Mathematical Introduction

Valter Moretti

Valter Moretti

Michael Helmling

Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman et al. At first celebrated mainly for its analytical powers, real-world applications of LP decoding are now within reach thanks to most recent research. This document gives an elaborate introduction into both mathematical optimization and coding theory as well as a review of the contributions by which these two areas have found common ground.

Ming‐Xing Luo

Pramode K. Verma, Mayssaa El Rifai, Kam Wai Clifford Chan

Anatoliy K. Prykarpatsky, Nikolai N. Bogolubov, Jolanta Golenia +1 more

Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.