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Florentin Smarandache

Publications and source records attributed to Florentin Smarandache.

At least 73 records · Page 4Linked to original sources
arXiv2011

Interval Algebraic Bistructures

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.

math.GM↗
arXiv2011

Uniform and Partially Uniform Redistribution Rules

This short paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

cs.AI↗
arXiv2011

Algebraic Structures using Natural Class of Intervals

This book has eleven chapters. Chapter one describes all types of natural class of intervals and the arithmetic operations on them. Chapter two introduces the semigroup of natural class of intervals using R or Zn and study the properties associated with them. Chapter three studies the notion of rings constructed using the natural class of intervals. Matrix theory using the special class of intervals is analyzed in chapter four of this book. Chapter five deals with polynomials using interval coefficients. New types of rings of natural intervals are introduced and studied in chapter six. The notion of vector space using natural class of intervals is built in chapter seven. In chapter eight fuzzy natural class of intervals are introduced and algebraic structures on them is built and described. Algebraic structures using natural class of neutrosophic intervals are developed in chapter nine.Chapter ten suggests some possible applications. The final chapter proposes over 200 problems of which some are at research level and some difficult and others are simple.

math.GM↗
arXiv2011

Interval Semirings

This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three introduces special types of interval semirings like matrix interval semirings and interval polynomial semirings. Chapter four for the first time introduces the notion of group interval semirings, semigroup interval semirings, loop interval semirings and groupoid interval semirings and these structures are studied. Interval neutrosophic semirings are introduced in chapter five. Applications of these structures are given in chapter six. The final chapter suggests around 120 problems for the reader.

math.GM↗
arXiv2011

A Class of Orthohomological Triangles

In this article we determine the class of triangles $A_iB_iC_i$ which are orthohomological with a given triangle $ABC$ and inscribed in the triangle $ABC$ (with $A_i \in BC$, $B_i \in CA$ and $C_i \in AB$).

math.GM↗
arXiv2011

Triplets of Tri-Homological Triangles

In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.

math.GM↗
arXiv2011

Interval Semigroups

In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval semigroups, interval matrix semigroups and interval polynomial semigroups are defined and discussed. This book has eight chapters. The main feature of this book is that we suggest 241 problems in the eighth chapter. In this book the authors have defined 29 new concepts and illustrates them with 231 examples. Certainly this will find several applications.

math.GM↗
arXiv2010

Interval Linear Algebra

In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or Q+ \cup {0} or R+ \cup {0}. A systematic development is made starting from set interval vector spaces to group interval vector spaces. Vector spaces are taken as interval polynomials or interval matrices or just intervals over suitable sets or semigroups or groups. Main feature of this book is the authors have given over 350 examples. This book has six chapters. Chapter one is introductory in nature. Chapter two introduces the notion of set interval linear algebras of type one and two. Set fuzzy interval linear algebras and their algebras and their properties are discussed in chapter three. Chapter four introduces several types of interval linear bialgebras and bivector spaces and studies them. The possible applications are given in chapter five. Chapter six suggests nearly 110 problems of all levels.

math.GM↗
arXiv2010

Determinants of Population Growth in Rajasthan: An Analysis

Rajasthan is the biggest State of India and is currently in the second phase of demographic transition and is moving towards the third phase of demographic transition with very slow pace. However, state's population will continue to grow for a time period. Rajasthan's performance in the social and economic sector has been poor in past. The poor performance is the outcome of poverty, illiteracy and poor development, which co-exist and reinforce each other. There are many demographic and socio-economic factors responsible for population growth. This paper attempts to identify the demographic and socio-economic variables, which are responsible for population growth in Rajasthan with the help of multivariate analysis.

math.GM↗
arXiv2010

Degree of Negation of an Axiom

In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood), or like in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but ambiguous, unknown, indeterminate)].

math.GM↗
arXiv2010

Ratio Estimators in Simple Random Sampling when Study Variable is an Attribute

In this paper we have suggested a family of estimators for the population mean when study variable itself is qualitative in nature. Expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An empirical study has been carried out to show the superiority of the constructed estimator over others.

math.GM↗
arXiv2010

Two Remarkable Ortho-Homological Triangles

In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously. In this article we call attention to two remarkable ortho-homological triangles (the given triangle and its first Brocard's triangle), and using the Sondat's theorem relative to orthological triangles, we emphasize on four important collinear points in the geometry of the triangle. Orthological / homological / orthohomological triangles in the 2D-space are generalized to orthological / homological / orthohomological polygons in 2D-space, and even more to orthological / homological / orthohomological triangles, polygons, and polyhedrons in 3D-space.

math.GM↗
arXiv2010

Interval Groupoids

This book introduces several new classes of groupoid, like polynomial groupoids, matrix groupoids, interval groupoids,polynomial interval groupoids, matrix interval groupoids and their neutrosophic analogues. Interval groupoid happens to be the first non-associative structure constructed using intervals built using Zn or Z or Q or R or Z+ \cup {0} or Q+ \cup {0} and so on. This book has five chapters. Chapter one is introductory in nature. In chapter two new classes of groupoids and interval groupoids are defined and described. The analogous neutrosophic study is carried out in chapter three. The applications of this new structure is given in chapter four. The final chapter suggests more than 200 problems. This book has given 77 new definitions, 426 examples of these new notions and over 150 theorems.

math.GM↗
arXiv2010

A Unifying Field in Logics: Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics (fourth edition)

In this book one makes an introduction to non-standard analysis in the first part, needed to the next four chapters in order to study the neutrosophics: 1. Neutrosophy - a new branch of philosophy. 2. Neutrosophic Logic - a unifying field in logics. 3. Neutrosophic Set - a unifying field in sets. 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics.

math.GM↗