Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Branch Mathematics and Statistics Faculty and Staff Publications

Discipline
Keyword
Publication Year

Articles 481 - 510 of 748

Full-Text Articles in Mathematics

Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram And Neutrosophic Degree Of Paradoxicity: Articles And Notes, Florentin Smarandache Jan 2015

Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram And Neutrosophic Degree Of Paradoxicity: Articles And Notes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book has four parts. In the first part, we collected five recent papers, published before in Progress in Physics, but reviewed. In the first paper, we approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists. That is the electron-positron plasma experiment of 2015 is the experimentum crucis verifying the mathematically predicted unmatter. In the second paper, we generalize the …

Go to article

Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy Jan 2015

Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …

Go to article

Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2015

Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place the fundamental theorem of algebra, “a nth degree polynomial has n and only n roots”, n is untrue in case of polynomial in polynomial quaternion rings in general. Further the very concept of derivative and integrals of these polynomials are untrue. Finally interval pseudo quaternion rings also behave in an erratic way. Not …

Go to article

Neutrosophic Crisp Set Theory, Florentin Smarandache, A.A. Salama Jan 2015

Neutrosophic Crisp Set Theory, Florentin Smarandache, A.A. Salama

Branch Mathematics and Statistics Faculty and Staff Publications

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need …

Go to article

Algebraic Structures On Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Algebraic Structures On Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Study of MOD planes happens to a very recent one. Authors have studied several properties of MOD real planes Rn(m); 2 ≤ m ≤ ∞. In fact unlike the real plane R × R which is unique MOD real planes are infinite in number. Likewise MOD complex planes Cn(m); 2 ≤ m ≤ ∞, are infinitely many. The MOD neutrosophic planes RnI(m); 2 ≤ m ≤ ∞ are infinite in number where as we have only one neutrosophic plane R(I) = 〈R ∪ I〉 = {a + bI | I2 = I; a, b ∈ R}. Further three other new …

Go to article

Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …

Go to article

Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m …

Go to article

Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …

Go to article

Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD …

Go to article

Multidimensional Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2015

Multidimensional Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors name the interval [0, m); 2 ≤ m ≤ ∞ as mod interval. We have studied several properties about them but only here on wards in this book and forthcoming books the interval [0, m) will be termed as the mod real interval, [0, m)I as mod neutrosophic interval, [0,m)g; g2 = 0 as mod dual number interval, [0, m)h; h2 = h as mod special dual like number interval and [0, m)k, k2 = (m − 1) k as mod special quasi dual number interval. However there is only one real interval (∞, ∞) but …

Go to article

Sampling Strategies For Finite Population Using Auxiliary Information, Florentin Smarandache, Rajesh Singh Jan 2015

Sampling Strategies For Finite Population Using Auxiliary Information, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The present book aims to present some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and in some cases when non-response is present. This volume is a collection of five papers, written by seven co-authors (listed in the order of the papers): Sachin Malik, Rajesh Singh, Florentin Smarandache, B. B. Khare, P. S. Jha, Usha Srivastava and Habib Ur. Rehman. The first and the second papers deal with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. In the third paper, problems related …

Go to article

Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz Jan 2015

Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz

Branch Mathematics and Statistics Faculty and Staff Publications

Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and articial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion. To overcome these di¢ culties of uncertainties, many theories have been developed such as rough sets theory, probability theory, fuzzy sets theory, theory of vague sets, theory of soft ideals and the theory of intuitionistic fuzzy sets, theory of neutrosophic sets, Dezert-Smarandache Theory (DSmT), etc. Zadeh introduced the degree of membership/truth (t) in 1965 and dened …

Go to article

Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan Jan 2015

Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan

Branch Mathematics and Statistics Faculty and Staff Publications

It is common knowledge that common models with their limited boundaries of truth and falsehood are not su¢ cient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and impaction. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not su¢ cient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh [67] introduced the concept of …

Go to article

Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache Jan 2015

Probleme De Geometrie Și Trigonometrie, Compilate Și Rezolvate, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Go to article

Algebraic Problems And Exercises For High School, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin Jan 2015

Algebraic Problems And Exercises For High School, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, you will find algebraic exercises and problems, grouped by chapters, intended for higher grades in high schools or middle schools of general education. Its purpose is to facilitate training in mathematics for students in all high school categories, but can be equally helpful in a standalone work. The book can also be used as an extracurricular source, as the reader shall find enclosed important theorems and formulas, standard definitions and notions that are not always included in school textbooks.

Go to article

Α-Discounting Method For Multi-Criteria Decision Making (Α-D Mcdm), Florentin Smarandache Jan 2015

Α-Discounting Method For Multi-Criteria Decision Making (Α-D Mcdm), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce a new procedure called αDiscounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is afterwards generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or nonhomogeneous equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are …

Go to article

255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache Jan 2015

255 Compiled And Solved Problems In Geometry And Trigonometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Go to article

Readup Buildup. Thync - Instant Α-Readings, Florentin Smarandache Jan 2015

Readup Buildup. Thync - Instant Α-Readings, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Go to article

Distance And Similarity Measures Of Interval Neutrosophic Soft Sets, Said Broumi, Irfan Deli, Florentin Smarandache Jul 2014

Distance And Similarity Measures Of Interval Neutrosophic Soft Sets, Said Broumi, Irfan Deli, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper several distance and similarity measures of interval neutrosophic soft sets are introduced. The measures are examined based on the geometric model, the set theoretic approach and the matching function. Finally, we have successfully shown an application of this similarity measure of interval neutrosophic soft sets.

Go to article

New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache Jul 2014

New Distance And Similarity Measures Of Interval Neutrosophic Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets.

Go to article

Determining The Duration Of R&D Processes Through Monte Carlo Simulation, Florentin Smarandache, Moga Monika, Calefariu Gavrila, Sarbu Flavius Aurelian Apr 2014

Determining The Duration Of R&D Processes Through Monte Carlo Simulation, Florentin Smarandache, Moga Monika, Calefariu Gavrila, Sarbu Flavius Aurelian

Branch Mathematics and Statistics Faculty and Staff Publications

The research and development (R&D) processes influence the economic development of a company, because in an industry that is changing fast, firms must continually revise their projects and range of products. Therefore in order to determine the specific costs of research and development activity we have to highlight the efforts and effects of these activities and to calculate some indicators of economic efficiency. In the cost calculation process in R & D we have emphasized the identification of the components of cost and the duration of the R & D processes, as a component of the R&D cost, that is …

Go to article

Computational-Communicative Actions Of Informational Processing, Florentin Smarandache, Stefan Vladutescu Apr 2014

Computational-Communicative Actions Of Informational Processing, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

This study is circumscribed to the Information Science. The zetetic aim of research is double: a) to define the concept of action of informational processing and b) to design a taxonomy of actions of informational processing. First, the investigation trays to demonstrate that the computational actions of informational processing or the informational actions are computational-investigative configurations for structuring information: clusters of highly-aggregated operations which are carried out in a unitary manner operate convergently and behave like a unique computational device. From a methodological point of view, they are comprised within the category of analytical instruments for the informational processing of …

Go to article

Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache Jan 2014

Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present an extension of the multicriteria decision making based on the Analytic Hierarchy Process (AHP) which incorporates uncertain knowledge matrices for generating basic belief assignments (bba’s). The combination of priority vectors corresponding to bba’s related to each (sub)- criterion is performed using the Proportional Conflict Redistribution rule no. 5 proposed in Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. The method presented here, called DSmT-AHP, is illustrated on very simple examples.

Go to article

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2014

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …

Go to article

Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache Jan 2014

Some Properties Of The Harmonic Quadrilateral, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.

Go to article

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu Jan 2014

Neutrosophic Principle Of Interconvertibility Matter-Energy Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does …

Go to article

Communication Neutrosophic Routes, Florentin Smarandache, Ştefan Vlăduţescu Jan 2014

Communication Neutrosophic Routes, Florentin Smarandache, Ştefan Vlăduţescu

Branch Mathematics and Statistics Faculty and Staff Publications

Any manifestation of life is a component of communication, it is crossed by a communication passage. People irrepressibly generate meanings. As structuring domain of meanings, communication is a place where meanings burst out volcanically. Manifestations of life are surrounded by a halo of communicational meanings. Human material and ideatic existence includes a great potential of communication in continuous extension. The human being crosses the path of or is at the intersection of different communicational thoroughfares. The life of human beings is a place of communication. Consequently, any cognitive or cogitative manifestation presents a route of communication. People consume their lives …

Go to article

Fusion Of Masses Defined On Infinite Countable Frames Of Discernment, Florentin Smarandache, Arnaud Martin Jan 2014

Fusion Of Masses Defined On Infinite Countable Frames Of Discernment, Florentin Smarandache, Arnaud Martin

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster’s rule and the PCR5 rule for Bayesian and non-Bayesian cases.

Go to article

Communicative Universal Convertibility Matter-Energy-Information, Florentin Smarandache, Stefan Vladutescu Jan 2014

Communicative Universal Convertibility Matter-Energy-Information, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The research aims to reveal and prove the thesis of the neutral and convertibility relationship between constituent constructive elements of the universe: matter, energy and information. The approach perspective is a computationally-communicative-neutrosophic one. We configure a coherent and cohesive ideation line. Matter, energy and information are fundamental elements of the world. Among them, there is an inextricable multiple, elastic and evolutionary connection. The elements are defined by the connections between them. Our hypothesis is that the relationship between matter, energy and information is a neutral one. This relationship is not required by the evidence. At this level, it does not …

Go to article

Towards A Practical Communication Intervention, Florentin Smarandache, Stefan Vladutescu Jan 2014

Towards A Practical Communication Intervention, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

The study starts from evidence that several communication acts fail, but nobody is called to intervene and nobody thinks of intervening. Examining different branches (specialties) of the communication discipline and focusing on four possible practices, by comparison, differentiation, collating and corroboration, the current study brings arguments for a branch of the communication discipline that has as unique practical aim the communicational intervention, the practical, direct and strict application of communication research. Communication, as discipline, must create an instrument of intervention. The discipline which studies communication globally (General Communication Science) has developed a strong component of theoretical and practical research of …

Go to article

First Prev Next Last