A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.

We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of {1, ..., n} containing no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form ax + by = cz with a + b 6= c.

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A certain decomposition of the coefficient matrix of the Fully Fuzzy Linear System (FFLS) is given to obtain a simple method for solving these systems. The new method can solve FFLS in a smaller computing process. Moreover, the method will be useful when the system is in the rectangular form. The method is described in detail and is illustrated by solving some examples. 2010 AMS Classification:...

Proceedings of the 29th Conference on Decision and Control Honolulu, Dec. 1990 Abstract In this paper, we study the general system of linear equations in the algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the algebra in the sense that every nondegenerate system of li...

This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear, half-linear, super-half-linear, and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included.

We will denote intervals and interval vectors by Latin letters a, b, e . . . . (with or without index), interval matrices by capital Latin letters A, B, C , . . . Real vectors and matrices will be denoted by Latin letters with lower dots q, .b,e.,..., A., B., C . , . . . Endpoints of intervals and of interval vectors will be denoted by a_, ~ (lower and upper endpoims, respectively), real n u m ...