On the oscillation of solutions of first-order delay differential inequalities and equations

Oscillation criteria generalizing a series of earlier results are established for first-order linear delay differential inequalities and equations.     

Generalizing Hopf and Lax-Oleînik formulae via conjugate integral

Using the second Fenchel conjugate transform the conjugate integral sums and the conjugate integral are introduced. An estimate of speed of convergence of the sums to the integral is obtained. In the case of a convex integrant the conjugate integral reduces to the Riemannian one. It is proved that the Fenchel conjugate transform of the conjugate integral with variable upper limit provides a formula for the viscosity solution to a Hamilton-Jacobi equation in which the Hamiltonian depends both on time and the gradient of the unknown function. In the autonomous case the obtained formula coincides with Hopf's one. Two examples are considered in which an application of the conjugate integral allows to find viscosity solutions explicitly. It is shown how the extension of the Lax-Oleînik formula to the nonautonomous case may be obtained using the generalized Hopf formula.This paper was prepared while the author was a Lise Meitner fellow at the Institut für Mathematik, Karl-Franzens-Universität Graz, Austria     

Corrected sequential linear programming for sparse minimax optimization

We present a new algorithm for nonlinear minimax optimization which is well suited for large and sparse problems. The method is based on trust regions and sequential linear programming. On each iteration a linear minimax problem is solved for a basic step. If necessary, this is followed by the determination of a minimum norm corrective step based on a first-order Taylor approximation. No Hessian information needs to be stored. Global convergence is proved. This new method has been extensively tested and compared with other methods, including two well known codes for nonlinear programming. The numerical tests indicate that in many cases the new method can find the solution in just as few iterations as methods based on approximate second-order information. The tests also show that for some problems the corrective steps give much faster convergence than for similar methods which do not employ such steps.Research supported partly by The Nordic Council of Ministers, The Icelandic Science Council, The University of Iceland Research Fund and The Danish Science Research Council.     

电流镜及其在多值I2L电路开关级设计中的应用

运用开关信号理论和有界算术运算理论，对电流镜的多种性质进行了讨论，并系统研究了利用电流镜实现电流信号的各种算术运算，其中倍除运算属于初次提出，最后通过N进制半加电路和N值比较电路等两个设计实例介绍了电流镜技术在I^2L电路开关级设计中的应用。     

图的L(3,2,1)-标号

无向图G的L(3,2,1)-标号是指从顶点集V(G)到非负整数集Z*的一个映射,满足:对i=1,2,3,只要dG(x,y)=i,则f(x)-f(y)|≥4-i.若一个L(3,2,1)-标号中的所有像元素都不超过整数k,则称之为k-L(3,2,1)-标号.图G的L(3,2,1)-标号数,记作3λ(G),是使得图G存在k-L(3,2,1)-标号的最小整数k.文中给出了路、圈、树等特殊图的L(3,2,1)-标号数,并给出了一般图的L(3,2,1)-标号数的一个上界.     

Grothendieck space ideals and weak continuity of polynomials on locally convex spaces

We introduce the classes of locally convex spaces with the local Dunford-Pettis property and locally dual Schur spaces. We examine their properties and their relationship to other classes of locally convex spaces. In the class of locally convex spaces with the local Dunford-Pettis property all polynomials are weakly sequentially continuous whereas in the class of locally dual Schur spaces all polynomials are weakly continuous on bounded sets. Research supported by Science Foundation Ireland, Basic Research Grant 2004.     

基于CPLD的VXI总线接口的研制

文章以VXI总线开关矩阵模块为例，介绍了其于可编程逻辑器件的VXIbus寄存器基接口的开发过程。给出了选用ALTERA公司的可编程逻辑器件FLEX 10K10在MAXPLUSII环境下，结合VXIbus时序对接口逻辑电路进行波形仿真和时序分析的方法。     

Consistency,stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems

Summary. In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situations, strongly nonlinear elliptic problems. This formalism gives rise to a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods applied to elliptic nonlinear problems. This theory is illustrated with the example: in a two dimensional domain with Dirichlet boundary conditions. Received June 10, 1992 / Revised version received February 28, 1994     

Approximate unitary equivalence of completely distributive commutative subspace lattices

In this note, we classify completely distributive CSLs up to approximate unitary equivalence. Our proof uses a new characterization of complete distributivity and leads to a generalization of a result of Arveson on ordered group lattices. As consequences of our results, we obtain a similarity theorem for hyperreflexive, completely distributive CSLs and some new perturbation results.Partially supported by an NSERC grantResearch partially supported by NSF grant DMS-9204811.