve a well-known inequality and deduce some new inequalities.     

Effective statistical weights of bound states in plasmas

Based on recent advances in the study of the statistics of interparticle distances and angles in plasmas, we develop an approach for the determination of the effective statistical weights of atomic (ionic) quantum states in ideal and nonideal plasmas. This approach allows one to account naturally for the effects of both the perturbation of the bound states by the neighboring ions and for the binding energy reduction due to the screening of the Coulomb interaction. We analyze the roles of tunneling and overbarrier escape of the optical electron from the parent ion potential well. The effects of neighbor ions and free electrons on these processes, and the simultaneous presence of several perturber ion species in the plasma are treated. We show that the present approach offers significantly more accurate effective-statistical-weight values in comparison to the existing theoretical treatments, and yields physical expressions for the empirical factors of the existing theories. Examples of calculations of effective statistical weights are given. The effects of the atomic (ionic) states collectivization on the collisional-radiative kinetics of dense plasmas are discussed. Received 10 August 2001     

The reaction of CH3 + O2: experimental determination of the rate coefficients for the product channels at high temperatures

The reaction of methyl radicals (CH₃) with molecular oxygen (O₂) has been investigated in high-temperature shock tube experiments. The overall rate coefficient, k₁ = k_1a + k_1b, and individual rate coefficients for the two high-temperature product channels, (1a) producing CH₃O + O and (1b) producing CH₂O + OH, were determined using ultra-lean mixtures of CH₃I and O₂ in Ar/He. Narrow-linewidth UV laser absorption at 306.7 nm was used to measure OH concentrations, for which the normalized rise time is sensitive to the overall rate coefficient k₁ but relatively insensitive to the branching ratio of the individual channels and to secondary reactions. Atomic resonance absorption spectroscopy measurements of O-atoms were used for a direct measurement of channel (1a). Through the combination of measurements using the two different diagnostics, rate coefficient expressions for both channels were determined. Over the temperature range 1590–2430 K, k_1a = 6.08 × 10⁷T^1.54 exp (−14005/T) cm³ mol⁻¹ s⁻¹ and k_1b = 68.6 T^2.86 exp (−4916/T) cm³ mol⁻¹ s⁻¹. The overall rate coefficient is in close agreement with a recent ab initio calculation and one other shock tube study, while comparison of k_1a and k_1b to these and other experimental studies yields mixed results. In contrast to one recent experimental study, reaction (1b) is found to be the dominant channel over the entire experimental temperature range.     

Elementary Operators on Standard Operator Algebras

We present a new simple proof of the structural result for elementary operators on standard operator algebras. Using the idea of this short proof we can characterize surjective maps between standard operator algebras having a certain multiplicativity-like property appearing in the abstract definition of elementary operators of length one. In particular, we show that such maps are automatically additive.     

基于Creator/Vega Prime的区域封锁作战系统

基于Multigen Creator/Vega Prime软件开发了子弹药封锁区域协同作战仿真系统;针对在作战区域实行封锁并打击封锁区域的敌方装备和有生力量进行了研究,实现延误敌方战机,减缓其兵力集结和部署,掌握战时主动的目的;主要通过围绕实体建模、模型驱动、碰撞检测、粒子特效等关键技术;综上所述,为实现对敌方飞机进行封锁区域协同打击的可视化仿真,重点研究了Creator和基于VC++的Vega Prime的视景仿真控制的过程和方法;研究结果表明,对子弹药区域封锁作战的实时仿真具有一定的参考价值。     

Reflections on the promise and complexity of mathematics coaching

If students are to develop mathematical proficiency, then mathematics teaching must both change and improve. In an effort to provide site-based professional development addressing the mathematical content and pedagogical demands that teachers encounter in reality of public schooling, many school districts are turning to elementary mathematics coaches. Knowledgeable coaches can have a significant positive impact on teachers, yet this study documents substantial variance in the amount of coaching delivered and in the nature of activity that coaches undertake within schools. Coaches are frequently responsive to the needs of individual teachers. If this support is primarily marked by shared teaching or provision of instructional materials, it may not transform either instruction or teacher knowledge. Similarly if coaches assume duties that primarily address an administrator’s needs, they will have less time to enhance a school’s mathematics program. Coaches need to engage teachers in fundamental dialogue about mathematical content, mathematical learning, and student understanding. It may be that this dialogue and the effectiveness of a coach’s work with individual teachers would benefit from a coach’s concurrent work with grade-level teams. When a coach leads a grade-level team through discussion of targeted goals and approaches, the coach may facilitate individual teacher learning while building collective learning. When coupled with the support of a principal, this partnership may foster instructional change across a school.     

燃烧反应机理构建的极小反应网络方法 氢氧燃烧

基于化学同时平衡原理, 提出复杂反应体系的极小反应网络方法(MRN), 在指定中间物种数目条件下, 构建反应步数最小的详细燃烧反应机理. 确定了8个物种的氢氧燃烧的6个独立反应, 对缺乏动力学参数的独立反应进行组合替代, 反应速率常数采用Arrhenius双参数形式. 采用构建的9步反应氢氧燃烧机理(MRN-C0)进行了点火延迟时间和层流火焰速度的模拟.