We present hidden veri cation as a means to make the power of computational logic available to users of computer algebra systems while shielding them from its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and di erentiability for functions in this class. These are cal...

Multigrid methods are studied for the solution of linear systems resulting from the 9-point discretization of a general linear second-order elliptic partial di erential equation in two dimensions. The rate of convergence of standard multigrid methods often deteriorates when the coe cients in the di erential equation are discontinuous, or when dominating rst-order terms are present. These di cul...

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

We consider cyclic nearest neighbor systems of di erential delay equations, in which the coupling between neighbors possesses a monotonicity property. Using a discrete (integer-valued) Lyapunov function, we prove that the Poincar e-Bendixson theorem holds for such systems. We also obtain results on piecewise monotonicity and stability of periodic solutions of such systems.

We develop the non-di erentiable embedding theory of di erential operators and Lagrangian systems using a new operator on non-di erentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-di erentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. First, we extend the characteristics method to the non-di erentiabl...

In this paper conditional hidden Markov model (HMM) lters and conditional Kalman lters (KF) are coupled together to improve demodulation of di erential encoded signals in noisy fading channels. We present an indicator matrix representation for di erential encoded signals and the optimal HMM lter for demodulation. The lter requires O(N) calculations per time iteration, where N is the number of m...

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic 9 di$erential equations 3rst. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–di$usion 11 systems (non-Newtonian 3ltration systems) are establish...

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...

Consider the Cauchy problem for an ordinary diierential equation _ x = g(t; x); x(0) = x; t 2 0; T]: (1:1) When g is continuous, the local existence of solutions is provided by Peano's theorem. Several existence and uniqueness results are known also in the case of a discontinuous right hand side 7]. We recall here the classical theorem of Carath eodory 8]: Theorem A. Let g : 0; T] IR n 7 ! IR n...

We deene continual queries as a useful tool for monitoring of updated information. Continual queries are standing queries that monitor the source data and notify the users whenever new data matches the query. In addition to periodic refresh, continual queries include Epsilon Transaction concepts to allow users to specify query refresh based on the magnitude of updates. To support eecient proces...