Coupled intervals in the discrete calculus of variations: necessity and sufficiency

In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: The nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [R. Hilscher, V. Zeidan, Comput. Math. Appl., to appear], where the right endpoint is fixed.     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Randomization helps to perform independent tasks reliably

This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Lifetime analysis of quasibound states in coupled quantum wells

A simple time-dependent model is presented to investigate lifetimes of the quasibound states in coupled quantum wells (CQWs). The transfer matrix approach is employed to discretize the conduction-band profile of the heterostructure and form a dispersion equation whose zeros correspond to the complex eigenenergies. Both the bound and quasibound states are extracted numerically in the complex plane by Newton's method. The lower and higher well subbands are found to have negative and positive energy shift, respectively, as following the no level crossing theorem. Besides, the decay rate of the quasibound state is approximately proportional to the absolute energy shift. The quasibound states, which have larger energy shift, have shorter lifetime and decay more quickly. Furthermore, the differences in lifetime between the quasibound states in CQWs can be easily realized as all the wave functions are specially adjusted to form the relative probability density distributions.     

The driving torque of a rotating levitated cylindrical permanent magnet above a superconductor

Due to the Meissner effect, a permanent magnet is levitated, when released above a high temperature superconductor. When there is an inhomogeneous temperature field around the magnet, the magnet might start to oscillate with increasing amplitude until it remains in a continuous rotation. A mathematical model for the described effect is presented which couples heat transfer and electromagnetic forces with the equation of motion, yielding to a multiphysics task. In a detailed analysis it is found, that the torque which drives the rotation of the magnet, is explicitly given in terms of Bessel functions and the Fourier coefficients of order zero and one of the temperature field of the surrounding air.     

基于偶联反应新极谱法测定痕量亚硝酸根的研究——Ⅱ.以苯酚为偶联试剂

本文研究了苯酚在氨性缓冲溶液中与NO_2~--磺胺重氮盐偶联反应的实验条件,建立了一个灵敏快速测定痕量NO_2~-的新方法。NO_2~-离子浓度在1.0×10~(-10)～4.8×10~(-7)g/ml范围内,与峰高呈良好的线性关系.4000倍量NO_3~-存在不干扰.     

An algebraic multigrid solver for Navier-Stokes problems

An efficient numerical method is presented for solving the equations of motion for viscous fluids. The equations are discretized on the basis of unstructured finite element meshes and then solved by direct iteration. Advective fluxes are temporarily fixed at each iteration to provide a linearized set of coupled equations which are then also solved by iteration using a fully implicit algebraic multigrid (AMG) scheme. A rapid convergence to machine accuracy is achieved that is almost mesh-independent. The scaling of computing time with mesh size is therefore close to the optimum.     

ICP－AES同时测定土壤和沉积物中全硼与其它微量及常量元素

本文阐述了用Ｈ３ＰＯ４、ＨＦ、ＨＮＯ３及ＨＣｌＯ４消化土壤及水系沉积物样品。其中磷酸的作用是避免在样品消化过程中硼的挥发损失。应用电感耦合等离子体发射光谱（简称ＩＣＰ－ＡＥＳ）同时测定样品中全硼及其它微量、常量元素的含量。该法具有高的准确度及精密度。方法快速、简便、适合土壤和沉积物的多元素测定。