Applied Mathematics Commons^™

Positive Solutions For Nth Order Differential Equations Under Some Conditions, S. N. Odda

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents an existence and nonexistence of positive solutions for the nonlinear boundary value problems. We prove that the nth order nonlinear differential equation has at least one positive solution by using appropriate fixed point theorems.

Analytic Investigation Of The Kp-Joseph-Egri Equation For Traveling Wave Solutions, N. Taghizadeh, M. Mirzazadeh

Applications and Applied Mathematics: An International Journal (AAM)

By means of the two distinct methods, the cosine-function method and the (G /G )  expansion method, we successfully performed an analytic study on the KP-Joseph-Egri (KP-JE) equation. We exhibited its further closed form traveling wave solutions which reduce to solitary and periodic waves.

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.

Inverse Heat Conduction Problem In A Semi-Infinite Cylinder And Its Thermal Stresses By Quasi-Static Approach, K. C. Deshmukh, S. D. Warbhe, G. D. Kedar, V. S. Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the determination of unknown temperature and thermal stresses on the curved surface of a semi-infinite circular cylinder defined as 0 ≤ r ≤ a , 0 ≤ z ≤ ∞. The circular cylinder is subjected to an arbitrary known temperature under unsteady state condition. Initially, the cylinder is at zero temperature and temperature at the lower surface is held fixed at zero. The governing heat conduction equation has been solved by using the integral transform method. The results are obtained in series form in terms of Bessel’s functions. A mathematical model has been constructed for …

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.

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 …