Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantum-Chemical Evaluation of the Protolytic Properties of Thiophenols

The enthalpies and free energies of proton affinity (PA) were calculated by the PM3 method for 27 thiophenoxide anions. For thiophenols, linear correlation has been found between the PAs and the values of pK _a measured by different authors in aqueous acetone, aqueous ethanol, and methanol media. The dependences found permit one to predict a priori the protolytic properties of thiophenols. The differential effects of aqueous ethanol media with different ethanol contents on thiophenol acidity were evaluated based on quantum-chemical data.Original Russian Text Copyright © 2004 by A. N. Pankratov and A. V. Shalabai__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 800–806, September–October, 2004.     

全变差有界函数列的一致(R)可积性

给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 .     

New 6-Arylsulfonyl-1,2-benzoisothiazol-3(2H)-one 1,1-Dioxides Derived from Diphenyl Sulfone Monosulfonyl Chlorides

Various methods were studied for the oxidation of 2-methyl-5-(phenylsulfonyl)benzenesulfamide and its derivatives. The oxidation by sodium dichromate in sulfuric acid was found most efficient. The effects of temperature, concentration, reagent ratio, and time of the oxidation reaction on the yield of the desired product were investigated. Conditions were proposed for obtaining the desired product in yields up to 95%. A synthesis was developed for a series of new saccharin derivatives.     

双光子吸收效应对孤子和孤子对传输的影响

用分步傅立叶变换法求解含双光子吸收效应的光孤子NLS方程,研究了双光子吸收效应对一阶孤子和孤子对传输的影响,发现双光子吸收效应除对孤子产生等效损耗外,还影响了孤子对在传输中的相互作用。在特定的双光子吸收系数条件下双光子吸收效应可以使孤子对平行地向前传输。     

高剥离类镁等电子序列的磁偶极M1和电四极E2光谱跃迁理论研究

利用全相对论性多组态Dirac-Fock广义平均能级方法，系统地计算了类镁离子3s3p磁偶极Ml^3P2--^3P1和电四极E2 ^2P2--^3P0(Z=20-103)光谱跃迁的能级间隔、跃迁几率和振子强度。计算中考虑了原子核的有限体积效应，进行了高阶Breit修正和QED修正，所得到的能级间隔和最近的实验数据及理论计算值进行了比较。计算结果表明：高原子序数的高荷电离子的磁偶极矩M1和电四极矩E2跃迁几率和中性原子的电偶极E1的相当，在ICF和MCF高温激光等离子体中，磁偶极矩M1和电四极矩E2跃迁过程不容被忽视。     

Kinetics and mechanism of free-surface vaporization of zinc, cadmium and mercury oxides analyzed by the third-law method

On the basis of critical comparison of experimental and theoretical values of the E parameter and investigation of the retardation effect of oxygen on the evaporation rate of ZnO, CdO and HgO, it was concluded that the dissociative evaporation of ZnO and HgO proceeds with releasing of atomic oxygen (O) as a primary product of decomposition. By contrast, the mechanism of dissociative evaporation of CdO corresponds to the equilibrium reaction with releasing of molecular oxygen (O₂) as a primary product of decomposition. As was shown, this difference in mechanisms is not related with interatomic OO distances in these oxides. From the analysis of crystal structure for 12 different oxides, which evaporate with releasing of atomic oxygen, and for 13 compounds, which evaporate with releasing of molecular oxygen, it was revealed that the first mechanism is observed for all oxides with the cubic crystal structure. It was proposed that a decisive role in this difference belongs to a local symmetry in the position of O atoms.     

Software Cold Test Simulation of Coupled Cavity Slow-Wave Structure in Millimeter Wave TWT

In this paper, the software cold-test simulation method to obtain RF dispersion, interaction impedance by MAFIA software is discussed considering effect of the conducting barrel in the millimeter-wave TWT. The dispersion simulation result is obtained more consistent with experiment data than the method that ignoring effect of the conducting barrel. By changing the structure parameter, high frequency characteristic will be affected. The change relationship of high frequency characteristic with structure parameter is obtained. The different calculation methods of the interaction impedance are discussed. These results are received and are consistent with experiment data.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

Coercive boundary value problems for regular degenerate differential-operator equations

This study focuses on nonlocal boundary value problems (BVP) for degenerate elliptic differential-operator equations (DOE), that are defined in Banach-valued function spaces, where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients. Several conditions obtained, that guarantee the maximal L_p regularity and Fredholmness. These results are also applied to nonlocal BVP for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties.