Applied Mathematics Commons^™

Multidimensional Inverse Boundary Value Problem For A System Of Hyperbolic Equations, M. A. Guliev, E. M. El-Hadidi

Applications and Applied Mathematics: An International Journal (AAM)

In the paper we investigate the solvability of the inverse multidimensional boundary value problem for the system of hyperbolic type equations. A method is proposed to reduce the considered problem to some non infinite system of differential equations. The proposed method allows one to prove the existence and uniqueness theorems for the multidimensional inverse boundary value problems in the class of the functions with bounded smoothness.

Acms 18th Biennial Conference Proceedings, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Association of Christians in the Mathematical Sciences 18th Biennial Conference Proceedings, June 1-4, 2011, Westmont College, Santa Barbara, CA.

Exact Travelling Wave Solutions For Konopelchenko-Dubrovsky Equation By The First Integral Method, N. Taghizadeh, M. Mirzazadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the first integral method is used to construct exact travelling wave solutions of Konopelchenko-Dubrovsky equation. The first integral method is algebraic direct method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to non-integrable equations as well as to integrable ones. This method is based on the theory of commutative algebra.

Constraint Qualifications And Optimality Conditions For Nonconvex Semi-Infinite And Infinite Programs, Boris S. Mordukhovich, T T. A. Nghia

Mathematics Research Reports

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We extend the classical Mangasarian-Fromovitz and Farkas-Minkowski constraint qualifications to such infinite and semi-infinite programs. The new qualification conditions are used for efficient computing the appropriate normal cones to sets of feasible solutions for these programs by employing advanced …

Shooting Neural Networks Algorithm For Solving Boundary Value Problems In Odes, Kais I. Ibraheem, Bashir M. Khalaf

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to use Neural Networks for solving boundary value problems (BVPs) in Ordinary Differential Equations (ODEs). The Neural networks use the principle of Back propagation. Five examples are considered to show effectiveness of using the shooting techniques and neural network for solving the BVPs in ODEs. The convergence properties of the technique, which depend on the convergence of the integration technique and accuracy of the interpolation technique are considered.

Exact Travelling Wave Solutions Of The Coupled Klein-Gordon Equation By The Infinite Series Method, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we employ the infinite series method for travelling wave solutions of the coupled Klein-Gordon equations. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons and periodic solutions.

A Group-Permutation Algorithm To Solve The Generalized Sudoku, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sudoku can be generalized to squares whose dimensions are n^2 × n^2 , where n ≥ 2, using various symbols (numbers, letters, mathematical symbols, etc.), written just one time on each row and on each column; and the large square is divided into n 2 small squares with the side n × n and each will contain all n 2 symbols written only once. In this paper we present an elementary solution for the generalized sudoku based on a group-permutation algorithm.

Predictability Time Of Chaotic Cosmologies, John Max Wilson

Mahurin Honors College Capstone Experience/Thesis Projects

We examine the predictability time scales for a cosmological model from the Einstein field equations coupled to the Klein-Gordon equations for a spin zero scalar field with an interaction potential V(φ). The cosmological equations resulting from this coupling are nonlinear in the scale cosmic parameter and scalar field, thus exhibiting characteristics of chaos. The equations can be linearized in the neighborhood of equilibrium points and then diagonalized to yield its Lyapunov exponents. One e-folding time of the system is then found to estimate the predictability time. This time is compared to the Big Rip time theorized by Yurov, Moruno, and …

A Parametric Analysis Of Domestic Electricity Consumption Patterns In Ireland, Fintan Mcloughlin, Aidan Duffy, Michael Conlon

Conference Papers

This paper reports findings from a study of electrical load profiles obtained from a survey of a representative cross section of approximately 4,000 Irish dwellings. Electricity demand was recorded at half-hourly intervals for each dwelling over a six month period from 1st July 2009 to 31st December 2009. Descriptive statistics are shown for each electrical parameter such as mean, maximum demand, load factor and time of use (ToU) of electricity consumption. The mean power demand and daily mean load factor of the sample was 0.512kW and 23.43% respectively for all dwellings over the monitoring period. A mean daily maximum demand …

Modeling Human Immune Response To The Lyme Disease-Causing Bacteria, Yevhen Rutovytskyy

Honors Scholar Theses

The purpose of this project is to develop and analyze a mathematical model

for the pathogen-host interaction that occurs during early Lyme disease.

Based on the known biophysics of motility of Borrelia burgdorferi and a

simple model for the immune response, a PDE model was created which tracks

the time evolution of the concentrations of bacteria and activated immune

cells in the dermis. We assume that a tick bite inoculates a highly

localized population of bacteria into the dermis. These bacteria can

multiply and migrate. The diffusive nature of the migration is assumed and

modeled using the heat equation. Bacteria …

Optimization And Simulation Of An Evolving Kidney Paired Donation (Kpd) Program, Yijiang Li, Jack Kalbfleisch, Peter Xuekun Song, Yan Zhou, Alan Leichtman, Michael Rees

The University of Michigan Department of Biostatistics Working Paper Series

The old concept of barter exchange has extended to the modern area of living-donor kidney transplantation, where one incompatible donor-candidate pair is matched to another pair with a complementary incompatibility, such that the donor from one pair gives an organ to a compatible candidate in the other pair and vice versa. Kidney paired donation (KPD) programs provide a unique and important platform for living incompatible donor-candidate pairs to exchange organs in order to achieve mutual benefit. We propose a novel approach to organizing kidney exchanges in an evolving KPD program with advantages, including (i) it allows for a more exible …

Rated Extremal Principles For Finite And Infinite Systems, Hung M. Phan, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints.

Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers

HMC Senior Theses

The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …

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.

Verification Of Solutions To The Sensor Location Problem, Chandler May

HMC Senior Theses

Traffic congestion is a serious problem with large economic and environmental impacts. To reduce congestion (as a city planner) or simply to avoid congested channels (as a road user), one might like to accurately know the flow on roads in the traffic network. This information can be obtained from traffic sensors, devices that can be installed on roads or intersections to measure traffic flow. The sensor location problem is the problem of efficiently locating traffic sensors on intersections such that the flow on the entire network can be extrapolated from the readings of those sensors. I build on current research …

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 …

Generalized Bathtub Hazard Models For Binary-Transformed Climate Data, James Polcer

Masters Theses & Specialist Projects

In this study, we use a hazard-based modeling as an alternative statistical framework to time series methods as applied to climate data. Data collected from the Kentucky Mesonet will be used to study the distributional properties of the duration of high and low-energy wind events relative to an arbitrary threshold. Our objectiveswere to fit bathtub models proposed in literature, propose a generalized bathtub model, apply these models to Kentucky Mesonet data, and make recommendations as to feasibility of wind power generation. Using two different thresholds (1.8 and 10 mph respectively), results show that the Hjorth bathtub model consistently performed better …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

This dissertation presents a redefined operator splitting method used in solving semilinear parabolic partial differential equations. As one such form, the reaction-diffusion equation is highly prevalent in mathematical modeling. Besides being physically meaningful as a separation of two distinct physical processes in this equation, operator splitting simplifies the solution method in several ways. The super-linear speed-up of computations is a rewarding simplification as it presents great benefits for large-scale systems. In solving these semilinear equations, we will develop a condition for oscillation-free methods, a condition independent of the usual stability condition. This numerical consideration is important to fully embody our …

Color Image Noise Reduction With The Total Variation Model And Proximity Operators, Aaron Katchen

Renée Crown University Honors Thesis Projects - All

The following paper discusses how efficient and effective color image noise reduction may be achieved through the use of mathematic numerical analysis. Digital image noise is a longstanding problem for which efficient and effective solutions are critical to the advancement of the field of digital imaging. Micchelli-Shen-Xu [3] used the Total Variation Model in conjunction with proximity operators to propose a set of algorithms to effectively and efficiently solve for noisy grayscale images. They proposed the use of the proximity operator in anisotropic and isotropic total variation in fixed point algorithms. The following paper will discuss their algorithms as well …