In this paper we construct sets of type (d1, d2) in the projective Hjelmslev plane. For computational purposes we restrict ourself to planes over Zps with p a prime and s > 1, but the method is described over general Galois rings. The existence of sets of type (d1, d2) is equivalent to the existence of a solution of a Diophantine system of linear equations. To construct these sets we prescribe ...

We prove that under certain spectral assumptions on the monodromy group, solutions of the Fuchsian system of linear equations on the Riemann sphere admit explicit global bounds on the number of their isolated zeros.

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the sy...

Given a cubic equation x1y1z1 + x2y2z2 + · · · + xnynzn = b over a finite field, it is necessary to determine the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the initial equation. The problem is solved for arbitrary size of the field. A covering with almost minimum complexity is constructed.

The aim of this paper is to prove the possibility of linearization of such equations by means of introduction of new variables. For n = 2 such a procedure is well known, when new variables are components of spinors and they are widely used in mathematical physics. For example, parametrization of Pythagoras threes a + b , a − b , 2ab may be cited as an example in number theory where two independ...

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods is that we can obtain solutions on a system comprising of continuous and/or discrete elements. After restricting the time scale to be R, these solutions are equivalent to those obtained using differential equatio...

Acceleration of the projection method for solving systems of linear equations " (1970). Retrospective Theses and Dissertations. Paper 4794. 1970 Signature was redacted for privacy.

A system is described which learns to compose sequences of operators into episodes for problem solving. The system incrementally learns when and why operators are applied. Episodes are segmented so that they are generalizable and reusable. The idea of *augmenting the instance language with higher level concepts is introduced. The technique of perturbation is described for discovering the essent...

The problem of representation and handling of constraints is here considered, mainly for picture processing purposes. A systematic specification and utilization of the available constraints could significantly reduce the amount of search in picture recognition. On the other hand, formally stated constraints can be embedded in the syntactic productions of picture languages. Only binary constrain...

In this paper we present a domain decomposition method for the solution of a linear equation as a direct two-step procedure (in contrast to iterativebased Schwarz and Aitken-Schwarz procedures): first, local solutions to the nonhomogeneous equation are calculated on overlapping domains, and second, connection functions, solutions to the homogeneous equation, are calculated which satisfy the Cou...