New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left quaternionic systems of linear equations have been obtained.

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...

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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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...

in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

Abstract   In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. M...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

Every year, people across the United States predict how the field of 65 teams will play in the Division I NCAA Men’s Basketball Tournament by filling out a tournament bracket for the postseason play. This article discusses two popular rating methods that are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. ...