Applied Mathematics Commons^™

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

A Comparison Of Five Malaria Transmission Models: Benchmark Tests And Implications For Disease Control, Dorothy I. Wallace, Ben S. Southworth, Xun Shi, Jonathan W. Chipman, Andrew K. Githeko

Dartmouth Scholarship

Background: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models.

Methods: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting …

Analysis Of A Mathematical Model For The Heave Motion Of A Micro Aerial Vehicle With Flexible Wings Having Non-Local Damping Effects, Jonathan B. Walters

Doctoral Dissertations

In this work we analyze a one dimensional model for a flexible wing micro aerial vehicle which can undergo heaving motion. The vehicle is modeled with a non-local type of internal damping known as spatial hysteresis as well as viscous external damping. We present a rigorous theoretical analysis of the model proving that the linearly approximated system is well-posed and the first order feedback system operators generate exponentially stable C0–semigroups.

Furthermore, we present numerical simulations of control designs used on the linearly approximated model to control the associated nonlinear model in two different strategies. The first strategy used to …

Using Second-Order Probabilities To Make Maximum Entropy Approach To Copulas More Reasonable, Hung T. Nguyen, Vladik Kreinovich, Berlin Wu

Departmental Technical Reports (CS)

Copulas are a general way of describing dependence between two or more random variables. When we only have partial information about the dependence, i.e., when several different copulas are consistent with our knowledge, it is often necessary to select one of these copulas. A frequently used method of selecting this copula is the maximum entropy approach, when we select a copula with the largest entropy. However, in some cases, the maximum entropy approach leads to an unreasonable selection -- e.g., even if we know that the two random variables are positively correlated, the maximum entropy approach completely ignores this information. …

Quasisymmetric (K; L)-Hook Schur Functions, Sarah K. Mason, Elizabeth Niese

Mathematics Faculty Research

We introduce a quasisymmetric generalization of Berele and Regev's (k,l)-hook Schur functions. These quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. The quasisymmetric hook Schur functions can be defined as the generating function for a certain set of composition tableaux on two alphabets. We will look at the combinatorics of the quasisymmetric hook Schur functions, including an analogue of the RSK algorithm and a generalized Cauchy Identity.

A Genetic Algorithm-Based Feature Selection, Oluleye Babatunde, Leisa Armstrong, Jinsong Leng, Dean Diepeveen

Grain and Other Field Crops Research Articles

This article details the exploration and application of Genetic Algorithm (GA) for feature selection. Particularly a binary GA was used for dimensionality reduction to enhance the performance of the concerned classifiers. In this work, hundred (100) features were extracted from set of images found in the Flavia dataset (a publicly available dataset). The extracted features are Zernike Moments (ZM), Fourier Descriptors (FD), Lengendre Moments (LM), Hu 7 Moments (Hu7M), Texture Properties (TP) and Geometrical Properties (GP). The main contributions of this article are (1) detailed documentation of the GA Toolbox in MATLAB and (2) the development of a GA-based feature …

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.

A Likelihood Approach To Estimate The Number Of Co-Infections, Kristian A. Schneider, Ananias A. Escalante

Harold W. Manter Laboratory of Parasitology: Library Materials

Article abstract:

The number of co-infections of a pathogen (multiplicity of infection or MOI) is a relevant parameter in epidemiology as it relates to transmission intensity. Notably, such quantities can be built into a metric in the context of disease control and prevention. Having applications to malaria in mind, we develop here a maximum-likelihood (ML) framework to estimate the quantities of interest at low computational and no additional costs to study designs or data collection. We show how the ML estimate for the quantities of interest and corresponding confidence-regions are obtained from multiple genetic loci. Assuming specifically that infections are …

Studies Of A Mathematical Model For Generating Rhythmic Behavior With A Simple Brain, Juan C. Morales

Theses and Dissertations - UTB/UTPA

The rhythmic behavior of feeding in the pond snail, Lymnaea stagnalis can be described computationally by a model describing its central pattern generator network (CPG). The model includes coupled Hodgkin-Huxley type nonlinear ordinary differential equations describing four neurons connected by both inhibitory and excitatory synapses. We studied the system’s dependence on current parameters to generate periodic behavior. We also considered the effect of eliminating specific connections from the network. In addition, experiments on the biological system were used to motivate application of the model in Parkinson’s disease.

Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Duality Of The Weak Parallelogram Laws On Banach Spaces, Charles Benjamin Harris

Mathematics & Statistics Theses & Dissertations

The first chapter of this thesis concerns the stability and convergence of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation

u'(t) + ∫^t₀ β (t--s) Au(s) ds = 0, t ≥ 0, u( 0) = u_0,

which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space and β(t) is locally integrable, nonnegative, nonincreasing, convex, with -- β'(t) and β''(t) convex. We establish …

A Discrete Density-Dependent Model Of The Solanum Virus, James Morgan

All Student Theses and Dissertations

Compartmental modeling has been used to model infectious diseases for roughly 100 years. Since 2009, several papers have modeled zombie outbreak using this method with various results. This paper will develop a unique model for the spread of the The Walking Dead zombie virus throughout the contiguous United States. Frequency dependent and density dependent transmission will be discussed, and density dependent transmission will be shown to be the appropriate choice for this model. Constant parameters, such as birth rate, bite rate, death rate, and turning rate will be determined using real-world and fictional data. After developing a basic model, modifications …

Monte Carlo Simulation: When Should A Contestant Stop Spinning?, Gregory Horn

All Student Theses and Dissertations

Every episode of the popular game show The Price Is Right contains two rounds called The Showcase Showdown or The Big Wheel. During these rounds, three contestants spin a large wheel that consists of monetary values from five cents through one dollar in 5 cent increments. The object of this game is to get closest to one dollar without going over in one or a combination of two spins. The two winners of these rounds get to compete for the most valuable prizes at the end of each show. Monte Carlo simulation will be used to find the range of …

Application Of Remotely Sensed Rainfall Data In Rainfall-Runoff Modelling. A Case Of Pangani River Basin, Tanzania, Joel Nobert

Tanzania Journal of Engineering and Technology (TJET)

Rainfall runoff modelling in a river basin is vital for number of hydrologic application including water resources assessment. However, rainfall data from sparse gauging stations are usually inadequate for modelling which is a major concern in Tanzania. This study presents the results of comparison of Tropical Rainfall Measuring Mission (TRMM) satellite rainfall products at daily and monthly time-steps with ground stations rainfall data; and explores the possibility of using satellite rainfall data for rainfall runoff modelling in Pangani River Basin, Tanzania. Statistical analysis was carried out to find the correlation between the ground stations data and TRMM estimates. It was …

Accuracy Of Dem-Based Topographic Data In Flood Inundation Modelling: A Case Of Wami River, Tanzania, Preksedis Ndomba

Tanzania Journal of Engineering and Technology (TJET)

Ihe objective of this Biper is to evaluate and further convnent on the accuracy of the DEW- based topographic data us input in flood mchdelling. Recent studies have indicated that hydraulic of the modified sections based on high resolution are geometrically and hydraulically similar to the measured ones, In the study hydraulic modelling intended to guide a developnent project whereby a protection embankment is contemplated. Therefore, accuracy in terns of positioning/alignment of natural features such as river banks and heights/elevarions was imperative m arrain. In order m achieve these, accuracy of various topographic data sources were qualitatively and/or quantitatively before …

Mathematically Modeling Fetal Electrocardiograms, Samuel Estes, Kiersten Utsey, Erick Kalobwe

Pursuit - The Journal of Undergraduate Research at The University of Tennessee

Abstract

Some of the most common and fatal birth defects are those related to the heart. In adults, possible heart conditions are often identified through the use of an electrocardiogram (ECG). However, due to the presence of other signals and noise in the recording, fetal electrocardiography has not yet proven effective in diagnosing these defects. This paper develops a mathematical model of three-dimensional heart vector trajectories, which was used to generate synthetic maternal and fetal ECG signals. The dipole model is a useful simplification in which the electrical activity of the heart is viewed as a single time-varying vector originating …

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 …

Different Formulations Of The Orthogonal Array Problem And Their Symmetries, Andrew J. Geyer

Theses and Dissertations

Modern statistical experiments routinely feature a large number of input variables that can each be set to a variety of different levels. In these experiments, output response changes as a result of changes in the individual factor level settings. Often, an individual experimental run can be costly in time, money or both. Therefore, experimenters generally want to gain the desired information on factor effects from the smallest possible number of experimental runs. Orthogonal arrays provide the most desirable designs. However, finding orthogonal arrays is a very challenging problem. There are numerous integer linear programming formulations (ILP) in the literature whose …

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 …

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.

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 …

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 …

On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews

Dissertations

Abstract attached as separate file.

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 …

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.

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.

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.

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 …

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 …

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

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.