A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

We give an explicit construction of the factorizing twists for the Yangian Y (sl2) in evaluation representations (not necessarily finite-dimensional). The result is a universal expression for the factorizing twist that holds in all these representations. The method is general enough to recover the universal R-matrix of Y (sl2) up to its character in the form specialized to generic evaluation re...

The aim of this paper is to analyse the gain of the update algorithm associated to the recently proposed D-iteration: the D-iteration is a fluid diffusion based new iterative method. It exploits a simple intuitive decomposition of the product matrix-vector as elementary operations of fluid diffusion (forward scheme) associated to a new algebraic representation. We show through experimentations ...

The relationship between the Jordan forms of the matrix products AB and BA for some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1. We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.

The proposed PKC has two main advantages that will make it applicable to the real world. The first one is a decoding algorithm with an expected runtime of O(n) elementary operations. The second advantage is that the corresponding matrix A is of the form A = [A′ | I], where I is the identity matrix and A′ being completely random, in contrast to e.g. McEliece-Type systems (cf. [1]), which means t...

Abstract Highly-skilled engineers are needed to reprogram a welding-robot upon new variant or product introduction. This paper addresses the complexity of programming process by proposing and demonstrating theoretical concept “elementary welding operation” (EWO). The EWO is fundamental building block for robot-welding programs containing most data necessary generate program automatically. descr...

Idempotent mathematics is based on replacing the usual arithmetic operations with a new set of basic operations, that is on replacing numerical fields by idempotent semirings. Exotic semirings such as the max-plus algebra Rmax or concatenation semiring P(Σ) have been introduced in connection with various fields: graph theory, Markov decision processes, language theory, discrete event systems th...

In this paper, we present a framework for synthesizing I/O eecient out-of-core programs for block recursive algorithms, such as the fast Fourier transform (FFT) and block matrix transposition algorithms. Our framework uses an algebraic representation which is based on tensor products and other matrix operations. The programs are optimized for the striped Vitter and Shriver's two-level memory mo...

Many linear algebra problems over the ring ZZN of integers modulo N can be solved by transforming via elementary row operations an n ⇥ m input matrix A to Howell form H. The nonzero rows of H give a canonical set of generators for the submodule of (ZZN ) m generated by the rows of A. In this paper we present an algorithm to recover H together with an invertible transformation matrix P which sat...

A new sliced orthogonal nonlinear generalized (SONG) decomposition for image processing can be useful for image representation. We examine the use of this representation for two-class pattern recognition in the presence of noise. The SONG correlation is defined and expressed by means of a diagonal matrix representation. Common linear correlation, binary correlation and morphological correlation...