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...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

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.

Why should wait for some days to get or receive the solution of large unsymmetric systems of linear equations series in microelectronics volume 17 book that you order? Why should you take it if you can get the faster one? You can find the same book that you order right here. This is it the book that you can receive directly after purchasing. This solution of large unsymmetric systems of linear ...

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...

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. ...

Mathematical norms are important cultural knowledge of mathematical activities. This paper reports an analysis of mathematical norms in ten consecutive lessons taught by an eighth-grade Japanese teacher. The lessons were located in the unit of simultaneous linear equations. The videotapes of the lessons, their transcripts, and the interview data were analyzed qualitatively. Several major mathem...