We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion

A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean 4-space. The physically relevant solutions were the ones with finite action—the so-called &apos

This paper proposes a mechanism for equation-based congestion control for unicast traffic. Most best-effort traffic in the current Internet is well-served by the dominant transport protocol, TCP. However, traffic such as best-effort unicast streaming multimedia could find use for a TCP

An iterative method is given for solving Ax ~ffi b and minU Ax- b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmation--least squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and

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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]

Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryptographic systems, which minimize the need for secure key distribution channels and supply the equivalent of a written signature. This paper

A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method