The missing link in teachers’ knowledge about common fractions division

The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers’ knowledge concerning this issue. Nine teachers who study towards a M.Ed. degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers’ pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using constructivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply – multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.     

他罗利姆对截肢大鼠NO和H2S的活化作用

目的观察大鼠截肢创伤应激后重要血管舒缩因子的变化及他罗利姆(FK506)对其调控作用,为截肢术后引起的远隔器官损伤的干预治疗提供依据。方法建立大鼠左后肢截肢创伤模型,将雄性Wistar大鼠80只随机分为10组:正常对照组、截肢后1h、2h、4h、6h、12h、24h、48h、72h组、他罗利姆干预组。测定血浆H2S、AngⅡ、NO的含量,心、肺、肝、肾组织CSE活性。结果与对照组比较,截肢创伤后1h血浆AngⅡ含量明显升高,于6h达峰值(684.497±77.515)pmol/L(P<0.05),72h恢复至正常水平;血浆NO、H2S截肢创伤后4h明显降低,6h达最低,分别为(8.553±0.896)μmol/L(P<0.05)、(55.654±6.332)μmol/L(P<0.05),24h恢复正常值。他罗利姆干预后,血浆H2S、NO,心、肺、肝、肾组织CSE活性较创伤6h组明显升高(P<0.05),血浆AngⅡ含量无明显变化。结论大鼠截肢创伤应激后血管收缩作用增强,他罗利姆主要升高血管舒张因子NO和H2S,对AngⅡ无明显调控作用。     

数字移动通信系统工程中的几个问题

数字蜂窝移动通信系统技术设备先进、运行成本大。如何使系统在满足用户基本需求的前提下达到最好的经济效益,这一系统工程课题已摆在网络运行部门的面前。本文从系统的质量要求出发,提出系统综合质量的实现有赖于网络运行中对软/硬件及参数进行适时调整。     

Stereochemically consistent reaction mapping and identification of multiple reaction mechanisms through integer linear optimization

Reaction mappings are of fundamental importance to researchers studying the mechanisms of chemical reactions and analyzing biochemical pathways. We have developed an automated method based on integer linear optimization, ILP, to identify optimal reaction mappings that minimize the number of bond changes. An alternate objective function is also proposed that minimizes the number of bond order changes. In contrast to previous approaches, our method produces mappings that respect stereochemistry. We also show how to locate multiple reaction mappings efficiently and determine which of those mappings correspond to distinct reaction mechanisms by automatically detecting molecular symmetries. We demonstrate our techniques through a number of computational studies on the GRI-Mech, KEGG LIGAND, and BioPath databases. The computational studies indicate that 99% of the 8078 reactions tested can be addressed within 1 CPU hour. The proposed framework has been incorporated into the Web tool DREAM ( http://selene.princeton.edu/dream/ ), which is freely available to the scientific community.     

Computational characterization of zeolite porous networks: an automated approach

An automated method has been developed to fully characterize the three-dimensional structure of zeolite porous networks. The proposed optimization-based approach starts with the crystallographic coordinates of a structure and identifies all portals, channels, and cages in a unit cell, as well as their connectivity. We apply our algorithms to known zeolites, hypothetical zeolites, and zeolite-like structures and use the characterizations to calculate important quantities such as pore size distribution, accessible volume, surface area, and largest cavity and pore limiting diameters. We aggregate this data over many framework types to gain insights about zeolite selectivity. Finally, we develop a continuous-time Markov chain model to estimate the probability of occupancy of adsorption sites throughout the porous network. ZEOMICS, an online database of structure characterizations and web tool for the automated approach is freely available to the scientific community (http://helios.princeton.edu/zeomics/).     

Solvent tuning of a conical intersection: direct experimental verification of a theoretical prediction

We report an ultrafast study of a merocyanine molecule, whose fluorescence lifetime was tuned by changing the solvent's polarity. A recent theoretical prediction that the fluorescence lifetime is considerably shortened upon lowering the polarity of the solvent, due to tuning of the conical intersection properties, is fully confirmed (Xu et al. J. Phys. Chem. A 2009, 113, 9779-9791). This constitutes a direct measurement of a previously predicted tunable property of a conical intersection.     

Cyclopropenyllithiums as a new source of 1,1-bismetalated cyclopropyl derivatives

The allylmetalation of functionalised cyclopropenyllithium derivatives leads to the unique formation of 1,1-bismetalated cyclopropyl species that react selectively with different electrophiles.     

公用无绳电话系统的技术及其发展策略

本文回顾了公用无绳电话系统从模拟到数字的演变过程，分析和比较了ＣＴ２、ＤＥＣＴ、ＰＨＳ和ＰＡＣＳ等几各数字无绳电话技术，进而提出了我国发展无绳电话的策略。     

EXACT BOUNDARY CONTROLLABILITY OF 1-D NONLINEAR SCHRDINGER EQUATION

In this paper,the boundary control problem of a distributed parameter system described by the Schrdinger equation posed on finite intervalα≤x≤β: iyt yxx |y|~2y=0, y(α,t)=h_`1(t),y(β,t)=h_2(t)for t>0(S) is considered.It is shown that by choosing appropriate control inputs(h_j),(j=1,2)one can always guide the system(S)from a given initial stateφ∈H~s(α,β),(s∈R)to a terminal stateΨ∈H~s(α,β),in the time period[0,T].The exact boundary controllability is obtained by considering a related initial value control problem of Schrdinger equation posed on the whole line R.The discovered smoothing properties of Schrdinger equation have played important roles in our approach;this may be the first step to prove the results on boundary controllability of(semi-linear)nonlinear Schrdinger equation.     

Stiefel–Whitney invariants for bilinear forms

We examine potential extensions of the Stiefel–Whitney invariants from quadratic forms to bilinear forms which are not necessarily symmetric. We show that as long as the symbolic nature of the invariants is maintained, some natural extensions carry only low dimensional information. In particular, the generic invariant on upper triangular matrices is equivalent to the dimension and determinant. Along the process, we show that every non-alternating matrix is congruent to an upper triangular matrix, and prove a version of Witt?s Chain Lemma for upper-triangular bases. (The classical lemma holds for orthogonal bases.)