BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

gi. IntroductionThis paper deals with solutionS of certain nonlinear wave equationS Of the formcorresponding to Antial conditionSwuersis the wave OPerstor.we are interested in showing the ~ up" Of solutions to (1.1)--(1.2). For that, wereIf ac ~ 1)(n ~ 1) > 2, global solutions of ~ equation subject to very general perturbationsof order p exist Provided the initial data are swhciently small (see I6] and references therein).We are also interested in esthaattw the take when "blow up" occurs. …     

用ABCD矩阵法计算四通式单光栅展宽器的展宽量

以激光束的ABCD传输矩阵理论及Collins积分公式为基础,计算简单实用的四通式单光栅展宽器的色散量,并求出相应展宽量。     

On the use of Laplace's equation for global predictions of internuclear separation and dissociation energy

Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed.     

Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞

Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map

Oscillatory properties of solutions of three-dimensional differential systems of neutral type

The purpose of this paper is to obtain oscillation criteria for the differential system

Properties of Standard n-Ideals of a Lattice

An n-ideal of a lattice L is a convex sublattice containing a fixed element n L and it is called standard if it is a standard element of the lattice of n-ideals I_n(L). In this paper we have shown that, for a neutral element n of a lattice L, the principal n-ideal a_n of a lattice L is a standard n-ideal if and only if a n is standard and a n is dual standard. We have also shown that if n is a neutral element and (n] and [n) are relatively complemented, then every homomorphism n-kernels of L is a standard n-ideal and every standard n-ideal is the n-kernel of precisely one congruence relation. Finally, we have shown that, for a relatively complemented lattice L with 0 and 1, C(L) is a Boolean algebra if and only if every standard n-ideal of L is a principal n-ideal.AMS Subject Classification (2000) 06B10 06B99 06C15     

On the Determination of Free Evolution in the Lax--Phillips Scattering Scheme for Second-Order Operator-Differential Equations

The paper presents some necessary and sufficient conditions on abstract positive self-adjoint operators L under which the operator-differential equation determines a free evolution in the Lax--Phillips scattering scheme.     

STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS

61. IntroductionLet (fi, F, P, {R}tZo) be a complete filtered probability space on which a standard onedimensional Brownian motion w(') is defined such that {R}tZo is the natural filtrationgenerated by w(.), augmented by all the p-null sets in i. We consider the following stateequationwhere T E T[0, TI, the set of all {R}tZo-stopping times taking values in [0, T], (E sigLlt (fi;IR"); A, B, C, D are matrix-valued {R}tZo-adapted bounded processes. In the above, u(.) EU[T, T]gLI(T, T…     

Numerical analysis of a quadratic matrix equation

The quadratic matrix equation AX²+ BX + C = 0in n x nmatricesarises in applications and is of intrinsic interest as oneof the simplest nonlinear matrix equations. We give a completecharacterization of solutions in terms of the generalized Schurdecomposition and describe and compare various numerical solutiontechniques. In particular, we give a thorough treatment offunctional iteration methods based on Bernoulli’s method.Other methods considered include Newton’s method with exact line searches, symbolic solution and continued fractions.We show that functional iteration applied to the quadraticmatrix equation can provide an efficient way to solve the associated quadratic eigenvalue problem (²A + B + C)x = 0.     

A Singular Equation of Length Four Over Groups

Let G be a group and t an unknown. In this paper we prove that the equation atbtct^–1dt^–1 = 1 (a,b,c,d G, a² 1, c² 1, bd 1) has a solution over G. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over G.2000 Mathematics Subject Classification: 20E06