Applied Mathematics Commons^™

Swarm Control Through Symmetry And Distribution Characterization, Georgi Dinolov

HMC Senior Theses

Two methods for control of swarms are described. The first of these methods, the Virtual Attractive-Repulsive (VARP) method, is based on potentials defined between swarm elements. The second control method, or the abstraction method, is based on controlling the macroscopic characteristics of a swarm. The derivation of a new control law based on the second method is described. Numerical simulation and analytical interpretation of the result is also presented.

Simulations Of Surfactant Spreading, Jeffrey Wong

HMC Senior Theses

Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical …

On Morrey Spaces In The Calculus Of Variations, Kyle Fey

Department of Mathematics: Dissertations, Theses, and Student Research

We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫_Ω f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(|·|)^α(x), where h is an N-function.

Following this, we provide a characterization of the class of Young measures that can be generated by a sequence …

Being Seen: An Art Historical And Statistical Analysis Of Feminized Worship In Early Modern Rome, Olivia J. Belote

History Honors Projects

Female saints in early Christianity found their place in public veneration often through violent means, martyrdom.  These saints, while publicly suffering in the imitation of Christ, were the original agents to navigate the gendered hierarchy within the religion.  Female saints created an avenue for later female worshippers to understand Christianity on a strictly feminine level.  Through the frescoed depictions of these female saints in 18 churches throughout Rome, this paper historically and statistically analyzes how the artistic representations of female saints added to or created a space for feminized worship.

Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng

Department of Mathematics: Faculty Publications

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum’s constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.

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

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which …

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas Hanes

Mathematics and Statistics Faculty Publications and Presentations

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

A Resource Based Stage-Structured Fishery Model With Selective Harvesting Of Mature Species, T. K. Kar, Swarnakamal Misra

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have considered a model in which revenue is generated from fishing and the growth of the fish depends upon the plankton which in turn follows a logistic law of growth. Here the fish population has two stages, a juvenile stage and a mature stage and we consider the harvesting of the mature fish species. Stability and permanence of the system are discussed. Maximum sustainable yield, maximum economic yield and optimal sustainable yield are obtained and different tax policies are discussed to achieve the reference points.

Bianchi Type I Bulk Viscous Fluid String Dust Cosmological Model With Magnetic Field In Bimetric Theory Of Gravitation, M. S. Borkar, S. S. Charjan

Applications and Applied Mathematics: An International Journal (AAM)

In the presence of both magnetic field and bulk viscosity, Bianchi Type I bulk viscous fluid string dust cosmological model in Rosen’s bimetric theory of gravitation have been investigated by using the technique of Letelier and Stachel. The nature of the model is discussed in the absence of both magnetic field and bulk viscosity. To get a determinate solution, we have assumed the condition that σ is proportional to θ and ζθ = constant where σ is the shear, θ is the expansion in the model and ζ is the coefficient of bulk viscosity. Further the physical and geometrical significance …

Improved Dust Acoustic Solitary Waves In Two Temperature Dust Fluids, E. K. El-Shewy, H. G. Abdelwahed, M. I. Abo El Maaty, M. A. Elmessary

Applications and Applied Mathematics: An International Journal (AAM)

A theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear dust-acoustic solitary waves (DASWs) in an unmagnetized two types of dust fluids (one cold and the other is hot) in the presence of Bolltzmannian ions and electrons. A KdV equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (KdV-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of hot and cold dust charge …

Exact Solutions For Wind-Driven Coastal Upwelling And Downwelling Over Sloping Bathymetry, Dana Lynn Duke, Paul Derek Sinz

Mathematics

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping bathymetries. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is …

Soliton And Periodic Solutions For (3+1)-Dimensional Nonlinear Evolution Equations By Exp-Function Method, A. Borhanifar, M. M. Kabir

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, (3+1)-dimensional Jimbo-Miwa and (3+1)-dimensional potential-YTSF equations are considered and the Exp-Function method is employed to compute the exact solutions. The solutions obtained by this method are compared with the exact solutions obtained through other methods. These equations play a very important role in mathematical physics and engineering sciences. It is shown that the Exp-Function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

Analyzing Fractals, Kara Mesznik

Renée Crown University Honors Thesis Projects - All

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is self- similar, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the Contraction Mapping Theorem and shifted using linear and affine transformations.

Fractals live in something called a metric space. A metric space, denoted (X, d), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals …

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.

Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of Long-Term Viabilities Of Annuals And Perennials, Anthony Delegge

Department of Mathematics: Dissertations, Theses, and Student Research

In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present …

Parametric Lp Analysis, Allen Holder

Mathematical Sciences Technical Reports (MSTR)

Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it is important since it highlights how a problem changes as what is often estimated data varies. We present what is a modern perspective on the classical analysis of the objective value's response to parametrizations in the right-hand side and cost vector. We also mention a few applications and provide citations for further study

Maximizing Strike Planning Efficiency For A Given Class Of Targets, Necip Dirik

Theses and Dissertations

Strike planning is one of the fundamental tasks of the Turkish Air Force and involves assignment of strike aircraft to targets with a maximum level of efficiency. Therefore, planning an optimal strike plan based on the preferences of the decision maker is crucial. The efficiency of the strike plan in this research implies attacking the maximum number of targets while considering target priority and the desired level of damage on each target. Another objective is to minimize the cost of the plan. This research develops an exact model that maximizes the efficiency of the strike plan using LINGO with Excel …

The Uav Continuous Coverage Problem, Taegyun Ha

Theses and Dissertations

The purpose of this research is to develop a method to find an optimal UAV cyclic schedule to provide maximum coverage over a target area to support an ISR mission. The goal is to reach continuous coverage. UAV continuous coverage of a target area is crucial for the success of an ISR mission. Even the smallest coverage gap may jeopardize the success of the mission. Ideally it is desirable to obtain continuous coverage of a target area but the stochastic nature of the problem makes continuous coverage without gaps unlikely. However, it is still possible to obtain a high coverage …

A Multi-Objective Approach To A Bipartite Assignment Matching Problem Using Weighted Values From Multiple Contraints, Greg S. Jeong

Theses and Dissertations

US Air Force recruiters routinely assign new recruits to available jobs every month. The goal is to find the best assignments in an efficient manner. Although this problem is modeled as a bipartite assignment matching problem, it is not new to the field of Operations Research. This research presents a new approach to solve assignment matching problems given multiple side constraints. Using two multi-criteria optimization techniques, lexicographic optimization and the elastic constraint method, the assignment matching algorithm efficiently produces an optimal solution in a fraction of the time currently spent. This approach is demonstrated in assigning new USAF recruits to …

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 …

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

An Amazing Mathematical Card Trick, Arthur T. Benjamin

All HMC Faculty Publications and Research

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether …

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng

Department of Mathematics: Faculty Publications

The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle

Conference papers

This paper discusses a new approach to ‘watermarking’ digital signals using linear frequency modulated or ‘chirp’ coding. The principles underlying this approach are based on the use of a matched filter to provide a reconstruction of a chirped code that is uniquely robust in the case of signals with very low signal-to-noise ratios. Chirp coding for authenticating data is generic in the sense that it can be used for a range of data types and applications (the authentication of speech and audio signals, for example). The theoretical and computational aspects of the matched filter and the properties of a chirp …

A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott

Department of Mathematics: Dissertations, Theses, and Student Research

Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperature-dependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate …

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

Ethnomathematics In The Dominican Republic: A Mathematics Education Approach To Knowledge And Emancipation, Sofia Pablo-Hoshino

Renée Crown University Honors Thesis Projects - All

This focus of this project was to look at the extent to which ethnomathematics is being used in the mathematics curriculum in theDominican Republic. Broadly described, ethnomathematics emphasizes that the culture, history, and experiences of the students are significant and therefore should be infused into the mathematics curriculum.

I read articles and books as well as traveled to theDominican Republicto conduct qualitative research. I interviewed 32 professionals consisting of mathematics teachers, mathematics professors, and mathematics education professors from theSantiagoandSanto Domingoareas. I then volunteered at the Dominican Republic Education and Mentoring (DREAM) Project where I was able to observe and participate …