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.     

广义椭圆积分对参数的依赖性

给出了由广义椭圆积分κa(r)和εa(r)定义的某些函数依赖于参数a的分析性质.同时,揭示了广义椭圆积分与完全椭圆积分κ(r)和ε(r)的一些联系.     

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.     

The (strong) rainbow connection numbers of Cayley graphs on Abelian groups

A path in an edge-colored graph G, whose adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the minimum integer i for which there exists an i-edge-coloring of G such that every two distinct vertices of G are connected by a rainbow path. The strong rainbow connection number src(G) of G is the minimum integer i for which there exists an i-edge-coloring of G such that every two distinct vertices u and v of G are connected by a rainbow path of length d(u,v). In this paper, we give upper and lower bounds of the (strong) rainbow connection numbers of Cayley graphs on Abelian groups. Moreover, we determine the (strong) rainbow connection numbers of some special cases.     

Sensitivity analysis of nonlinear fractional order control systems with state delay

In this paper, we consider a class of nonlinear fractional order control system with delay in state variable. Existence and uniqueness of solution are shown by using method of steps. The sensitivity of the state and control with respect to the parameters of the system is shown. Finally, analytical results are substantiated by numerical examples.