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Applied Mathematics Commons™

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2014

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Articles 91 - 120 of 264

Full-Text Articles in Applied Mathematics

An Analysis Of The Impact Of Variation In Mean Time Between Demand On Air Force Fleet Level Aircraft Parts Inventories, Andrew J. Berger, Caleb S. Murphy Jun 2014

An Analysis Of The Impact Of Variation In Mean Time Between Demand On Air Force Fleet Level Aircraft Parts Inventories, Andrew J. Berger, Caleb S. Murphy

Theses and Dissertations

This thesis researched the accuracy of demand forecasting and impact of demand variation on requirements definition for Air Force aircraft secondary items. Specifically, this thesis sought to answer three questions: How does the Air Force calculate item requirements? , How accurate is the current system at predicting future item requirements? , and How do variations in predicted demand change item requirements? The literature review described the Air Force supply system for aircraft secondary items. Analysis into current demand forecast accuracy found that the level of error between actual and predicted historic demand was as high as 92% for the items …

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Morphological Active Contours For Texture And Multiphase Segmentation, Victoria Lynn Fox Jun 2014

Morphological Active Contours For Texture And Multiphase Segmentation, Victoria Lynn Fox

Theses and Dissertations

Natural images, in the context of this work, are images that contain complicated, local covariance structures in their statistical analysis. Owing to compound textural features, intensity inhomogeneity, image layers and variations of statistics inherent in such images, segmenting complicated images into areas of similarity is a challenging task. In this work, a morphological active contour is developed to increase efficiency of current active contour schemes and a fuzzy clustering energy is incorporated into the active contour algorithm to increase accuracy and flexibility. The savings in computational efficiency garnered from using a morphological curve evolution rather than a partial differential equation …

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Ermakov-Lewis Invariants And Reid Systems, S.C. Mancas, Haret C. Rosu Jun 2014

Ermakov-Lewis Invariants And Reid Systems, S.C. Mancas, Haret C. Rosu

Publications

Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy.

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Observable Causality Implies Lorentz Group: Alexandrov-Zeeman-Type Theorem For Space-Time Regions, Olga Kosheleva, Vladik Kreinovich Jun 2014

Observable Causality Implies Lorentz Group: Alexandrov-Zeeman-Type Theorem For Space-Time Regions, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The famous Alexandrov-Zeeman theorem proves that causality implies Lorentz group. The physical meaning of this result is that once we observe which event can causally affect which other events, then, using only this information, we can reconstruct the linear structure of the Minkowski space-time. The original Alexandrov-Zeeman theorem is based on the causality relation between events represented by points in space-time. Knowing such a point means that we know the exact moment of time and the exact location of the corresponding event - and that this event actually occurred at a single moment of time and at a single spatial …

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How To Modify Grade Point Average (Gpa) To Make It More Adequate, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich Jun 2014

How To Modify Grade Point Average (Gpa) To Make It More Adequate, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At present, the amounts of knowledge acquired by different graduates of the same program are usually compared by comparing their GPAs. We argue that this is not always the most adequate description: for example, if, after completing all required classes with the highest grade of "excellent" (A), a student takes an additional challenging class and gets a "satisfactory" grade (C), the amount of her knowledge increases, but the GPA goes down. We propose a modification of the GPA which is free of this drawback and is, thus, more adequate for describing the student's knowledge. We also provide a psychological explanation …

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Investr: An R Package For Inverse Estimation, Brandon M. Greenwell, Christine M. Schubert Kabban Jun 2014

Investr: An R Package For Inverse Estimation, Brandon M. Greenwell, Christine M. Schubert Kabban

Faculty Publications

Inverse estimation is a classical and well-known problem in regression. In simple terms, it involves the use of an observed value of the response to make inference on the corresponding unknown value of the explanatory variable. To our knowledge, however, statistical software is somewhat lacking the capabilities for analyzing these types of problems. In this paper, we introduce investr (which stands for inverse estimation in R), a package for solving inverse estimation problems in both linear and nonlinear regression models.

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The Generalized Laguerre Matrix Method Or Solving Linear Differential-Difference Equations With Variable Coefficients, Z. K. Bojdi, S. Ahmadi-Asl, A. Aminataei Jun 2014

The Generalized Laguerre Matrix Method Or Solving Linear Differential-Difference Equations With Variable Coefficients, Z. K. Bojdi, S. Ahmadi-Asl, A. Aminataei

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new and efficient approach based on the generalized Laguerre matrix method for numerical approximation of the linear differential-difference equations (DDEs) with variable coefficients is introduced. Explicit formulae which express the generalized Laguerre expansion coefficients for the moments of the derivatives of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. In the scheme, by using this approach we reduce solving the linear differential equations to solving a system of linear algebraic equations, thus greatly simplify the problem. In addition, several numerical experiments are given to …

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Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed Jun 2014

Reichenbach Fuzzy Set Of Transitivity, Samina Ashraf, Muhammad A. Javed

Applications and Applied Mathematics: An International Journal (AAM)

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

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Application Of The Extended G'/G-Expansion Method To The Improved Eckhaus Equation, Nasir Taghizadeh, Seyyedeh R. Moosavi Noori, Seyyedeh B. Moosavi Noori Jun 2014

Application Of The Extended G'/G-Expansion Method To The Improved Eckhaus Equation, Nasir Taghizadeh, Seyyedeh R. Moosavi Noori, Seyyedeh B. Moosavi Noori

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the extended (G'/G)-expansion method is used to seek more general exact solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.

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A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar Jun 2014

A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar

Applications and Applied Mathematics: An International Journal (AAM)

This work purpose suggest a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving time fractional Bloch NMR (nuclear magnetic resonance) flow equations, which are a set of macroscopic equations that are used for modeling nuclear magnetization as a function of time. The true beauty of this article is the coupling of the homotopy analysis method and the Laplace transform method for systems of fractional differential equations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

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Delay Analysis Of A Discrete-Time Non-Preemptive Priority Queue With Priority Jumps, Deepak C. Pandey, Arun K. Pal Jun 2014

Delay Analysis Of A Discrete-Time Non-Preemptive Priority Queue With Priority Jumps, Deepak C. Pandey, Arun K. Pal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a discrete-time non-preemptive priority queueing model with priority jumps. Two classes, real-time (high priority) and non-real time (low priority), of traffic will be considered with providing jumps from lower priority traffic to the queue of high priority traffic. We derive expressions for the joint probability generating function of the system contents of the high and the low priority traffic in the steady state and also for some performance measures such as the mean value of the system contents and the packet delay. The behavior of the priority queues with priority jumps will be illustrated by …

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Growth Patterns Of Ethnic Groups In Bexar County With Dynamic Leslie Models, Judith Arriaza, Zhanbo Yang, Flor De María García-Wukovits Jun 2014

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 …

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Unstable Solutions To Nonlinear Vector Differential Equations Of Sixth Order With Delay, Cemil Tunç Jun 2014

Unstable Solutions To Nonlinear Vector Differential Equations Of Sixth Order With Delay, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

This paper investigates the instability of the zero solution of a certain vector differential equation of the sixth order with delay. Using the Lyapunov- Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustrations

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Stability Of An Inhomogeneous Damped Vibrating String, Siddhartha Misra, Ganesh C. Gorain Jun 2014

Stability Of An Inhomogeneous Damped Vibrating String, Siddhartha Misra, Ganesh C. Gorain

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the vibrations of an inhomogeneous damped string under a distributed disturbing force which is clamped at both ends. The well-possedness of the system is studied. We prove that the amplitude of such vibrations is bounded under some restriction of the disturbing force. Finally, we establish the uniform exponential stabilization of the system when the disturbing force is insignificant. The results are established directly by means of an exponential energy decay estimate.

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Stochastic Modeling Of A Concrete Mixture Plant With Preventive Maintenance, Ashish Kumar, Monika Saini, S. C. Malik Jun 2014

Stochastic Modeling Of A Concrete Mixture Plant With Preventive Maintenance, Ashish Kumar, Monika Saini, S. C. Malik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a stochastic model for concrete mixture plant with Preventive Maintenance (PM) is analyzed in detail by using a supplementary variable technique. In a concrete mixture plant eight subsystems are arranged in a series. The system goes under PM after a maximum operation time and work as new after PM. The time to failure of each subsystem follows a negative exponential distribution while PM and repair time distributions are taken as arbitrary. A sufficient repair facility is provided to the system for conducting PM and repair of the system. Repair, maintenance and switch devices are perfect. All random …

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Modelling The Flow Of Aqueous Humor In Schlemm’S Canal In The Eye, Ram Avtar, Swati Srivastava, Rashmi Srivastava Jun 2014

Modelling The Flow Of Aqueous Humor In Schlemm’S Canal In The Eye, Ram Avtar, Swati Srivastava, Rashmi Srivastava

Applications and Applied Mathematics: An International Journal (AAM)

A simple mathematical model for the transient flow of aqueous humor in the canal of Schlemm is developed to investigate the acceleration effects of a sudden elevation in the intraocular pressure on the flow characteristics of the aqueous humor in the canal. The model treats a canal segment as a tube of elliptic cross-section. Exact analytical solution to the model is obtained using separation of variables method. The effects of some important model parameters on the maximum and minimum shear stresses exerted on the Schlemm’s canal epithelial cells (wall) by flowing aqueous humor are investigated for the steady-state flow.

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Dynamics Of Phytoplankton, Zooplankton And Fishery Resource Model, B. Dubey, Atasi Patra, R. K. Upadhyay Jun 2014

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 …

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Reliable Study Of Nonhomogeneous Bbm Equation With Time-Dependent Coefficients By The Modified Sine-Cosine Method, Aminah Qawasmeh, Marwan Alquran Jun 2014

Reliable Study Of Nonhomogeneous Bbm Equation With Time-Dependent Coefficients By The Modified Sine-Cosine Method, Aminah Qawasmeh, Marwan Alquran

Applications and Applied Mathematics: An International Journal (AAM)

The modified sine-cosine method is an efficient and powerful mathematical tool in finding exact traveling wave solutions to nonlinear partial differential equations (NLPDEs) with time-dependent coefficients. In this paper, the proposed approach is applied to study a nonhomogeneous generalized form of Benjamin-Bona-Mahony (BBM) equation with time-dependent coefficients. Explicit traveling wave solutions of the equation are obtained under certain constraints on the coefficient functions.

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Numerical Solution For The Systems Of Variable-Coefficient Coupled Burgers’ Equation By Two-Dimensional Legendre Wavelets Method, Hossein Aminikhah, Sakineh Moradian Jun 2014

Numerical Solution For The Systems Of Variable-Coefficient Coupled Burgers’ Equation By Two-Dimensional Legendre Wavelets Method, Hossein Aminikhah, Sakineh Moradian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method for solving the systems of variable-coefficient coupled Burgers’ equation is proposed. The method is based on two-dimensional Legendre wavelets. Two-dimensional operational matrices of integration are introduced and then employed to find a solution to the systems of variable-coefficient coupled Burgers’ equation. Two examples are presented to illustrate the capability of the method. It is shown that the numerical results are in good agreement with the exact solutions for each problem.

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On Some Summation Formulae For The I-Function Of Two Variables, Shantha K. Kumari, Vasudevan T. M. Nambisan Jun 2014

On Some Summation Formulae For The I-Function Of Two Variables, Shantha K. Kumari, Vasudevan T. M. Nambisan

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we aim to establish three interesting summation formulae for the I-function of two variables recently introduced in the literature. The results are derived with the help of classical summation theorems due to Watson, Dixon and Whipple. A few known results are also obtained as special cases of our main findings. Since the I-function of two variables is the most generalized function of two variables and it includes as special cases many of the known functions appearing in the literature, the results derived in this paper will therefore serve as the key formulas from which a large …

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Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani Jun 2014

Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study an impulsive fractional evolution equation with nonlinear boundary conditions. Sufficient conditions for the existence and uniqueness of solutions are established. To illustrate our results, an example is presented.

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A Ranking Method Based On Common Weights And Benchmark Point, Ali Payan, Abbas A. Noora, Farhad H. Lotfi Jun 2014

A Ranking Method Based On Common Weights And Benchmark Point, Ali Payan, Abbas A. Noora, Farhad H. Lotfi

Applications and Applied Mathematics: An International Journal (AAM)

The highest efficiency score 1 (100% efficiency) is regarded as a common benchmark for Decision Making Units (DMUs). This brings about the existence of more than one DMU with the highest score. Such a case normally occurs in all Data Envelopment Analysis (DEA) models and also in all the Common Set of Weights (CSWs) methods and it may lead to the lack of thorough ranking of DMUs. And ideal DMU based on its specific structure is a unit that no unit would do better than. Therefore, it can be utilized as a benchmark for other units. We are going to …

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On The Evolution Of Virulence, Thi Nguyen Jun 2014

On The Evolution Of Virulence, Thi Nguyen

Electronic Theses, Projects, and Dissertations

The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.

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On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews Jun 2014

On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews

Dissertations

Abstract attached as separate file.

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Smarticles: A Method For Identifying And Correcting Instability And Error Caused By Explicit Integration Techniques In Physically Based Simulations, Susan Aileen Marano Jun 2014

Smarticles: A Method For Identifying And Correcting Instability And Error Caused By Explicit Integration Techniques In Physically Based Simulations, Susan Aileen Marano

Master's Theses

Using an explicit integration method in physically based animations has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of particles most susceptible to error. This results in the need for smaller time steps than required for the majority of the system. These sections can be diverse and dynamic, quickly changing in size and location based on forces in the system. Identifying and handling these trou- blesome sections could allow …

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High-Order Short-Time Expansions For Atm Option Prices Of Exponential Lévy Models, José E. Figueroa-López, Ruoting Gong, Christian Houdré May 2014

High-Order Short-Time Expansions For Atm Option Prices Of Exponential Lévy Models, José E. Figueroa-López, Ruoting Gong, Christian Houdré

Mathematics Faculty Research

The short-time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In this work, a novel second-order approximation for at-the-money (ATM) option prices is derived for a large class of exponential Lévy models with or without Brownian component. The results hereafter shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration. In the presence of a Brownian component, the second-order term, in time-t, is of the form , with d 2 only depending …

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Applying The Poincaré Recurrence Theorem To Billiards, Aaron Smith May 2014

Applying The Poincaré Recurrence Theorem To Billiards, Aaron Smith

Honors Theses

The Poincaré recurrence theorem is one of the first and most fundamental theorems of ergodic theory. When applied to a dynamical system satisfying the theorem's hypothesis, it roughly states that the system will, within a finite amount of time, return to a state arbitrarily close to its initial state. This result is intriguing and controversial, providing a contradiction with the Second Law of Thermodynamics known as the recurrence paradox. Here, we treat a set of pool balls on a billiard table as a dynamical system that satisfies the hypotheses of the Poincaré recurrence theorem. We prove that time is a …

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Live Musical Steganography, Latia Hutchinson May 2014

Live Musical Steganography, Latia Hutchinson

Senior Theses

Live Musical Steganography is a project created as a way to combine the two typically unrelated fields of music and information security into a cohesive entity that will hopefully spark one’s imagination and inspire further development that could one day be beneficial in the world of security. For those who are unfamiliar with the term steganography, it can be defined as the art and science of preserving the integrity and confidentiality of a message by hiding the existence of that message within some larger body of data. In the field of steganography, much research and development has gone into methods …

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Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon May 2014

Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon

Masters Theses & Specialist Projects

Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further calculations. …

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Analysis Of A Partial Differential Equation Model Of Surface Electromigration, Selahittin Cinar May 2014

Analysis Of A Partial Differential Equation Model Of Surface Electromigration, Selahittin Cinar

Masters Theses & Specialist Projects

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal …

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