Multidimensional wave digital lters yield robust algorithms for the computer simulation of certain distributed parameter systems described by partial di erential equations. Here, a multidimensional wave digital lter algorithm for the spacetime discretization of the physical laws of acoustics is discussed. Its implementation by state equations is presented. An example for the propagation of a so...

ADi erentially controlled monolithic LC-VCO along with a di erential charge pump are used to implement a di erential PLL for substrate noise immunity. The di erential VCO control is achieved with minimal increase in the power consumption and without sacri cing the tuning range. In a 0.5 m CMOS technology the measured VCO phase noise is -119dBc @1.0MHz and the tuning range is 26% of the 1.25GHz ...

In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

This report presents experimental results for new NAG Fortran Library software for the solution of large sparse symmetric linear systems of algebraic equations Preconditioned conjugate gradient methods introduced at Mark are compared against iterative and direct methods previously available in the library Test problems include discrete approximations to d elliptic partial di erential equations ...

Optimal control theory of partial di erential equations has emerged as a new way to attack problem of D atmospheric oceanic data assimilation problems These variational techniques attempt to achieve a best t between data observations and forecast model subject to some a priori criteria This review paper presents new trends for utilizing model adjoint equations for variational data assimilation ...

The stabilized march technique is extended to nonlinear two-point boundary value problems via a new Generalized Brent Method for systems of nonlinear algebraic equations. The resulting algorithms can be used to solve systems of nonlinear rst-order ordinary di erential equations under partially separated nonlinear boundary conditions economically. Numerical results which compare the nonlinear st...

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...

Once ReΨ and ImΨ are found from these two coupled di erential equations, the time-dependent probability density |Ψ| for a particle represented by the wave function Ψ can be calculated from |Ψ| = Ψ∗Ψ = (ReΨ) + (ImΨ), where the * denotes the complex conjugate. Our task, then, is to solve Equations (2) and (3) numerically, and this computational approach requires that the partial derivatives be ap...

To solve boundary value problems of stationary heat distribution in composite materials, one has to solve partial di¤erential equations with rapidly oscillating coe¢cients. These equations are in general impossible to solve numerically by standard methods. Instead, one wants to ...nd constant, effective conductivities and solve the corresponding boundary value problem to get an approximate solu...

This paper considers two related problems of state estimation and model validation for a class of uncertain linear systems. The main contribution of the paper is that it considers a general information structure which allows for discrete and continuous measurements as well as missing data. The results are given in terms of a recursive state estimator involving a jump Riccati di€erential equatio...