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Articles 1 - 13 of 13
Full-Text Articles in Mathematics
Delay-Induced Destabilization Of Entrainment Of Nerve Impulses On Ephaptically Coupled Nerve Fibers, Evangelos A. Coutsias, Mohit H. Adhikari, John K. Mciver
Delay-Induced Destabilization Of Entrainment Of Nerve Impulses On Ephaptically Coupled Nerve Fibers, Evangelos A. Coutsias, Mohit H. Adhikari, John K. Mciver
Branch Mathematics and Statistics Faculty and Staff Publications
We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delay-coupled Fitzhugh-Nagumo equations. A multiple-scale perturbation approach is used for the analysis of these equations in the limit of weak coupling. In the absence of delay, two pulses with identical speeds are shown to be entrained precisely. However, as the delay is increased beyond a critical value, we show that this precise entrainment becomes unstable. We make quantitative estimates for the actual values of delay at which this can occur in …
Algorithmic Dimensionality Reduction For Molecular Structure Analysis, Evangelos A. Coutsias, W. Michael Brown, Shawn Martin, Sara N. Pollock, Jean-Paul Watson
Algorithmic Dimensionality Reduction For Molecular Structure Analysis, Evangelos A. Coutsias, W. Michael Brown, Shawn Martin, Sara N. Pollock, Jean-Paul Watson
Branch Mathematics and Statistics Faculty and Staff Publications
Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation\u2014a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a …
Cultural Advantage For Cities: An Alternative For Developing Countries, Florentin Smarandache, Victor Christianto
Cultural Advantage For Cities: An Alternative For Developing Countries, Florentin Smarandache, Victor Christianto
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal
Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal
Branch Mathematics and Statistics Faculty and Staff Publications
The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or …
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
N-Linear Algebra Of Type Ii, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to …
Set Linear Algebra And Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Set Linear Algebra And Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is comfortable working with it. It is with the passage of time, that we can think of set linear algebras as a paradigm shift from linear algebras. Here, the authors have also given the fuzzy parallels of these new classes of set linear algebras. This book abounds with examples to enable the reader to understand these new concepts easily. Laborious theorems and …
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set ncodes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the …
New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy
New Classes Of Codes For Cryptologists And Computer Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Historically a code refers to a cryptosystem that deals with linguistic units: words, phrases etc. We do not discuss such codes in this book. Here codes are message carriers or information storages or information transmitters which in time of need should not be decoded or read by an enemy or an intruder. When we use very abstract mathematics in using a specific code, it is difficult for non-mathematicians to make use of it. At the same time, one cannot compromise with the capacity of the codes. So the authors in this book have introduced several classes of codes which are …
Methods In Industrial Biotechnology For Chemical Engineers, Florentin Smarandache, W.B. Vasantha Kandasamy
Methods In Industrial Biotechnology For Chemical Engineers, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Industrial Biotechnology is an interdisciplinary topic to which tools of modern biotechnology are applied for finding proper proportion of raw mix of chemicals, determination of set points, finding the flow rates etc., This study is significant as it results in better economy, quality product and control of pollution. The authors in this book have given only methods of industrial biotechnology mainly to help researchers, students and chemical engineers. Since biotechnology concerns practical and diverse applications including production of new drugs, clearing up pollution etc. we have in this book given methods to control pollution in chemical industries as it has …
Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie
Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Cultural Advantages In China: Tale Of Six Cities, Florentin Smarandache, Fu Yuhua, Victor Christianto
Cultural Advantages In China: Tale Of Six Cities, Florentin Smarandache, Fu Yuhua, Victor Christianto
Branch Mathematics and Statistics Faculty and Staff Publications
Nowadays, plenty of factories from Europe and other developed countries have been relocated to this country, considering its tremendous economic scale and rapid growth rate during the past three decades. But most of what happens inside the China nowadays is deeply hidden from the outside world (“the foreigners” as China people would call). This fact is partly because most reports on China were written by the so‐called fly‐high experts who are busy completing their reports despite a busy schedule. Very few books or reports were written by people inside, or at least “foreigners” who spent a few years in China. …
Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Super Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized …