Erasure Techniques in MRD codes

This book is organized into six chapters. The first chapter introduces the basic algebraic structures essential to make this book a self contained one. Algebraic linear codes and their basic properties are discussed in chapter two. In chapter three the authors study the basic properties of erasure decoding in maximum rank distance codes. Some decoding techniques about MRD codes are described and discussed in chapter four of this book. Rank distance codes with complementary duals and MRD codes with complementary duals are introduced and their applications are discussed. Chapter five introduces the notion of integer rank distance codes. The final chapter introduces some concatenation techniques.Comment: 162 pages; Published by Zip publishing in 201

Unfolding the Labyrinth: Open Problems in Mathematics, Physics, Astrophysics, and Other Areas of Science

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation. The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plau-sible solutions, it is merely to keep the fun of readers in discovering the answers by themselves.Comment: 139 pages, many figure

Easier to break from inside than from outside / Mai ușor să distrugi din interior decât din exterior

Abstract in English: This book contains concrete examples from history, economy, biology, digital world, nuclear physics, agriculture and so on about breaking a neutrosophic dynamic system (i.e. a dynamic system that has indeterminacy) from inside. We define a neutrosophic mathematical model using a system of ordinary differential equations and the neutrosophic probability in order to approximate the process of breaking from inside a neutrosophic complex dynamic system. It shows that for breaking from inside it is needed a smaller force than for breaking from outside the neutrosophic complex dynamic system. Methods that have been used in the past for breaking from inside are listed. Simulation and animation of this neutrosophic dynamical system are needed for the future since, by changing certain parameters, various types of breaking from inside may be simulated. Abstract in Romana: Această carte conține exemple concrete din istorie, economie, biologie, spațiu digital, fizică nucleară, agricultură și altele, de distrugere unui sistem neutrosofic dinamic (adică a unui sistem care are indeterminări), acționând din interiorul acestuia. Descriem un model neutrosofic matematic folosind un sistem de ecuații diferențiale ordinare și probabilitatea neutrosofică, cu scopul de a aproxima procesul de distrugere din interior a unui sistem neutrosofic dinamic complex. Se demonstrează că, pentru distrugerea din interior a unui astfel de sistem, este necesară o forță mai mică decât pentru distrugerea din exterior. Sunt enumerate metode folosite în trecut pentru distrugerea din interior. Simularea și animația acestui sistem neutrosofic dinamic sunt necesare pentru viitor, deoarece, schimbând diferiți parametri, se pot simula diferite tipuri de distrugeri din interior

Introduction to plithogenic sociogram with preference representations by plithogenic number

The theory of Plithogeny is gaining momentum in recent times as it generalizes the concepts of fuzzy, intuitionistic, neutrosophy and other extended representations of fuzzy sets. The relativity of the comprehensive and accommodative nature of plithogenic sets in dealing with attributes shall be applied to handle the decision–making problems in the field of sociology.  This paper introduces the concepts of Plithogenic Sociogram (PS) and Plithogenic Number (PN) where the former is the integration of plithogeny to the sociometric technique of sociogram and the latter is the generalization of fuzzy, intuitionistic and neutrosophic numbers that shall be used in representations of preferences in group dynamics. This research work outlines the conceptual development of these two newly proposed concepts and discusses the merits of the existing theory of similar kind with suitable substantiation. The plithogenic sociogram model encompassing the attributive preferences with plithogenic number representation is also developed to explicate how it can be materialized in the real social field. A conjectural illustration is put forth to analyze the efficiency and the feasibility of the proposed plithogenic sociogram model and its function in decision-making. This paper also throws light on generalized plithogenic number, dominant attribute constrained plithogenic number and combined dominant attribute constrained plithogenic number together with its operations and suitable illustrations

Compact Open Topology and Evaluation Map via Neutrosophic Sets

The concept of neutrosophic locally compact and neutrosophic compact open topology are introduced and some interesting propositions are discussed

On Neutrosophic Semi-Supra Open Set and Neutrosophic Semi-Supra Continuous Functions

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively

On Neutrosophic Semi-Supra Open Set and Neutrosophic Semi-Supra Continuous Functions

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively