An (n, k) binary self-orthogonal code is an (n, k) binary linear code C that is contained in its orthogonal complement C⊥. A self-orthogonal code C is self-dual if C = C⊥. Two codes, C1 and C2, are equivalent if and only if there exists a coordinate permutation of C1 that takes C1 into C2. The automorphism group of a code C is the set of all coordinate permutations of C that takes C into itself...

Earlier work has shown how to recognize handwritten characters by representing coordinate functions or integral invariants as truncated orthogonal series. The series basis functions are orthogonal polynomials defined by a Legendre-Sobolev inner product. It has been shown that the free parameter in the inner product, the “jet scale”, has an impact on recognition both using coordinate functions a...

The term “manifold of n dimensions” in this setting describes a set of n variables that independently take on the real values from −∞ to ∞ ([12], p 116). Motivated by this idea, one can assert that Euclidean geometry of E (Euclidean space) can be completely characterized by the invariants of the Euclidean group of transformations. As is well-known, this Lie group of (orientation-preserving) iso...

A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of th...

Integrability criterion for the Egorov hydrodynamic type systems is presented. The general solution by the generalized hodograph method is found. Examples are given. A description of three orthogonal curvilinear coordinate nets is discussed from the viewpoint of reciprocal transformations. In honour of Sergey Tsarev

This report discusses the ways in which Linear Algebra is applied to the manipulation of an object in three-space. This topic has a variety of useful applications, in fields ranging from Computer Animation to Aerospace Engineering. Specifically, the “object” considered in this paper is the Space Shuttle. The linear algebra topics necessary for this analysis include orthogonal coordinate systems...

One-way wave equations conveniently describe wave propagation in media with discontinuous and/or rapid variations in one direction, but with smooth and slow variations in the complementary transverse directions. In the past, reciprocity theorems have been developed in terms of one-way wave fields. The boundaries of the integration volumes and the variations of the medium parameters must adhere ...