关于薛定谔算子的极点散射: 基于狄利克雷级数的视角

本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论.     

The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a,b and z

In a recent paper (Temme, 2021) new asymptotic expansions are given for the Kummer functions $M(a,b,z)$ and $U(a,b+1,z)$ for large positive values of $a$ and $b$, with $z$ fixed and special attention for the case $a～b$. In this paper we extend the approach and also accept large values of $z$. The new expansions are valid when at least one of the parameters $a$, $b$, or $z$ is large. We provide numerical tables to show the performance of the expansions.     

Counting master integrals: Integration by parts vs. differential reduction

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the standard integration-by-parts technique is found.     

Syntheses of 1,5-Benzothiazepines-Part XXXI: Syntheses and Antimicrobial Studies of 10-Substituted-7- (monochlorophenyl/dichlorophenyl)-6H-6a,7-dihydro-6-phenyl[1]benzopyrano[3,4-c]-[1,5]benzothiazepines

Abstract

Two flavindogenides, 3-(2-chlorobenzylidene)-flavanone and 3-(2,4-dichloro- benzylidene)-flavanone reacted with six 5-substituted-2-aminobenzenethiols, the substituents being fluoro, chloro, bromo, methyl, methoxyl, and ethoxyl, to give respective 12 new compounds, 10-substituted-7-(2-chlorophenyl/2,4-dichlorophenyl)- 6H-6a,7-dihydro-6-phenyl[1]benzopyrano[3,4?c][1,5]benzothiazepines (5a–l) in 60–70% yields. The products were characterized on the basis of microanalytical data for elements and IR, ¹ H, and ¹³ C NMR and mass spectral studies. All the synthesized compounds were evaluated for their antimicrobial activity against the bacteria,Escherichia coli and GFC,and the fungi,Aspergillus niger, Aspergillus flavus,and Curvularia lunata.     

Study on Dyeing Properties of Functional Acrylic Fiber

Anti‐mite acrylic fiber is a new type of functional fiber which incorporates a small amount of anti‐mite agent. Basic dye can be used in the dyeing of the functional acrylic fiber. Compared with the dyeing properties of conventional fibers, the dyeing properties of the functional acrylic fiber have new characteristics such as different dyeing temperature, time, amount of leveling agent and pH level due to the rough surface and larger size of micro‐channels in the functional fiber structure that helps basic dye molecules to diffuse into the fiber.     

Parametric inference for multiple repairable systems under dependent competing risks

The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd.