Physical Sciences and Mathematics Commons^™

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.

Exact Optimal Solution Of Fuzzy Critical Path Problems, Amit Kumar, Parmpreet Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a fuzzy critical path problem is chosen to show that the results, obtained by using the existing method [Liu, S.T.: Fuzzy activity times in critical path and project crashing problems. Cybernetics and Systems 34 (2), 161-172 (2003)], could be improved to reflect, more appropriate real life situations. To obtain more accurate results of fuzzy critical path problems, a new method that modifies the existing one is proposed here. To demonstrate the advantages of the proposed method it is used to solve a specific fuzzy critical path problem.

Exact Soliton Solutions For Second-Order Benjamin-Ono Equation, Nasir Taghizadeh, Mohammad Mirzazadeh, Foroozan Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The homogeneous balance method is proposed for seeking the travelling wave solutions of the second-order Benjamin-Ono equation. Many exact traveling wave solutions of second-order Benjamin-Ono equation, which contain soliton like and periodic-like solutions are successfully obtained. This method is straightforward and concise, and it may also be applied to other nonlinear evolution equations.

Mathematical Modeling, A Small Step In A Right Direction, Reza D. Noubary

Applications and Applied Mathematics: An International Journal (AAM)

Models developed by mathematicians/statisticians based on criterion such as goodness of fit often leads to a “best” model only for the data utilized. Moreover the parameters in such models often do not have physical interpretations and as such their validity cannot be checked by other means. This article makes argument against modeling processes that do not incorporate information from discipline related to the origin of data and presents an example to demonstrate benefits of doing so.

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.

The Multisoliton Solutions Of Some Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we obtain multisoliton solutions of the Camassa-Holm equation and the Joseph- Egri (TRLW) equation by using the formal linearization method. The formal linearization method is an efficient instrument for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones.

Algorithms To Solve Singularly Perturbed Volterra Integral Equations, Marwan T. Alquran, Bilal Khair

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the Differential Transform Method (DTM) and Variational Iterative Method (VIM) to develop algorithms for solving singularly perturbed volterra integral equations (SPVIEs). The study outlines the significant features of the two methods. A comparison between the two methods for the solution of SPVIs is given for three examples. The results show that both methods are very efficient, convenient and applicable to a large class of problems.

Asean+3 Monetary And Financial Integration: What We Need For A New Framework?, Reza Moosavi Mohseni

Reza Moosavi Mohseni

In this paper at first we investigate the viability of creating an optimum currency area (OCA) in the East Asia. Then we try to find the currency bloc which is more suitable for this region. A ten-variable VAR model employed to estimate the underlying shocks and test the symmetry of them. The results show that forming an OCA for all of the countries in the region is costly and difficult to sustain. But at first five countries called Japan, China, Korea, Malaysia, and the Philippine with symmetric supply shocks can create the single currency area. The rest of the countries …

Generalized Exponential Euler Polynomials And Exponential Splines, Tian-Xiao He

Tian-Xiao He

Here presented is constructive generalization of exponential Euler polynomial and exponential splines based on the interrelationship between the set of concepts of Eulerian polynomials, Eulerian numbers, and Eulerian fractions and the set of concepts related to spline functions. The applications of generalized exponential Euler polynomials in series transformations and expansions are also given.

A Practical Approach To Prescribe The Amount Of Used Insulin Of Diabetic Patients, Mehran Mazandarani, Ali Vahidian Kamyad

Mehran Mazandarani

To assess of diabetes mellitus, extensive mathematical studies have been done to date. Up to now, many crisp mathematical models have described this phenomenon, but with the aim of controlling and modelling diabetes mellitus in more realistic and practical form, the models that consider most aspects of the problem should be considered. This kind of attitude to the disease can be modelling with mathematics called fuzzy mathematics. In this paper, modelling of diabetes mellitus type 2 has been studied by using IF-Then fuzzy rules based on the medical information of diabetic patients of Parsian clinic in Mashhad-Iran who were treated …

On The Derivation Of Boundary Conditions From The Global Principles Of Continuum Mechanics, Gerald G. Kleinstein

Gerald G. Kleinstein

We consider the motion of a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. The boundary conditions, such as the no-slip condition and the condition of an isothermal wall, applied in the solution of the system of differential equations describing these motions, are currently assumed to be an approximation derived from experimental observation rather than an exact law. It is the purpose of this paper to show that the boundary conditions at a material interface between a fluid and a solid are derivable from the global principles of balance of continuum mechanics and the …

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 …

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 …

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.

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 …

Global Well-Posedness For A Nonlinear Wave Equation With P-Laplacian Damping, Zahava Wilstein

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation deals with the global well-posedness of the nonlinear wave equation
u_tt − Δu − Δ_pu_t = f (u) in Ω × (0,T),
{u(0), u_t(0)} = {u₀,u₁} ∈ H¹₀ (Ω) × L ² (Ω),
u = 0 on Γ × (0, T ),
in a bounded domain Ω ⊂ ℜ ⁿ with Dirichlét boundary conditions. The nonlinearities f (u) acts as a strong source, which is allowed to …

Emergence Of Switch-Like Behavior In A Large Family Of Simple Biochemical Networks, Dan Siegal-Gaskins, Maria K. Mejia-Guerra, Gregory D. Smith, Erich Grotewold

Arts & Sciences Articles

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the …

The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji

Faculty Articles

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

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 …

Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He

Scholarship

We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.

Energy Efficient Compressed Sensing In Wireless Sensor Networks Via Random Walk, Robert Brian Fletcher

Masters Theses and Doctoral Dissertations

In this paper, we explore the problem of data acquisition using compressive sensing (CS) in wireless sensor networks. Unique properties of wireless sensor networks require we minimize communication cost for efficient power usage. At first, a compressive distributed sensing (CDS) algorithm is proposed but is then modified to decrease communication costs. The final algorithm presented is compressive distributed sensing with random walk CDS(RW); an algorithm that combines the data gathering and projection generation process of CDS.CDS(RW) uses rateless encoding, graph algorithms, and belief propagation decoding to improve upon the communication cost associated with CDS. In the end, we show that …

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 …

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.

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 …

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 …

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.

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …