Algebraic methods for the construction, design and analysis of series of convolutional codes using row or block structures of unit schemes are developed. The general methods lead to the construction and analysis of series and infinite series of types of convolutional codes and of codes with specific properties. Explicit examples are given and properties may be shown algebraically. Algebraic dec...

Let G be a connected, simply-connected, almost simple algebraic group of simplylaced type over C and let σ be a diagram automorphism of G. Let Gσ = ((G)) be the L-dual of the fixed point subgroup of σ on the L-dual of G. In this paper we relate the character of a finite dimensional irreducible representation of the disconnected algebraic group G〈σ〉 (generated by G and σ) on the connected compon...

We introduce three types of the four-component number systems which are constructed by joining the compΙex , binary and dual two-component numbers. We study their algebraic properties and rewrite the Euler and Moivre formułas for them. The most general mułticomponent number system joining the compalex, binary dual numbers is the eight-component number system, for which we determine the algebrai...

The algebraic operations of addition, intersection, elimination, and quotient are fundamental to computational algebraic geometry. This article describes how to perform these operations on homogeneous ideals using Macaulay dual spaces. If F is a polynomial system with finitely many solutions, these operations are used to compute the homogenization of the ideal generated by F which, in particula...

We construct the general algebraic curve of degree four solving the classical sigma model on R × S. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N = 4 SYM, also constructed here. We explicitly reproduce some particular solutions. Membre de l’Institut Universitaire de France

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

For weakly regular bent functions in odd characteristic the dual function is also bent. We analyse a recently introduced construction of nonweakly regular bent functions and show conditions under which their dual is bent as well. This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self-duality fo...

We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic der...

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governi...

If F is a full factorial design and D is a fraction of F , then for a givenmonomial ordering, the algebraic method gives a saturated polynomial basis for D which can be used for regression. Consider now an algebraic basis for the complementary fraction of D in F , built under the same monomial ordering. We show that the basis for the complementary fraction is the Alexander dual of the first bas...