关于Witt代数基本子代数的一点注记

设g=W_1是特征p3的代数闭域k上的Witt代数.本文确定了g的极大基本子代数.进一步具体给出了最大维数的基本子代数的G共轭类,这里G是g的自同构群.从而证明了最大维数为(p-1)/2的基本子代数射影簇E((p-1)/2,g)是不可约的且是一维的.更进一步,证明了E(1,g)是不可约的,具有维数p-2,而E(2,g)是等维的,共有(p-3)/2个不可约分支,且每个不可约分支的维数是p-4.而当3≤r≤(p-3)/2时,E(r,g)是可约的.给出了E(r,g)(3≤r≤(p-3)/2)维数的一个下界.     

An RNA-Cleaving DNAzyme That Requires an Organic Solvent to Function

Engineering functional nucleic acids that are active under unusual conditions will not only reveal their hidden abilities but also lay the groundwork for pursuing them for unique applications. Although many DNAzymes have been derived to catalyze diverse chemical reactions in aqueous solutions, no prior study has been set up to purposely derive DNAzymes that require an organic solvent to function. Herein, we utilized in vitro selection to isolate RNA-cleaving DNAzymes from a random-sequence DNA pool that were “compelled” to accept 35 % dimethyl sulfoxide (DMSO) as a cosolvent, via counter selection in a purely aqueous solution followed by positive selection in the same solution containing 35 % DMSO. This experiment led to the discovery of a new DNAzyme that requires 35 % DMSO for its catalytic activity and exhibits drastically reduced activity without DMSO. This DNAzyme also requires divalent metal ions for catalysis, and its activity is enhanced by monovalent ions. A minimized, more efficient DNAzyme was also derived. This work demonstrates that highly functional, organic solvent-dependent DNAzymes can be isolated from random-sequence DNA libraries via forced in vitro selection, thus expanding the capability and potential utility of catalytic DNA.     

Applications of Michael's selection theorems to fixed point theory

Applying some of Ernest Michael's selection theorems, from recent fixed point theorems on u.s.c. multimaps, we deduce generalizations of the classical Bolzano theorem, several fixed point theorems on multimaps defined on almost convex sets, almost fixed point theorems, coincidence theorems, and collectively fixed point theorems. These results are related mainly to Michael maps, that is, l.s.c. multimaps having nonempty closed convex values.     

基于模糊需求的多产品供应商选择的多目标规划模型

由决策于环境的不确定性,供应商选择问题存在大量的模糊信息,传统的确定性规划模型已经不能够很好地处理此类问题。本文基于模糊需求量信息,对于多产品供应商问题建立了模糊多目标规划模型。同时考虑到各目标及约束的重要性程度不同的影响,通过引进适当的权重对多目标规划模型进行求解。文中结合实际算例验证模型的可行性和有效性。     

Variable Selection in Regression via Repeated Data Splitting

Abstract

A new algorithm—backward elimination via repeated data splitting (BERDS)—is proposed for variable selection in regression. Initially, the data are partitioned into two sets {E, V}, and an exhaustive backward elimination (BE) is performed in E. For each p value cutoff α used in BE, the corresponding fitted model from E is validated in V by computing the sum of squared deviations of observed from predicted values. This is repeated m times, and the α minimizing the sum of the m sums of squares is used as the cutoff in a final BE on the entire data set. BERDS is a modification of the algorithm BECV proposed by Thall, Simon, and Grier (1992). An extensive simulation study shows that, compared to BECV, BERDS has a smaller model error and higher probabilities of excluding noise variables, of selecting each of several uncorrelated true predictors, and of selecting exactly one of two or three highly correlated true predictors. BERDS is also superior to standard BE with cutoffs .05 or .10, and this superiority increases with the number of noise variables in the data and the degree of correlation among true predictors. An application is provided for illustration.     

On when small semiprime rings are slender

Various semiprime rings with less than 2^w elements are shown to be slender     

MODEL SELECTION METHOD BASED ON MAXIMAL INFORMATION COEFFICIENT OF RESIDUALS

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this ar- ticle, we give a new model selection criterion, based on the assumption that noise term in the model is independent with explanatory variables, of minimizing the association strength between regression residuals and the response, with fewer assumptions. Maximal Information Coe~cient （MIC）, a recently proposed dependence measure, captures a wide range of associ- ations, and gives almost the same score to different type of relationships with equal noise, so MIC is used to measure the association strength. Furthermore, partial maximal information coefficient （PMIC） is introduced to capture the association between two variables removing a third controlling random variable. In addition, the definition of general partial relationship is given.     

Selection rules for optical transition probabilities in superlattices

Based on numerical evaluations of the transition probabilities, and using true superlattice eigenfunctions derived from the theory of finite periodic systems, new superlattice selection rules are obtained. We show that the evaluation of the large number N   of the possible recombination transitions reduces by a factor of two. We also show that taking into account these selection rules, the theoretical calculations for specific blue emitting GaN?(In_xGa_1-xN?In_yGa_1-yN)ⁿ?GaN$\text{GaN}?({\text{In}}_x{\text{Ga}}_{1-x}\text{N}?{\text{In}}_y{\text{Ga}}_{1-y}\text{N}{)}^n?\text{GaN}$ superlattices agree with those reported by Nakamura et al. [1].     

Set-valued functions,Lebesgue extensions and saturated probability spaces

Recent advances in the theory of distributions of set-valued functions have been shaped by counterexamples which hinge on the non-existence of measurable selections with requisite properties. These examples, all based on the Lebesgue interval, and initially circumvented by Sun in the context of Loeb spaces, have now led Keisler and Sun (KS) to establish a comprehensive theory of the distributions of set-valued functions on saturated probability spaces (introduced by Hoover and Keisler). In contrast, we show that a countably-generated extension of the Lebesgue interval suffices for an explicit resolution of these examples; and furthermore, that it does not contradict the KS necessity results. We draw the fuller implications of our theorems for integration of set-valued functions, for Lyapunov's result on the range of vector measures and for the theory of large non-anonymous games.     

发动机余热利用蒸气动力循环的工质筛选

本文针对汽油发动机余热温度的特点,采用有机Rankine循环(Organic Rankine Cycle,ORC)回收发动机的排气和冷却水废热。利用计算机程序对循环中各主要状态点的热力参数和热力性能进行了理论计算,确定了最佳参数值,进行了有机工质的筛选。最终选定环戊烷和R113作为发动机余热回收利用蒸气动力循环的工质。