Calculation of second virial coefficients and gaseous viscosities of the refrigerants HFC-32 (CH2 F2), HFC-23 (CHF3), and HCFC-22 (CHC1F2)

The second virial coefficients of refrigerants HFC-32 (CH₂F₂), HFC-23 (CHF₃), and HCFC-22 (CHC1F₂) have been correlated on the bisis of site site model potential and have been compared with experimental results. The molecular interactions consisted of repulsion dispersion and electrostatic parts. From the site site potentials adjusted to the experimental second virial coefficients, spherically averaged potentials have been determined and a subsequent calculation of gaseous viscosity has been carried out. Agreement between measured and calculated values of second virial coellicients and gaseous viscosity is satisfactory. Calculated values of second virial coefficients and gaseous viscosity beyond available experimental data, therefore. can be assumed as a reliable extrapolation to lower and higher temperatures.     

Reactive path integral quantum simulations of molecules solvated in superfluid helium

A hybrid ab initio   path integral molecular dynamics/bosonic path integral Monte Carlo simulation method has been developed, implemented and tested, which allows for the reactive simulations of molecules, clusters or complexes solvated by superfluid ⁴${}^4$He. The simulation takes into account “on-the-fly” the electronic structure and thus the chemical reactivity of the solutes, in conjunction with the Bose–Einstein statistics, and thus the superfluid character of this peculiar solvent. This enables investigations into cryochemical reactions taking place in helium nanodroplets, such as those used in helium nanodroplet isolation (HENDI) spectroscopy.     

关于广义椭圆积分的几个性质

揭示了由广义椭圆积分定义的一些函数的单调性,从而获得若干不等式。这些结果有助于对广义Grtzsch环函数和Ramanujan模方程及其解φak(r)、φk(r)的研究,这些函数在拟共形理论、数论、几何学等领域中具有非常广泛的应用;同时,从这些结果中可以得到关于完全椭圆积分的一些新的性质。     

弹性力学问题中拟奇异积分的变换法

剖析了弹性力学问题中拟奇异积分产生的原因,提出了处理拟奇异积分的一种有效的变换法,成功地消除了拟奇异积分的拟奇异性,在不增加计算量的情况下大大改进了拟奇异积分的计算精度。     

磁弹性理论中的守恒定律和路径无关积分

守恒定律与路径无关积分是传统力学中的重要工具,在位错、断裂力学和其他缺陷理论中具有重要的应用价值。由于力场和磁场的共同作用,以及磁弹性材料本身的耦合性质,所以磁弹性体具有更为广泛的守恒定律和路径无关积分。文中通过定义4种不同的热力学函数,应用电磁场理论中的能量矩概念,建立了磁弹性理论中对偶形式的守恒定律,并由这些对偶形式的守恒定律得到了相应的路径无关积分。文中建立的守恒定律和路径无关积分,对研究磁弹性体中的缺陷理论将起到十分重要的作用。     

Computing integrals over polynomially defined regions and their boundaries in 2 and 3 dimensions

We use the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions and their boundaries in two and three dimensions. Using these results, we can implement the divergence theorem in three dimensions or the Green's theorems in two dimensions. These theorems are of central importance in the applications of multidimensional integration. They also provide a strong correctness test for the implementation of our results in a computer algebra system. The resulting software can solve many of the two and some of the three dimensional integration problems in vector calculus textbooks. The three dimensional results are being extended. The results in this paper are being included in an automated student assistant for vector calculus.     

Fuzzy posterior-probabilistic fusion

The paradigm of the permanence of updating ratios, which is a well-proven concept in experimental engineering approximation, has recently been utilized to construct a probabilistic fusion approach for combining knowledge from multiple sources. This ratio-based probabilistic fusion, however, assumes the equal contribution of attributes of diverse evidences. This paper introduces a new framework of a fuzzy probabilistic data fusion using the principles of the permanence of ratios paradigm, and the theories of fuzzy measures and fuzzy integrals. The fuzzy sub-fusion of the proposed approach allows an effective model for incorporating evidence importance and interaction.     

Recursive algorithm and accurate computation of dyadic Green’s functions for stratified uniaxial anisotropic media

A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.     

A symbolic summation approach to Feynman integral calculus

Given a Feynman parameter integral, depending on a single discrete variable N$N$ and a real parameter ε$\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in ε$\epsilon$. In a first step, the integrals are expressed by hypergeometric multi-sums by means of symbolic transformations. Given this sum format, we develop new summation tools to extract the first coefficients of its series expansion whenever they are expressible in terms of indefinite nested product–sum expressions. In particular, we enhance the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and we present new algorithms to find formal Laurent series solutions of a given recurrence relation.     

关于第二积分中值定理渐近性的一个注记

对于第二积分中值定理中的搴，本文给出并证明了比文献[3]更一般的结论，文献[3]的有关定理可以看成本文定理的直接推论．