Applied Mathematics Commons^™

Resilience For Asynchronous Iterative Methods For Sparse Linear Systems, Evan Coleman

Computational Modeling & Simulation Engineering Theses & Dissertations

Large scale simulations are used in a variety of application areas in science and engineering to help forward the progress of innovation. Many spend the vast majority of their computational time attempting to solve large systems of linear equations; typically arising from discretizations of partial differential equations that are used to mathematically model various phenomena. The algorithms used to solve these problems are typically iterative in nature, and making efficient use of computational time on High Performance Computing (HPC) clusters involves constantly improving these iterative algorithms. Future HPC platforms are expected to encounter three main problem areas: scalability of code, …

On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda

Electrical & Computer Engineering Theses & Dissertations

Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …

Partially Isometric Matrices: A Brief And Selective Survey, Stephan Ramon Garcia, Matthew Okubo Patterson, William T. Ross

Department of Math & Statistics Faculty Publications

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also discuss the unitary similarity problem and several other results.

University Scholar Series: Tatiana Shubin, Tatiana Shubin

University Scholar Series

Moving in Circles: the Beauty and Joy of Mathematics for Everyone

Tatiana Shubin joined the faculty of San Jose State University in 1985 after earning her Ph.D. in Math­ematics from University of California, Santa Barbara. In 1998, she founded San Jose Math Circle and the Bay Area Math Adventures. In 2006, Shubin became a co-founder of the first Math Teachers' Circle in the US. This circle proved to be a seed which germinated to produce the entire Math Teachers' Circle Network. She launched the Navajo Nation Math Circles project in 2012, became a co-founder and co-director of the Alliance of …

Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko

Western Research Forum

One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced. For …

Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt

Theses and Dissertations

An equiangular tight frame (ETF) is a sequence of equal-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs, which are formed by restricting the characters of a finite abelian group to a difference set. Recently, it was shown that some harmonic ETFs are themselves comprised of regular simplices. In this thesis, we continue the …

Modeling The Distribution Of Lightning Strike Distances Outside A Preexisting Lightning Area, Dawn L. Sanderson

Theses and Dissertations

Air Force Instruction 91-203 (AFI 91-203) directs that a lightning warning be issued when lightning is occurring or imminent within a 5 nautical mile (NM) radius of a predetermined location or activity. The 45 Weather Squadron (WS), located on the central eastern coast of Florida, balances the safety of personnel and space launch vehicles with lost productivity of taking shelter from lightning. The primary objective of this study investigates if this 5 NM safety radius can be reduced while maintaining a desired level of safety. The research uses processed Lightning Detection and Ranging (LDAR) data to map the movement of …

An Imputation Approach To Developing Alternative Futures Of Country Conflict, Zachary J. Kane

Theses and Dissertations

Understanding what causes countries to be in a state of violent conflict is of vital importance to developing realistic national strategies on both a regional and global scale. Given these causes, it is important to understand the effects of missing data, how to impute that data, and the interrelation between data elements. Utilizing both open source data and previously generated equations that predict a country’s likelihood to transition conflict statuses, this research projects data into the future and predicts each nations’ subsequent conflict statuses. Future data is populated using a novel approach inspired by stochastic regression imputation. The replicated future …

Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose

Rose-Hulman Undergraduate Mathematics Journal

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested with an …

Field Quantization For Radiative Decay Of Plasmons In Finite And Infinite Geometries, Maryam Bagherian

USF Tampa Graduate Theses and Dissertations

We investigate field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing.

Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest.

Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the …

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …

Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, M. Hafiz Uddin, Md. Ashrafuzzaman Khan, M. Ali Akbar, Md. Abdul Haque

Karbala International Journal of Modern Science

The space time fractional modified regularized long wave equation is a model equation to the gravitational water waves in the long-wave occupancy, shallow waters waves in coastal seas, the hydro-magnetic waves in cold plasma, the phonetic waves in dissident quartz and phonetic gravitational waves in contractible liquids. In nonlinear science and engineering, the mentioned equation is applied to analyze the one way tract of long waves in seas and harbors. In this study, the closed form traveling wave solutions to the above equation are evaluated due to conformable fractional derivatives through double (G'⁄G,1⁄G)-expansion method and the Exp-function method. The existence …

Numerical Investigation Of Inclination On The Thermal Performance Of Porous Fin Heatsink Using Pseudospectral Collocation Method, George Oguntala, Gbeminiyi Sobamowo, Raed Abd-Alhameed, James Noras

Karbala International Journal of Modern Science

Numerical investigation of inclination effect on the thermal performance of a porous fin heat sink is presented. The developed thermal model is solved using pseudo-spectral collocation method (PSCM). Parametric studies are carried out using PSCM, and the thermal characterization of heat sink with the inclined porous fin of rectangular geometry is presented. Results show that heat sink of inclined porous fin exhibits higher thermal performance than heat sink of vertical porous fin operating under the same thermal conditions with the same geometrical configurations. Performance of inclined or tilted fin increases with decrease in length-thickness aspect ratio. However, increase in the …

Associations Of Hemodynamics, Morphology, And Patient Characteristics With Aneurysm Rupture Stratified By Aneurysm Location, Felicitas J. Detmer, Bong Jae Chung, Carlos Jimenez, Farid Hamzei-Sichani, David Kallmes, Christopher Putman, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Purpose: The mechanisms of cerebral aneurysm rupture are not fully understood. We analyzed the associations of hemodynamics, morphology, and patient age and gender with aneurysm rupture stratifying by location. Methods: Using image-based models, 20 hemodynamic and 17 morphological parameters were compared in 1931 ruptured and unruptured aneurysms with univariate logistic regression. Rupture rates were compared between males and females as well as younger and older patients and bifurcation versus sidewall aneurysms for different aneurysm locations. Subsequently, associations between hemodynamics and morphology and patient as well as aneurysm characteristics were analyzed for aneurysms at five locations. Results: Compared to unruptured aneurysms, …

Studies Of Boundary Layer Transition From Laminar To Turbulent, Elizabeth Spaulding

Honors Program: Senior Projects (Public)

In engineering applications, there is a strong desire to reduce energy losses due to turbulent energy production. However, the theoretical understanding of turbulent and transition flow is still lacking due to the absence of an exact mathematical solution for turbulent flow. In the current project, transition and turbulent behavior in wall-bounded flow is studied, with an emphasis on concepts from boundary layer theory. Organized structures, such as streaks, waves, and vortices, which occur in such flows, are analyzed. Especially for near-wall structures, control strategies for suppressing such structures are discussed. Using mathematical equations which govern fluid flow, models for different …

Neural Machine Translation, Quinn M. Lanners, Thomas Laurent

Honors Thesis

Neural Machine Translation is the primary algorithm used in industry to perform machine translation. This state-of-the-art algorithm is an application of deep learning in which massive datasets of translated sentences are used to train a model capable of translating between any two languages. The architecture behind neural machine translation is composed of two recurrent neural networks used together in tandem to create an Encoder Decoder structure. Attention mechanisms have recently been developed to further increase the accuracy of these models. In this senior thesis, the various parts of Neural Machine Translation are explored towards the eventual creation of a tutorial …

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

UNO Student Research and Creative Activity Fair

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet …

Parametric Natura Morta, Maria C. Mannone

The Transdisciplinary STEAM+ Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Scale-Invariance-Based Pre-Processing Drastically Improves Neural Network Learning: Case Study Of Diagnosing Lung Dysfunction In Children, Nancy Avila, Julio Urenda, Nelly Gordillo, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately treat different types of lung dysfunctions in children, it is important to properly diagnose the corresponding dysfunction, and this is not an easy task. Neural networks have been trained to perform this diagnosis, but they are not perfect in diagnostics: their success rate is 60%. In this paper, we show that by selecting an appropriate invariance-based pre-processing, we can drastically improve the diagnostic success, to 100% for diagnosing the presence of a lung dysfunction.

Lost At Sea: Introduction To Numerical Methods Through Navigation, R. Corban Harwood

Faculty Publications - Department of Mathematics

Excerpt: "The ship, El Perdido, was damaged during a storm which knocked out its main and backup power generators. Before the backup generator failed, Captain Miguel Gomez sent a distress call and the crew have been able to keep El Perdido a oat, but the ship is adrift in the Pacific Ocean off the coast of California. Thankfully, a US Coast Guard rescue operation is underway after receiving the distress call. The Coast Guard has El Perdido's last known position and has mapped out the surface water velocities in this area as slope fields for longitude (x) and latitude (y), …

Is "No Trade Theorem" Really A Paradox: Analysis Based On Decision Theory, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the challenges in foundations of finance is the so-called "no trade theorem" paradox: if an expert trader wants to sell some stock, that means that this trader believes that this stock will go down; however, the very fact that another expert trader is willing to buy it means that this other expert believes that the stock will go up. The fact that equally good experts have different beliefs should dissuade the first expert from selling -- and thus, trades should be very rare. However, in reality, trades are ubiquitous. In this paper, we show that a detailed application …

From Big Science To “Deep Science”, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The Standard Model of particle physics has accomplished a great deal including the discovery of Higgs boson in 2012. However, since the supersymmetric extension of the Standard Model has not been successful so far, some physicists are asking what alternative deeper theory could be beyond the Standard Model? This article discusses the relationship between mathematics and physical reality and explores the ways to go from Big Science to “Deep Science”.

Mhd Boundary Layer Flow And Heat Transfer To Sisko Nanofluid Past A Nonlinearly Stretching Sheet With Radiation, Macha Madhu, B. J. Gireesha, Naikoti Kishan

Applications and Applied Mathematics: An International Journal (AAM)

The steady flow of a Sisko fluid model in the presence of nanoparticles is studied. The governing partial differential equations are converted to a set of coupled non-linear ordinary differential equations by using suitable similarity transformations. Numerical solutions for the coupled non-linear ordinary differential equations are carried out by a variational finite element method. A suitable comparison has been made with previously published results in the literature as a limiting case of the considered problem. The comparison confirmed an excellent agreement. The results for the local Nusselt number are tabulated and discussed. Behavior of essential physical parameters are presented graphically …

The Influence Of Thermal Radiation On Mhd Tangent Hyperbolic Fluid Flow With Zero Normal Flux Of Nanoparticles Over An Exponential Stretching Sheet, T. Gangaiah, N. Saidulu, A. Venkata Lakshmi

Applications and Applied Mathematics: An International Journal (AAM)

This article presents the two-dimensional MHD flow of tangent hyperbolic fluid with zero normal flux of nano-particles over an exponentially stretching sheet in presence of thermal radiation. The governing system of non-linear partial differential equations along with boundary conditions for this fluid flow is converted into a system of non-linear ordinary differential equations by using appropriate similarity transformations. The reduced system is numerically solved by Runge-Kutta fourth order method with shooting technique. The effects of emerging non-dimensional parameters on velocity, temperature and nanoparticle volume fraction profiles have been discussed and presented graphically. Furthermore, the impacts of these parameters on skin …

Mhd Boundary Layer Slip Flow Over A Flat Plate With Soret And Dufour Effects, B. Shashidar Reddy, K. Saritha

Applications and Applied Mathematics: An International Journal (AAM)

The present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the …

Brownian Motion And Thermophoresis Effects On Casson Nanofluid Over A Chemically Reacting Stretching Sheet With Inclined Magnetic Field, D. Gopal, N. Kishan

Applications and Applied Mathematics: An International Journal (AAM)

The contemporary study explores the impact of thermophoresis and Brownian motion on two-dimensional magnetohydrodynamic boundary layer flow of Casson nanofluid over a chemically reacting stretching sheet. To control the heat and mass transport phenomena we also included the thermophoresis diffusion coefficient, Brownian motion parameter, and thermal radiation. The regular physical governing systems of partial differential equations are transmogrifying into ordinary differential equations. The transmogrifying governing equations are checked numerically by using Runge-Kutta-Fehlberg method. The numerical solutions for heterogeneous governing parameters such as Schmidt number, Joule heating parameter, and permeability parameter, chemical reaction parameters on velocity, temperature, and concentration profiles were …

Joule Heat Parameter Effects On Unsteady Mhd Flow Over A Stretching Sheet With Viscous Dissipation And Heat Source, Srinivas Maripala, Kishan Naikoti

Applications and Applied Mathematics: An International Journal (AAM)

In the present investigation, we studied the effects of heat source and Joule heating parameter on unsteady magneto-hydro-dynamic and heat transfer of a fluid flow over a radiating stretching sheet. The governing partial differential equations of nonlinear with boundary conditions are solved numerically by implicit finite difference method with Gauss Seidel iteration scheme. The obtained numerical solutions of velocity and temperature profiles are discussed and represented graphically. The effects of various parameters on the velocity and temperature profiles are shown graphically and numerical values of physical quantities such as the skin friction coefficient and the local Nusselt number are presented …

Optimal Homotopy Asymptotic Solution For Thermal Radiation And Chemical Reaction Effects On Electrical Mhd Jeffrey Fluid Flow Over A Stretching Sheet Through Porous Media With Heat Source, Gossaye Aliy, Naikoti Kishan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed.

Mhd Boundary Layer Flow Of Darcy-Forchheimer Mixed Convection In A Nanofluid Saturated Porous Media With Viscous Dissipation, S. Jagadha, P. Amrutha

Applications and Applied Mathematics: An International Journal (AAM)

The steady laminar viscous incompressible nanofluid flow of mixed convection and mass transfer about an isothermal vertical flat plate embedded in Darcy porous medium in the presence of magnetic field and viscous dissipation is analyzed. The governing partial differential equations are converted into ordinary differential equations by similarity transformations. The coupled nonlinear ordinary differential equations are linearized by Quasi-linearization technique. The linear ordinary differential equations are solved by using implicit finite difference scheme with the help of C-programming. Numerical calculations are carried out for different values of dimensionless parameter such as magnetic field, mixed convection parameter, inertia parameter, buoyancy ratio …

Classification Of Solutions Of Non-Homogeneous Non-Linear Second Order Neutral Delay Dynamic Equations With Positive And Negative Coefficients, N. Sikender, P. Rami Reddy, M. Chenna Krishna Reddy, S. V. Sailaja

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have studied the non-homogeneous non-linear second order neutral delay dynamic equations with positive and negative coefficients of the form classified all solutions of this type equations and obtained conditions for the existence or non-existence of solutions into four classes and these four classes are mutually disjoint. Examples are included to illustrate the validation of the main results.