In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1) -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applicat...

This paper is concerned with solving equations on xed and non-xed size bit-vector terms. We deene an equational transformation system for solving equations on terms where all sizes of bit-vectors and extraction positions are known. This transformation system suggests a generalization for dealing with bit-vectors of unknown size and unknown extraction positions. Both solvers adhere to the princi...

A stochastic optimal control strategy for partially observable nonlinear systems is proposed. The optimal control force consists of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dyn...

We present the atomic decomposition technique as a general method for reducing reasoning about cardinalities of sets, in the DL case the cardinalities of role llers, to equation solving problems. Then we apply the technique to a particular description logic with complex role terms and role hierarchies and a strong arithmetic component.

This paper describes LP*, a program that learns new techniques for solving equations by examining worked examples. Unlike most of the work in this field, e.g. (Neves, 1978), where the equations used have been very simple, LP uses complex equations, see below. LP can learn from one example, using concepts from the planning field. In order to be able to successfully use a new technique, LP learns...

It is proved that the construction and enumeration of the number of balanced symmetric functions over GF (p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF (p), and the lower bound provides best known results.

To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group G. If the Vessiot group G is solvable then the Cauchy problem can...

It has been proved that, among the polyominoes that tile the plane by translation, the so-called squares tile the plane in at most two distinct ways. In this paper, we focus on double squares, that is, the polyominoes that tile the plane in exactly two distinct ways. Our approach is based on solving equations on words, which allows to exhibit properties about their shape. Moreover, we describe ...

By utilizing the second and fourth order linear prediction errors, a novel estimator for a single noisy sinusoid is devised. The frequency estimate is obtained from a solving a cubic equation and a simple root selection procedure is provided. Asymptotical variance of the estimated frequency is derived and confirmed by computer simulations. It is demonstrated that the proposed estimator is super...