Limitations of the Clausius‐Mossotti function used in dielectrophoresis and electrical impedance studies of biomacromolecules

Dielectrophoresis (DEP) studies have progressed from the microscopic scale of cells and bacteria, through the mesoscale of virions to the molecular scale of DNA and proteins. The Clausius‐Mossotti function, based on macroscopic electrostatics, is invariably employed in the analyses of all these studies. The limitations of this practice are explored, with the conclusion that it should be abandoned for the DEP study of proteins and modified for native DNA. For macromolecular samples in general, a DEP theory that incorporates molecular‐scale interactions and the influence of permanent dipoles is more appropriate. Experimental ways to test these conclusions are proposed.     

Bilateral generating functions and operational methods

Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here.     

激光除冰研究

架空输送电线路因覆冰而导致的事故危害性很大,本文总结了目前国内外输电线路导线覆冰的现状。统计国内外探索出来的各种预防,融化,除冰等很多解决方案。通过研究和探讨,分析导线覆冰的传热和能量,运用了多种激光器进行激光熔(除)冰实验,比较研究二氧化碳激光器的除冰情况。以及提出激光熔冰的方法、研究方向和前景。     

Banach空间中优化问题的最优性条件

首先在Contingent切锥意义下界定了Banach空间中非空集合的伪切锥和伪凸性的概念，并讨论了相应的性质，然后针对可微优化问题，在广义凸性假设下，建立了最优性条件。     

Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

The Best Lower Bound for the Permanent of a Correlation Matrix of Rank Two

If 1≤k≤n, then Cor(n,k) denotes the set of all n×n real correlation matrices of rank not exceeding k. Grone and Pierce have shown that if A∈Cor (n, n-1), then per(A)≥n/(n-1). We show that if A∈Cor(n,2), then , and that this inequality is the best possible.     

Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

PuN基态分子势能函数与热力学函数的理论计算

在Pu的相对论有效原子实势近似和N原子 6 - 311G 全电子基函数下 ,用密度泛函B3LYP方法计算得到PuN分子基态X6Σ+ 的结构与势能函数、力常数与光谱数据 .同时计算得到PuN(g)分子在 2 98K时的标准生成热力学函数ΔfH0 、ΔS0 和ΔfG0 ,分别为 - 4 87.2 39kJ/mol、95 .345J/molK和 - 5 15 .6 6 6 1kJ/mol.     

Combinatorics of normal sequences of braids

Many natural counting problems arise in connection with the normal form of braids—and seem to have not been much considered so far. Here we solve some of them. One of the noteworthy points is that a number of different induction schemes appear. The key technical ingredient is an analysis of the normality condition in terms of permutations and their descents, in the vein of the Solomon algebra. As was perfectly summarized by a referee, the main result asserts that the size of the automaton involved in the automatic structure of Bn associated with the normal form can be lowered from n! to p(n), the number of partitions of n.     

Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives

In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method.