Analysis Commons^™

An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich

Department of Mathematics: Dissertations, Theses, and Student Research

In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson

Analysis Of Bank Failure And Size Of Assets, Guancun Zhong

UNLV Theses, Dissertations, Professional Papers, and Capstones

The financial health of the banking industry is an important prerequisite for economic stability and growth. Bank failures in the United States have run in cycles largely associated with the collapse of economic bubbles. The number of bank failures has increased dramatically over the last thirty years (Halling and Hayden, 2007). In this thesis, we try to address the following two questions: 1) What is the relationship, if any, between a bank's asset size and its likelihood of failures? 2) How can we use statistical tools to predict the numbers of bank failures in the future? Various modeling techniques are …

Math Moment, Paige S. Orland

Journal of Humanistic Mathematics

A short poem comparing Exponential and Logistic functions.

Numerical Analysis And Design Optimization Of Organic Bulk Hetero-Junction Solar Cells Using The Mixed Finite Element And Arc-Length Methods, James L. Dean

Mechanical & Aerospace Engineering Theses & Dissertations

Due to the high coupling and non-linear nature of the semiconductor equations, numerical stability becomes a major problem when using a purely Newtonian numerical method in solving these equations. Presented is a robust mixed finite element formulation with application for organic solar cell devices that incorporates the arc-length predictor-corrector method to bypass such stability issues. The simulated device represents a multilayered solar cell using organic bulk hetero-junction materials including donor materials Poly[2,1,3-benzothiadiazole-4,7-diyl[4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b:3,4- b']dithiophene-2,6-diyl]] (PCPDTBT) and poly 3-hexylthiophene (P3HT) with acceptor fullerene materials [6,6]-phenyl C61 butyric acid methyl ester (PC61BM) or [6,6]-phenyl C71 butyric acid methyl ester (PC71BM) as the photoactive …

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

Coding Theorems On A Non-Additive Generalized Entropy Of Havrda-Charvat And Tsallis, Satish Kumar, Arun Choudhary

Applications and Applied Mathematics: An International Journal (AAM)

A new measure L^β_α, called average code word length of order α and type β is defined and its relationship with a generalized information measure of order α and type β is discussed. Using L^β_α , some coding theorems are proved.

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …

Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper.

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.

Renormalized Square Of White Noise Quantum Time Shift, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

Integral Representations Of Some Functionals Of Fractional Brownian Motion, Heikki Tikanmäki

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs I, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Limiting Distributions Of Galton-Watson Branching Processes With Immigration, Yoshinori Uchimura, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Wick Product And Clark-Ocone Formula In Abstract Wiener Space, Fariborz Asadian

Communications on Stochastic Analysis

No abstract provided.

Generalised Clark-Ocone Formulae For Differential Forms, Y Yang

Communications on Stochastic Analysis

No abstract provided.

Functional Itô'S Calculus And Dynamic Convex Risk Measures For Derivative Securities, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.

Chaos Representations For Marked Point Processes, Samuel N Cohen

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs Ii, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Asymptotic Spectral Analysis Of A Distance K-Graph Of N-Fold Direct Product Of A Graph, Jun Kurihara

Communications on Stochastic Analysis

No abstract provided.