Mathematics Commons^™

Unsolved Problems In Special And General Relativity, Florentin Smarandache, Fu Yuhua, Zhao Fengjuan

Branch Mathematics and Statistics Faculty and Staff Publications

This book includes 21 papers written by 23 authors and co-authors. All papers included herein are produced by scholars from People’s Republic of China, except two papers written by Prof. L. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov from Russia, and by Prof. Florentin Smarandache from USA. The editors hope that all these papers will contribute to the advance of scholarly research on several aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies on physics. The first paper is written by Hua Di. He writes that Einstein’s general theory of relativity cannot …

Oblique-Length Contraction Factor In The Special Theory Of Relativity, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper one generalizes the Lorentz Contraction Factor for the case when the lengths are moving at an oblique angle with respect to the motion direction. One shows that the angles of the moving relativistic objects are distorted.

N-Valued Refined Neutrosophic Logic And Its Applications To Physics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, …

Unsolved Problems In Special And General Relativity, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book includes 21 papers written by 23 authors and co-authors: Hua Di, Li Zifeng, Li Wen-Xiu, Shi Yong-Cheng, Xu Jianmin, Dong Jingfeng, Duan Zhongxiao, Fu Yuhua, Guo Kaizhe, Guo Chongwu, Guo Ying-Huan, Guo Zhen-Hua, Hu Chang-Wei, Jiang Chun-Xuan, Liu Taixiang, Tu Runsheng, Wu Fengming, Yang Shijia, Cao Shenglin, Leo G. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov, and Florentin Smarandache.

The editors hope that all these papers will contribute to the advance of scholarly research on several aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies of physics.

Subset Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study the new notion of the algebraic structure of the subset semirings using the subsets of rings or semirings. This study is innovative and interesting for the authors feel giving algebraic structure to collection of sets is not a new study, for when set theory was introduced such study was in vogue. But a systematic development of constructing algebraic structures using subsets of a set is absent, except for the set topology and in the construction of Boolean algebras. The authors have explored the study of constructing subset algebraic structures like semigroups, groupoids, semirings, non commutative …

Subset Polynomial Semirings And Subset Matrix Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the notion of subset polynomial semirings and subset matrix semirings. The study of algebraic structures using subsets were recently carried out by the authors. Here we define the notion of subset row matrices, subset column matrices and subset m × n matrices. Study of this kind is developed in chapter two of this book. If we use subsets of a set X; say P(X), the power set of the set X....

Hence if P(X) is replaced by a group or a semigroup we get the subset matrix to be only a subset matrix semigroup. If …

Subset Non Associative Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time we introduce the notion of subset non associative semirings. It is pertinent to keep on record that study of non associative semirings is meager and books on this specific topic is still rare. Authors have recently introduced the notion of subset algebraic structures. The maximum algebraic structure enjoyed by subsets with two binary operations is just a semifield and semiring, even if a ring or a field is used. In case semigroups or groups are used still the algebraic structure of the subset is only a semigroup. To construct a subset non associative …

Subset Interval Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of groupoids is meager and we have recently introduced the new notion of subset groupoids and have studied them. It is interesting to keep on record that interval groupoids have been studied by us in 2010. Further when the subsets of a loop are taken they also form only a subset groupoid and not a subset loop. Thus we do not have the concept of subset interval loop they only form a subset interval groupoid. Special elements like subset interval zero divisors, subset interval idempotents and subset interval units are studied. Concept of subset interval groupoid homomorphism is …

Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of subsets and giving algebraic structure to these subsets of a set started in the mid 18th century by George Boole. The first systematic presentation of Boolean algebra emerged in 1860s in papers written by William Jevons and Charles Sanders Peirce. Thus we see if P(X) denotes the collection of all subsets of the set X, then P(X) under the op erations of union and intersection is a Boolean algebra. Next the subsets of a set was used in the construction of topological spaces. We in this book consider subsets of a semigroup or a group or a …

Fuzzy Analysis Of School Dropouts And Their Life After, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved. A school dropout can be a child labourer, a rag picker or a social miscreant or be in police custody or be in a rehabilitation home if he/she is a runaway. …

Algebraic Structures Using [0,N), Florentin Smarandache, Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce a new method of building algebraic structures on the interval [0, n). This study is interesting and innovative. However, [0, n) is a semigroup under product, × modulo n and a semigroup under min or max operation. Further [0, n) is a group under addition modulo n. We see [0, n) under both max and min operation is a semiring. [0, n) under + and × is not in general a ring. We define S = {[0, n), +, ×} to be a pseudo special ring as the distributive law is …

Fuzzy Neutrosophic Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, authors give the notion of different neutrosophic models like, neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NEMs), neutrosophic relational equations (NREs), neutrosophic bidirectional associative memories (NBAMs) and neutrosophic associative memories (NAMs) for socio scientists. This book has six chapters. The first chapter introduces the basic concepts of neutrosophic numbers and notions about neutrosophic graphs which are essential to construct these neutrosophic models. In chapter two we describe the concept of neutrosophic matrices and the essential operations related with them which are used in the study and working of these neutrosophic models. However the reader must be familiar …

On Improvement In Estimating Population Parameter(S) Using Auxiliary Information, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers, written by eight coauthors (listed in the order of the papers): Manoj K. Chaudhary, Sachin Malik, Rajesh Singh, Florentin Smarandache, Hemant Verma, Prayas Sharma, Olufadi Yunusa, and Viplav Kumar Singh, from India, Nigeria, and USA. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved …

Proceedings Of The First International Conference On Smarandache Multispace & Multistructures, Florentin Smarandache, Linfan Mao

Branch Mathematics and Statistics Faculty and Staff Publications

In recent decades, Smarandache’s notions of multispace and multistructure were widely spread and have shown much importance in sciences around the world. Organizedby Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

Clan Capitalism, Graph Distance, And Other Issues, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book consists of 6 papers focusing on social and economic issues. The topics covered include graph distance and optimal communication, migration in Jaipur, urbanization, clan capitalism, world population growth rate, and scientific inquiry. These papers were written in the period between 20092010. Hopefully the readers will find some new insights in this collection of papers.

The Hyperbolic Menelaus Theorem In The Poincare Disc Model Of Hyperbolic Geometry, Florentin Smarandache, Catalin Barbu

Branch Mathematics and Statistics Faculty and Staff Publications

In this note, we present the hyperbolic Menelaus theorem in the Poincar´e disc of hyperbolic geometry.

Correlation Coefficient Of Interval Neutrosophic Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.

Intuitionistic Neutrosophic Soft Set, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study the concept of intuitionistic neutrosophic set of Bhowmik and Pal. We have introduced this concept in soft sets and defined intuitionistic neutrosophic soft set. Some definitions and operations have been introduced on intuitionistic neutrosophic soft set. Some properties of this concept have been established.

Identifying Requirements For The Invasion Of A Tick Species And Tick-Borne Pathogen Through Ticksim, Holly Gaff, Robyn Nadolny

Biological Sciences Faculty Publications

Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the success of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and …

Ricean Over Gaussian Modelling In Magnitude Fmri Analysis—Added Complexity With Negligible Practical Benefits, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

It is well known that Gaussian modelling of functional magnetic resonance imaging (fMRI) magnitude time-course data, which are truly Rice distributed, constitutes an approximation, especially at low signal-to-noise ratios (SNRs). Based on this fact, previous work has argued that Rice-based activation tests show superior performance over their Gaussian-based counterparts at low SNRs and should be preferred in spite of the attendant additional computational and estimation burden. Here, we revisit these past studies and, after identifying and removing their underlying limiting assumptions and approximations, provide a more comprehensive comparison. Our experimental evaluations using Receiver Operating Characteristic (ROC) curve methodology show that …