Characteristic frequencies of bodies with thin spikes III. Frequency splitting

The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem and obtain closed formulas for the leading asymptotic terms. Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 494–502, April, 1997. Translated by V. E. Nazaikinskii     

poly(4,4′-oxybibenzoate): Polymerization,morphology, transitions,and crystal structures

4-Acetoxy 4′-carboxy biphenyl has been polymerized from solution, the bulk melt, and in constrained thin films, all below the melting point of the monomer as measured by differential scanning calorimetry (DSC). An isothermal sublimation–recrystallization–melting (and chemical change)–polymerization–crystallization process is proposed. From solution and in the thin films, single crystals consisting of ca. 100 Å thick lamellae are observed, with evidence for monomer addition–reaction on the end (top and bottom) surfaces. The bulk samples are fibrous, the “fibers” consisting of whisker-like single crystals. The polymer is highly heat and radiation (electron beam) resistant, with numerous successive electron diffraction (ED) patterns from the same crystal or sheared sample permitting comparison of the changes in ED patterns with transitions seen by DSC at ca. 350, 530, and 590°C. Phase I (a = 7.8, b = 5.5, c = 10.8 Å), a possible phase II (a = 15.6, b = 3.6 Å c = unknown), and a phase III (a = 9.0, b = 5.2 = √3a, c = 10.8 Å). Phases I and II are seen in samples polymerized at temperatures at and below 310°C; phase III is observed in samples polymerized at and above 350°C and in sheared samples. © 1993 John Wiley & Sons, Inc.     

Vorticity—velocity formulation in the computation of flows in multiconnected domains

The thermofluid dynamic fields in two-dimensional multiconnected domains are analysed by solving the Navier–Stokes equations with the Boussinesq approximation in the vorticity–velocity formulation. The need of an integral condition for the pressure to be single-valued on each independent irreducible loop, in analogy with the ω–Ψ formulation, is demonstrated. The field equations are discretized by a finite difference technique and solved at the steady state via an alternating direction implicit method of a scalar type. Two test cases at low Reynolds and Rayleigh numbers are considered: the multiconnected driven cavity and an annulus with isothermal walls and stationary or rotating inner cylinder.     

The Nested Substructures Method for Solving Large Finite-Element Systems as Applied to Thin-Walled Shells with High Ribs

A direct method is proposed to solve large systems of linear algebraic equations that arise in using the finite-element method. The method suggests to subdivide the initial structure into nonoverlapping, deeply nested substructures. The subdivision is performed automatically by the nested dissection method. Initially, the structure is subdivided into isolated finite elements. The solution process is step-by-step assembly of subsystems with simultaneous elimination of unknowns for completely assembled ones. The efficiency of the method is demonstrated by comparing it with the incomplete Cholesky conjugate-gradient method and the traditional envelope method as applied to a circular cylindrical shell with high ribs     

Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms

We consider the null controllability problem for the semilinear heat equation with nonlinearities involving gradient terms in an unbounded domain of ^N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain such that the uncontrolled region \ is bounded. Using Carleman inequalities, we prove first the null controllability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is ^C1 and globally Lipschitz, the system is null controllable.     

Random iterations of holomorphic maps in complex Banach spaces

Conditions guaranteeing the uniform convergence to constant maps of random iterations of holomorphic contractions on unbounded domains in complex Banach spaces are established.

     

On fundamental domains of arithmetic Fuchsian groups

Let be a totally real algebraic number field and an order in a quaternion algebra over . Assume that the group of units in with reduced norm equal to is embedded into as an arithmetic Fuchsian group. It is shown how Ford's algorithm can be effectively applied in order to determine a fundamental domain of as well as a complete system of generators of .

     

激光等离子体X射线源的应用

激光等离子体作为X射线光源，具有光源体积小、亮度高、脉冲短等优点。因此，激光等离子体X射线光源在时间分辨诊断测量等方面具有重要的应用。文章简单介绍了这种光源在软X射线投影光刻技术、医学成像、晶体研究以及惯性约束核聚变（ICF）研究等方面的应用。这四个方面分别属于信息，生物，材料和能源等四个科学领域。作者的目的在于让这些科研领域及其对应工业界的研究同行了解我们的工作，从而能够实现跨学科、跨领域的合作。     

On the unstable discrete spectrum of the linearized 2-D Euler equations in bounded domains

We investigate the behavior of the unstable discrete spectrum of the linearized 2-D Euler equation when the domain is smoothly perturbed. It is shown that when a self-adjoint Schrödinger-type operator undergoes a codimension-1 bifurcation it translates into a bifurcation in the linearized Euler equation associated with an instability either appearing or disappearing.We give sufficient conditions in order to observe smooth quadratic growth of the unstable eigencurves of the linearized Euler equation. The critical exponent is explicitly given as a function of the null-vector involved into the codimension-1 bifurcation using first and second-order moments of a Laplace transform.This analysis provides an explanation for the successive symmetry-breaking bifurcations observed in models of the mid-latitude oceans. An explicit example is also given.