Modified Nosé–Hoover thermostat for solid state for constant temperature molecular dynamics simulation

Nosé–Hoover (NH) thermostat methods incorporated with molecular dynamics (MD) simulation have been widely used to simulate the instantaneous system temperature and feedback energy in a canonical ensemble. The method simply relates the kinetic energy to the system temperature via the particles’ momenta based on the ideal gas law. However, when used in a tightly bound system such as solids, the method may suffer from deriving a lower system temperature and potentially inducing early breaking of atomic bonds at relatively high temperature due to the neglect of the effect of the potential energy of atoms based on solid state physics.     

The exact distribution of indefinite quadratic forms in noncentral normal vectors

The exact density of the difference of two linear combinations of independent noncentral chi-square variables is obtained in terms of Whittaker's function and expressed in closed forms. Two distinct representations are required in order to cover all the possible cases. The corresponding expressions for the exact distribution function are also given.     

A hypergeometric approach,via linear forms involving logarithms,to criteria for irrationality of Euler’s constant

Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler’s constant γ. The proof is by reduction to known irrationality criteria for γ involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in 1, γ, and logarithms from Nesterenko-type series of rational functions. In the Appendix, S. Zlobin gives a change-of-variables proof that the series and the double integral are equal.      

Bilinear forms through the binary Bell polynomials,N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach

Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-Bäcklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and Bäcklund transformations are different from those in the existing literature. All of our results are dependent on the water-wave dispersive power.     

尼龙1012的Brill转变

作为一类重要的结晶性聚合物 ,尼龙在加热或冷却过程中的晶型转变 [1,2 ]一直为人们所关注 .其中对尼龙 66的晶型转变研究得最多 [3～ 6 ] .在加热过程中尼龙 66室温下三斜的α晶型转变为高温下的假六方晶型 ,尼龙 66的这一晶型转变称为 Brill转变 [3] .在变温 X射线衍射测试中可明显观察到 Brill转变 :室温下α晶型的两个强的衍射峰随温度升高逐渐靠近 ,并在某一温度下合并为一个峰 ,这一温度称为 Brill转变温度 .近年来研究表明 ,许多脂肪族的尼龙升温时均表现出 Brill转变 ,并且 Brill转变温度随尼龙结晶条件及其结构的不同而不同 [7…     

气相色谱–火焰光度法测定进口天然气中4种形态硫

建立气相色谱–火焰光度法测定进口液化天然气中4种形态硫的方法。探讨了色谱柱、进样口温度、分流比、柱流速、升温程序和FPD检测器等对测定结果的影响。在优化的实验条件下,评价了方法的可靠性。4种形态硫化物的质量浓度在10.0~200.0μg/L范围内,其对数与峰面积对数呈良好的线性关系,线性相关系数r在0.983 3~0.999 2之间,检出限为1.7~7.7μg/L,测定结果的相对标准偏差为0.56%~0.68%(n=5)。用该法测定天然气形态硫标准气体,测定值与标准值相比,相对误差为–1.6%~–1.2%。该方法具有较高的准确度,可应用于进口天然气中4种形态硫的分析。     

Limit algebras of differential forms in non-commutative geometry

Given a C*-normed algebra A which is either a Banach *-algebra or a Frechet *-algebra, we study the algebras Ω_∞ A and Ω_ε A obtained by taking respectively the projective limit and the inductive limit of Banach *-algebras obtained by completing the universal graded differential algebra Ω*A of abstract non-commutative differential forms over A. Various quantized integrals on Ω_∞ A induced by a K-cycle on A are considered. The GNS-representation of Ω_∞ A defined by a d-dimensional non-commutative volume integral on a d ⁺-summable K-cycle on A is realized as the representation induced by the left action of A on Ω*A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]).     

Calculus and Quantizations Over Hopf Algebras

In this paper we outline an approach to calculus over quasitriangular Hopf algebras. We construct braided differential operators and introduce a general notion of quantizations in monoidal categories. We discuss some applications to quantizations of differential operators.     

Splitting Patterns and Invariants of Quadratic Forms

Let φ be an anisotropic quadratic form over a field F of characteristic not 2. The splitting pattern of φ is defined to be the increasing sequence of nonnegative integers obtained by considering the Witt indices i_W(φ_k) of φ over K where K ranges over all field extensions of F. Restating earlier results by HURRELBRINK and REHMANN , we show how the index of the Clifford algebra of φ influences the splitting pattern. In the case where F is formally real, we investigate how the signatures of φ influence the splitting behaviour. This enables us to construct certain splitting patterns which have been known to exist, but now over much “simpler” fields like formally real global fields or ?(t). We also give a full classification of splitting patterns of forms of dimension less than or equal to 9 in terms of properties of the determinant and Clifford invariant. Partial results for splitting patterns in dimensions 10 and 11 are also provided. Finally, we consider two anisotropic forms φ and φ of the same dimension m with φ ? ? φ ∈ Iⁿ F and give some bounds on m depending on n which assure that they have the same splitting pattern.     

Normal Form in Filtered Lie Algebra Representations

This paper gives a setup for normal form theory and the computation of normal forms with emphasis on the dual character of the transformation generators and the objects to be transformed into normal form. Spectral sequence techniques will be used to define unique normal forms. Theoretical estimates are given for the rate of convergence in terms of the spectral sequence.Mathematics Subject Classifications (2000) primary: 34E, secondary: 18G40.