Applied Mathematics Commons^™

Santa Clara Magazine, Volume 57 Number 3, Summer 2016, Santa Clara University

Santa Clara Magazine

26 - CAN’T THREAD A MOVING NEEDLE To tackle sexual assault on college campuses, a playwriting project comes to the screen. By Danae Stahlnecker ’15.

28 - MISSION CRITICAL When three students fell ill from meningitis-causing bacteria—which can be fatal—it meant the clock was ticking. And to get through this, it would take everybody’s help. By Harold Gutmann.

36 - “WHERE ARE THEY TAKING US?” A journal from the front lines of the Syrian refugee crisis in Greece. By Colleen Sinsky ’10.

40 - NO STRANGERS HERE Refugees, home, and work by Ameera Naguib ’16 from Jordan to Silicon Valley. …

Thermal Analysis In A Triple-Layered Skin Structure With Embedded Vasculature, Tumor, And Gold Nanoshells, Casey O. Orndorff

Doctoral Dissertations

In hyperthermia skin cancer treatment, the objective is to control laser heating of the tumor (target temperatures of 42-46 °C) so that the temperatures of the normal tissue surrounding the tumor remains low enough not to damage the normal tissue. However, obtaining accurate temperature distributions in living tissue related to hyperthermia skin cancer treatment without using an intruding sensor is a challenge. The objective of this dissertation research is to develop a mathematical model that can accurately predict the temperature distribution in the tumor region and surrounding normal tissue induced by laser irradiation. The model is based on a modified …

Computational Micro-Flow With Spectral Element Method And High Reynolds Number Flow With Discontinuous Galerkin Finite Element Method, Haibo Zhang

Doctoral Dissertations

In this dissertation, two numerical methods with high order accuracy, Spectral Element Method (SEM) and Discontinuous Galerkin Finite Element Method (DG-FEM), are chosen to solve problems in Computational Fluid Dynamics (CFD). The merits of these two methods will be discussed and utilized in different kinds of CFD problems. The simulations of the micro-flow systems with complex geometries and physical applications will be presented by SEM. Moreover, the numerical solutions for the Hyperbolic Flow will be obtained by DG-FEM. By solving problems with these two methods, the differences between them will be discussed as well.

Compressible Navier-Stokes equations with Electro-osmosis body …

An Interactive Likelihood For The Multi-Bernoulli Filter, Anthony B. Hoak

Master's Theses (2009 -)

In this thesis, a simple yet effective technique is presented for increasing the accuracy of multi-target tracking algorithms with a focus on sequential Monte-Carlo implementations of random finite set-based approaches. This technique, referred to throughout this work as an interactive likelihood, exploits the spatial information that exists in any given measurement, reducing the need for data association and allowing for more target interaction thereby increasing overall tracking accuracy. The interactive likelihood is constructed entirely within the random finite set framework and is integrated with a multi-Bernoulli filter. In addition, a state-of-the-art deep neural network for pedestrian detection is combined in …

Model For Computing Kinetics Of The Graphene Edge Epitaxial Growth On Copper, Mikhail Khenner

Mathematics Faculty Publications

A basic kinetic model that incorporates a coupled dynamics of the carbon atoms and dimers ona copper surface is used to compute growth of a single-layer graphene island. The speed of theisland's edge advancement on Cu[111] and Cu[100] surfaces is computed as a function of the growthtemperature and pressure. Spatially resolved concentration pro les of the atoms and dimers aredetermined, and the contributions provided by these species to the growth speed are discussed.Island growth in the conditions of a thermal cycling is studied.

Upper And Lower Solution Method For Boundary Value Problems At Resonance, Samerah Al Mosa, Paul W. Eloe

Mathematics Faculty Publications

We consider two simple boundary value problems at resonance for an ordinary differential equation. Employing a shift argument, a regular fixed point operator is constructed. We employ the monotone method coupled with a method of upper and lower solutions and obtain sufficient conditions for the existence of solutions of boundary value problems at resonance for nonlinear boundary value problems. Three applications are presented in which explicit upper solutions and lower solutions are exhibited for the first boundary value problem. Two applications are presented for the second boundary value problem. Of interest, the upper and lower solutions are easily and explicitly …

Global Attractors And Random Attractors Of Reaction-Diffusion Systems, Junyi Tu

USF Tampa Graduate Theses and Dissertations

The dissertation studies about the existence of three different types of attractors of three multi-component reaction-diffusion systems. These reaction-diffusion systems play important role in both chemical kinetics and biological pattern formation in the fast-growing area of mathematical biology.

In Chapter 2, we prove the existence of a global attractor and an exponential attractor for the solution semiflow of a reaction-diffusion system called Boissonade equations in the L² phase space. We show that the global attractor is an (H, E) global attractor with the L^∞ and H² regularity and that the Hausdorff dimension and the …

Self-Correcting Kelly Strategies For Skeptical Traders, Aaron C. Brown

International Conference on Gambling & Risk Taking

The Kelly criterion gives the appropriate bet size in idealized situations with known parameters. In financial trading situations parameters are generally unknown and the mathematical assumptions underlying the Kelly proof are not met precisely. Moreover a risk manager typically must cooperate with a trader who may be skeptical about both the Kelly criterion specifically and the concept of mathematical optimization of bet size in general.

This presentation tackles the problem of designing a Kelly-based system for setting trade risk management parameters that is both self-correcting (the system delivers good results even if initial parameter are misestimated or parameters change) and …

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Statistical Analysis And Modeling Health Data: A Longitudinal Study, Bhikhari Prasad Tharu

USF Tampa Graduate Theses and Dissertations

Lung cancer has been considered one of the leading causes of deaths while cancer re- mains the second most common cause of deaths in the USA. Understanding the behavior of a disease over time could yield important information to make decisions about the disease. Statistical models could provide crucial clues and help to make a decision about the dis- ease, budget allocation, evaluation, and implement prevention. Longitudinal trend analysis of the diseases helps to understand long term effects and nature. Cholesterol level is one of the most contributing risk factors for Coronary Heart Disease. Studying cholesterol statistically helps to know …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model …

An Averaging Method For Advection-Diffusion Equations, Nicholas Spizzirri

Dissertations, Theses, and Capstone Projects

Many models for physical systems have dynamics that happen over various different time scales. For example, contrast the everyday waves in the ocean with the larger, slowly moving global currents. The method of multiple scales is an approach for approximating the solutions of differential equations by separating out the dynamics at slower and faster time scales. In this work, we apply the method of multiple scales to generic advection-diffusion equations (both linear and non-linear, and in arbitrary spatial dimensions) and develop a method for 'averaging out' the faster scale phenomena, giving us an 'effective' solution for the slower scale dynamics. …

Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski

Dissertations, Theses, and Capstone Projects

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$.

In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also …

Stochastic Processes And Their Applications To Change Point Detection Problems, Heng Yang

Dissertations, Theses, and Capstone Projects

This dissertation addresses the change point detection problem when either the post-change distribution has uncertainty or the post-change distribution is time inhomogeneous. In the case of post-change distribution uncertainty, attention is drawn to the construction of a family of composite stopping times. It is shown that the proposed composite stopping time has third order optimality in the detection problem with Wiener observations and also provides information to distinguish the different values of post-change drift. In the case of post-change distribution uncertainty, a computationally efficient decision rule with low-complexity based on Cumulative Sum (CUSUM) algorithm is also introduced. In the time …

Why Compaction Meter Value (Cmv) Is A Good Measure Of Pavement Stiffness: Towards A Possible Theoretical Explanation, Andrzej Pownuk, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

To measure stiffness of the compacted pavement, practitioners use the Compaction Meter Value (CMV); a ratio between the amplitude for the first harmonic of the compactor's acceleration and the amplitude corresponding to the vibration frequency. Numerous experiments show that CMV is highly correlated with the pavement stiffness, but as of now, there is no convincing theoretical explanation for this correlation. In this paper, we provide a possible theoretical explanation for the empirical correlation. This explanation also explains why, the stiffer the material, the more higher-order harmonics we observe.

Approximate Analytical Solution Of Boussinesq Equation In Homogeneous Medium With Leaky Base, Rajeev K. Bansal

Applications and Applied Mathematics: An International Journal (AAM)

Approximate analytical solutions of Boussinesq equation are widely used for approximation of subsurface seepage flow in confined and unconfined aquifers under varying hydrological conditions. In this paper, we use a 2-dimensional linearized Boussinesq equation to simulate the water table fluctuations in an isotropic aquifer overlying a semi pervious bed under multiple localized recharge and withdrawal. The unconfined aquifer is considered to be in contact with two water bodies of constant water head along opposite cost lines, while the remaining two faces have no flow condition. The mathematical model is solved analytically using finite Fourier sine transform and the application of …

Black Holes Modeled As Fluid Droplets On Membranes, Anthony Bardessono

Physics

No abstract provided.

Development Of Utility Theory And Utility Paradoxes, Timothy E. Dahlstrom

Lawrence University Honors Projects

Since the pioneering work of von Neumann and Morgenstern in 1944 there have been many developments in Expected Utility theory. In order to explain decision making behavior economists have created increasingly broad and complex models of utility theory. This paper seeks to describe various utility models, how they model choices among ambiguous and lottery type situations, and how they respond to the Ellsberg and Allais paradoxes. This paper also attempts to communicate the historical development of utility models and provide a fresh perspective on the development of utility models.

The Importance Of Prediction Model Validation And Assessment In Obesity And Nutrition Research, Andrada Ivanescu, P. Li, B. George, A. W. Brown, S. W. Keith, D. Raju, D. B. Allison

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Deriving statistical models to predict one variable from one or more other variables, or predictive modeling, is an important activity in obesity and nutrition research. To determine the quality of the model, it is necessary to quantify and report the predictive validity of the derived models. Conducting validation of the predictive measures provides essential information to the research community about the model. Unfortunately, many articles fail to account for the nearly inevitable reduction in predictive ability that occurs when a model derived on one data set is applied to a new data set. Under some circumstances, the predictive validity can …

Math Department Newsletter, 2016, University Of Dayton. Department Of Mathematics

Department of Mathematics Newsletters

No abstract provided.

Splash Dynamics Of Paint On Dry, Wet, And Cooled Surfaces, David Baron, Haiyan Su, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington's experiments has now been clarified. One specific set of such recent studies, which motivates this paper, concerns the fluid dynamics behind Jackson Pollock's drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors …

Waldschmidt Constant For Squarefree Monomial Ideals, Christian Bocci, Susan Cooper, Elena Guardo, Brian Harbourne, Mike Janssen, Uwe Nagel, Alexandra Seceleanu, Adam Van Tuyl, Thanh Vu

Faculty Work Comprehensive List

Given a squarefree monomial ideal I ⊆ R = k[x1, . . . , xn], we show that α(I), the Waldschmidt constant of I, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of I. By applying results from fractional graph theory, we can then express α(I) in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of I. Moreover, expressing α(I) as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on α(I), thus verifying …

Non-Newtonian Prandtl Fluid Over Stretching Permeable Surface, N. R. Jain, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction …

A New Approach For Solving System Of Local Fractional Partial Differential Equations, Hossein Jafari, Hassan K. Jassim

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a new method for solving system of partial differential equations within local fractional derivative operators. The approximate analytical solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm. The obtained results show that the introduced approach is a promising tool for solving system of linear and nonlinear local fractional differential equations. Furthermore, we show that local fractional Laplace variational iteration method is able …

Color Image Encryption And Decryption Using Hill Cipher Associated With Arnold Transform, Rakesh Ranjan, R. K. Sharma, M. Hanmandlu

Applications and Applied Mathematics: An International Journal (AAM)

Image security over open network transmission is a big concern nowadays. This paper proposes another methodology for color image encoding and decoding using two stage Hill Cipher method which is connected with Arnold Transformation. The forgoing created a strategy for encryption and decryption of color image information and touched on just the premise of keys. In this plan, keys and the agreement of Hill Cipher (HC) are basic. Moreover, keys multiplication (pre or post) over an RGB image information framework is inevitable to know to effectively decrypt the first image information. We have given a machine simulation with a standard …

Dynamic Network Flows With Uncertain Costs Belonging To Interval, Gholam H. Shirdel, Hassan Rezapour

Applications and Applied Mathematics: An International Journal (AAM)

This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model.

Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman

Applications and Applied Mathematics: An International Journal (AAM)

Let X be a Hausdorff topological vector space and f be a real valued continuous function on X: In this paper we introduce and study the concept of f􀀀simultaneous approximation of a nonempty subset K of X as a generalization to the problem of simultaneous approximation. Further we present some results regarding f􀀀simultaneous approximation in the quotient space.

On Local Asymptotic Stability Of Q-Fractional Nonlinear Dynamical Systems, Ilknur Koca, Elif Demirci

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, locally asymptotic stability of q-fractional order nonlinear dynamical systems is introduced and studied. The sufficient conditions for local stability of such dynamical systems are obtained. Also, useful definitions of fractional order q-integrals and q-derivatives are recalled. Finally, a q-fractional order nonlinear dynamical model is considered.

Upper, Lower Solutions And Analytic Semigroups For A Model With Diffusion, Yannick T. Kouakep

Applications and Applied Mathematics: An International Journal (AAM)

In this discussion we consider an autonomous parabolic epidemic 2-dimensional system modelling the dynamics of transmission of immunizing diseases for a closed population into bounded regular domain. Our model takes into account diffusion of population with external influx as well as one class of infected individuals. We study the well-posedness two-component diffusion equations including external supplies with Neumann conditions using upper/lower solutions and analytic semigroups. In case of constant population or not, with non-oscillatory solution and constant diffusion, this problem admits travelling wave solutions whose minimum wave speed is surveyed here.