Other Physical Sciences and Mathematics Commons^™

Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon …

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Long Wavelength Analysis Of A Model For The Geographic Spread Of A Disease, Layachi Hadji

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the temporal and spatial evolution of the spread of an infectious disease by performing a long-wavelength analysis of a classical model for the geographic spread of a rabies epidemic in a population of foxes subject to idealized boundary conditions. We consider twodimensional and three-dimensional landscapes consisting of an infinite horizontal strip bounded by two walls a finite distance apart and a horizontal region bounded above and below by horizontal walls, respectively. A nonlinear partial differential evolution Equation for the leading order of infectives is derived. The Equation captures the space and time variations of the spread of the …

An Optimal Harvesting Strategy Of A Three Species Syn-Ecosystem With Commensalism And Stochasticity, M. N. Srinivas, A. Sabarmathi, K. S. Reddy, M. A. S. Srinivas

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have studied the stability of three typical species syn-ecosystem. The system comprises of one commensal S₁ and two hosts S₂ and S₃ . Both S₂ and S₂ benefit S₁ without getting themselves affected either positively or adversely. Further S₂ is a commensal of S₃ and S₃ is a host of both S₁ and S₂. Limited resources have been considered for all the three species in this case. The model equations of the system constitute a set of three first order non-linear ordinary differential equations. …

Growth Patterns Of Ethnic Groups In Bexar County With Dynamic Leslie Models, Judith Arriaza, Zhanbo Yang, Flor De María García-Wukovits

Applications and Applied Mathematics: An International Journal (AAM)

The purpose of this study is to modify the Leslie model with a dynamic matrix for better population projections in Bexar County, where UIW is located and the authors reside. A dynamic matrix was used to improve the static Leslie model used in the previous study since human population growth is dynamic and complex. The matrix was constructed with functions that modeled the birth rates and survival rates. This allowed the rates to change from year to year. The population projections using the dynamic matrix were compared to the real population data and the static matrix. The researcher concluded that …

Dynamics Of Phytoplankton, Zooplankton And Fishery Resource Model, B. Dubey, Atasi Patra, R. K. Upadhyay

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new mathematical model has been proposed and analyzed to study the interaction of phytoplankton- zooplankton-fish population in an aquatic environment with Holloing’s types II, III and IV functional responses. It is assumed that the growth rate of phytoplankton depends upon the constant level of nutrient and the fish population is harvested according to CPUE (catch per unit effort) hypothesis. Biological and bionomical equilibrium of the system has been investigated. Using Pontryagin’s Maximum Principal, the optimal harvesting policy is discussed. Chaotic nature and bifurcation analysis of the model system for a control parameter have been observed through …

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

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 …

Spread Of Malicious Objects In Computer Network: A Fuzzy Approach, Bimal K. Mishra, Apeksha Prajapati

Applications and Applied Mathematics: An International Journal (AAM)

We propose an e-epidemic fuzzy SEIQRS (Susceptible-Exposed-Infectious-Quarantine- Recovered-Susceptible) model for the transmission of malicious codes in a computer network. We have simulated the result for various parameters and analyzed the stability of the model. The efficiency of antivirus software and crashing of the nodes due to attack of malicious code is analyzed. Furthermore, initial simulation results illustrate the behavior of different classes for minimizing the infection in a computer network. It also reflects the positive impact of anti-virus software on malicious code propagation in a computer network. The basic reproduction number R0 f and its formulation is also discussed.

Numerical Solution Of Fuzzy Arbitrary Order Predator-Prey Equations, Smita Tapaswini, S. Chakraverty

Applications and Applied Mathematics: An International Journal (AAM)

This paper seeks to investigate the numerical solution of fuzzy arbitrary order predator-prey equations using the Homotopy Perturbation Method (HPM). Fuzziness in the initial conditions is taken to mean convex normalised fuzzy sets viz. triangular fuzzy number. Comparisons are made between crisp solution given by others and fuzzy solution in special cases. The results obtained are depicted in plots and tables to demonstrate the efficacy and powerfulness of the methodology.

Grayscale-Image Encryption Using Random Hill Cipher Over Sln(F) Associated With Discrete Wavelet Transformation, D. C. Mishra, R. K. R. K. Sharma

Applications and Applied Mathematics: An International Journal (AAM)

Image data are highly sensitive and prone to incidental decoding by intruders. The security of image data in an insecure network is therefore a major issue. In this paper, we have presented a novel approach for grayscale-image encryption and decryption using Random Hill cipher over SLn(F) associated with discrete wavelet transformation. Earlier techniques for encryption and decryption of image data discussed missing the keys, but in this approach, both the keys and the arrangement of RHC are emphasized. Additionally, keys multiplication side (pre or post) over a grayscale-image data matrix also inevitable to know, to correctly decrypt the encrypted image …

Accuracy Analysis Of Parallel Method Based On Non-Overlapping Domain Decomposition Method, Moonho Tak, Yooseob Song, Hye-Kwan Jeon, Taehyo Park

Civil Engineering Faculty Publications

In this paper, an accuracy analysis of parallel method based on non-overlapping domain decomposition method is carried out. In this approach, proposed by Tak et al.(2013), the decomposed subdomains do not overlap each other and the connection between adjacent subdomains is determined via simple connective finite element named interfacial element. This approach has two main advantages. The first is that a direct method such as gauss elimination is available even in a singular problem because the singular stiffness matrix from floating domain can be converted to invertible matrix by assembling the interfacial element. The second is that computational time and …

On Fuzzy Soft Matrix Based On Reference Function, Florentin Smarandache, Said Broumi, Mamoni Dhar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study fuzzy soft matrix based on reference function. Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function. Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the …

Scalars And Generating Bases For The Module Of Splines With Boundary Conditions C(R;0)(I, Gordon Michael Jones

Renée Crown University Honors Thesis Projects - All

See Full Document for Abstract

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal

Applications and Applied Mathematics: An International Journal (AAM)

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …

Set Ideal Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as …

Fuzzy Linguistic Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

The Principle Of Linearized Stability For Size-Structured Population Models, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance

Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly …

Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.

The Four-Color Theorem And Chromatic Numbers Of Graphs, Sarah E. Cates

Undergraduate Theses and Capstone Projects

We study graph colorings of the form made popular by the four-color theorem. Proved by Appel and Haken in 1976, the Four-Color Theorem states that all planar graphs can be vertex-colored with at most four colors. We consider an alternate way to prove the Four-Color Theorem, introduced by Hadwiger in 1943 and commonly know as Hadwiger’s Conjecture. In addition, we examine the chromatic number of graphs which are not planar. More specifically, we explore adding edges to a planar graph to create a non-planar graph which has the same chromatic number as the planar graph which we started from.

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Computational Modeling In Applied Problems: Collected Papers On Econometrics, Operations Research, Game Theory And Simulation, Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan

Branch Mathematics and Statistics Faculty and Staff Publications

Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Generalized Linear Inversion Using Tau-P Forward Modeling, Stephen Dade Walker

Graduate Theses

The Generalized Linear Inversion (GLI) method is used in conjunction with a tau-p forward model to successfully perform inversions of test and real-data examples. All data examples used are one-dimensional velocity profiles that represent several different cases. The stability of the technique is demonstrated in all the test-data sets. The use of simple models and wel1-control 1ed test data results in a minimum of iterations of the inversion process. Different levels of perturbation of the model and test-data examples are used to reveal insight into the robust nature of the inversion.