脚本语言及其应用

介绍了脚本语言的基本组成、主要特征及其与系统编程语言的互补性,给出了使用该类语言开发应用程序的基本方法． 通过分析相关实例数据获得的结论是：脚本语言编程在减少编程工作量、提高组件重用率、缩短开发周期、降低开发费用等方面较系统编程语言具有明显的优势,并具有广阔的应用前景．     

From global to local bifurcations in a forced Taylor–Couette flow

The unfolding due to imperfections of a gluing bifurcation occurring in a periodically forced Taylor–Couette system is analyzed numerically. In the absence of imperfections, a temporal glide-reflection Z₂ symmetry exists, and two global bifurcations occur within a small region of parameter space: a heteroclinic bifurcation between two saddle two-tori and a gluing bifurcation of three-tori. As the imperfection parameter increase, these two global bifurcations collide, and all the global bifurcations become local (fold and Hopf bifurcations). This severely restricts the range of validity of the theoretical picture in the neighborhood of the gluing bifurcation considered, and has significant implications for the interpretation of experimental results. PACS 47.20.Ky, 47.20.Lz, 47.20.Ft     

Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.     

A nonlocal problem with integral gluing condition for a third-order loaded equation with parabolic-hyperbolic operator involving fractional derivatives

This work devoted to prove of uniqueness and existence of solution of the nonlocal problem with integral gluing condition for the loaded parabolic-hyperbolic type equation involving Caputo derivatives which loaded parts in Riemann-Liouville integral-differential operator. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations.     

Index computations in FJRW theory

We compute the index of the real Cauchy–Riemann operator defined in FJRW theory in case of the smooth metric.For the cylindrical metric,we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev spaces.     

The Gellerstedt problem for a parabolic-hyperbolic equation of the second kind

In this paper we consider the Gellerstedt problem for a parabolic-hyperbolic equation of the second kind. We prove the unique solvability of this problem by means of a new representation for a solution to the modified Cauchy problem in a generalized class R.     

Random perturbations of 1:1-resonant systems with SO(2) symmetry

^** Email: narayananramakrishnan{at}maxtor.com^*** Email: navam{at}uiuc.edu The near-resonant motion of trajectories of an integrable systemsubject to small dissipation and random perturbations is analysed.Under an appropriate change of time, we identify a reduced model.Our principal technique of dimensional reduction will be themethod of stochastic averaging for non-linear systems with smallnoise. A scheme to obtain the averaged motion of trajectoriesnear resonances is developed. The method of reduction is presentedusing the example of a two-degree-of-freedom Hamiltonian systemwith SO(2) symmetry subject to random perturbations. The averagedmotion of trajectories close to the 1:1-resonance surface isobtained and the effects of random perturbations on the near-resonantdynamics are analysed.     

Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains

This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation α~2Δu + u(1- u~2) = 0 in a smooth bounded domain Ω R~3, with Neumann boundary condition and α 0 a small parameter. These solutions have the property that as α→ 0, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting ?Ω orthogonally and that is non-degenerate respect to ?Ω. The authors provide explicit examples of surfaces to which the result applies.     

The completeness of the eigenfunctions of the Tricomi problem for the Lavrent'ev–Bitsadze equation with the Frankl gluing condition

The Tricomi and Tricomi–Neumann problems for the Lavrent'ev-Bitsadze equation. It is proved in this work that when the Frankl gluing condition is fulfilled, the system of eigenfunctions can either be: a Riesz basis; not complete; not minimal; complete and minimal, but not a basis.