Generalizations of Rodrigues type formulas for hypergeometric difference equations on nonuniform lattices

ABSTRACT

By building a second-order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second-order difference equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a ‘generalized’ Rodrigues formula is also established.     

Octonionic Yang–Mills instanton on quaternionic line bundle of Spin(7) holonomy

The total space of the spinor bundle on the four-dimensional sphere S⁴ is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang–Mills instanton on this eight-dimensional gravitational instanton. This is a higher dimensional generalization of (anti-) self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang–Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7). The existence of more general Spin(7) valued solutions can be seen by making an asymptotic expansion.     

A mathematical model of external electrostatic field of a special collector for electrospinning of nanofibers

This article focuses on the analysis of electrostatic field generated by a special collector consisting of two parallel cylindrical conductors used for electrospinning. Computed values of critical electrical potential obtained by an analytical model are compared with measurements. Here we show that the gap distance between the special collector and a spinning electrode, i.e., a syringe needle, has not substantial effect on the critical potential if the special collector distance from the syringe needle is higher than the gap distance between cylindrical conductors. The presented model is a good analytical approximation of electric field created by the used special collector.     

Modeling of relativistic plasmas with the Particle-In-Cell method

Standard methods employed in relativistic electromagnetic Particle-In-Cell codes are reviewed, as well as novel techniques that were introduced recently. Advances in the analysis and mitigation of the numerical Cherenkov instability are also presented with comparison between analytical theory and numerical experiments. The algorithmic and numerical analytic advances are expanding the range of applicability of the method in the ultra-relativistic regime in particular, where the numerical Cherenkov instability is the strongest without corrective measures.     

特种设备信息加密系统设计

对特种设备信息的加密系统进行设计,目前存在信息加密不彻底和采集的可靠性较低等问题。为此,提出特种设备加密系统设计方法,通过信息接口模块完成特种设备中信息的输入和输出,信息流程编辑模块负责开发设备中信息加密流程的组件,完成对特种设备中任务流程的检验,信息流程调度模块对信息流程任务进行调度管理。系统软件设计部分采用数据加密改进方法使信息源节点将要传输的多份信息数据分解成互不相关的信息数据,完成特种设备信息加密系统的设计。实验结果表明,所设计系统信息加密效果好、信息的完备性较高。     

Kähler manifolds with homothetic foliation by curves

The aim of this paper is to classify compact, simply connected Kähler manifolds which admit totally geodesic, holomorphic complex homothetic foliations by curves.     

Some integral inequalities for logarithmically convex functions

The main aim of the present note is to establish new Hadamard like integral inequalities involving log-convex function. We also prove some Hadamard-type inequalities, and applications to the special means are given.     

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar. Received 28 March 2000