Efficient characteristic set methods for computing solutions of a polynomial equation system in a finite field is proposed. We introduce the concept of proper triangular sets and prove that proper triangular sets are square-free in certain sense. We present an improved algorithm which can be used to reduce the zero set of an equation system in general form as the union of zero sets of proper tr...

Theories of cognitive control suggest that goal representation is both amodal and specialized. The GLAM-PS (Glamorgan Problem Solver) Cognitive Architecture has no specialised goal representation or goal handling. In addition, GLAM-PS, a distributed production system theory, does not use amodal representation (it is an embodied/grounded architecture). The current paper demonstrates that it is, ...

A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium is considered and the limiting equation for the field in the medium is derived. The impedance boundary conditions are imposed on the boundaries of small bod...

The subject of this study is the solution a fractional Bernoulli equation and chaotic system by using novel scheme for derivative comparison approximate exact solutions. It found that suggested method produces solutions are identical to solution. We can therefore generalize strategy different systems get more accurate results. think has been offered algorithm will be utilized in future construc...

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

One of the most fundamental problems in mathematics is to solve linear equations of the form Tf = g, where T is a linear transformation, g is known, and f is some unknown quantity. The simplest example of this comes from elementary linear algebra, which deals with solutions to matrix-vector equations of the form Ax = b. More generally, if V,W are vector spaces (or, in particular, Hilbert or Ban...