Special Functions Commons^™

(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali

Applications and Applied Mathematics: An International Journal (AAM)

This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type ₄F₃(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.

Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Fast Multipole Methods For Wave And Charge Source Interactions In Layered Media And Deep Neural Network Algorithms For High-Dimensional Pdes, Wenzhong Zhang

Mathematics Theses and Dissertations

In this dissertation, we develop fast algorithms for large scale numerical computations, including the fast multipole method (FMM) in layered media, and the forward-backward stochastic differential equation (FBSDE) based deep neural network (DNN) algorithms for high-dimensional parabolic partial differential equations (PDEs), addressing the issues of real-world challenging computational problems in various computation scenarios.

We develop the FMM in layered media, by first studying analytical and numerical properties of the Green's functions in layered media for the 2-D and 3-D Helmholtz equation, the linearized Poisson--Boltzmann equation, the Laplace's equation, and the tensor Green's functions for the time-harmonic Maxwell ...

On A Stochastic Model Of Epidemics, Rachel Prather

Master's Theses

This thesis examines a stochastic model of epidemics initially proposed and studied by Norman T.J. Bailey [1]. We discuss some issues with Bailey's stochastic model and argue that it may not be a viable theoretical platform for a more general epidemic model. A possible alternative approach to the solution of Bailey's stochastic model and stochastic modeling is proposed as well. Regrettably, any further study on those proposals will have to be discussed elsewhere due to a time constraint.

Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio

All Graduate Plan B and other Reports

Changes in the spatial distribution of vegetation respond to variations in the production and transportation mechanisms of seeds at different locations subject to heterogeneities, often because of soil characteristics. In semi-arid environments, the competition for water and nutrients pushes the superficial plant’s roots to obtain scarce resources at long ranges. In this report, we assume that vegetation biomass interacts with itself in two different ways, facilitation and inhibition, depending on the relative distances. We present a 1-dimensional Integro-difference model to represent and study the emergence of patterns in the distribution of vegetation.

Bessel-Maitland Function Of Several Variables And Its Properties Related To Integral Transforms And Fractional Calculus, Ankita Chandola, Rupakshi M. Pandey, Ritu Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In the recent years, various generalizations of Bessel function were introduced and its various properties were investigated by many authors. Bessel-Maitland function is one of the generalizations of Bessel function. The objective of this paper is to establish a new generalization of Bessel-Maitland function using the extension of beta function involving Appell series and Lauricella functions. Some of its properties including recurrence relation, integral representation and differentiation formula are investigated. Moreover, some properties of Riemann-Liouville fractional operator associated with the new generalization of Bessel-Maitland function are also discussed.

Axisymmetric Thermoelastic Response In A Semi-Elliptic Plate With Kassir’S Nonhomogeneity In The Thickness Direction, Sonal Bhoyar, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of ...

Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we prove the Hyers-Ulam stability of the 2-dimensional Pexider quadratic functional equation in fuzzy normed spaces. Moreover, we prove the Hyers-Ulam stability of this functional equation, where f, g are functions defined on an abelian group with values in a topological vector space.

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations 𝑥=𝐴𝑐𝑜𝑠(𝑎𝑡) and 𝑦=𝐵𝑠𝑖𝑛(𝑏𝑡) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their ...

The Binomial Transform Of P-Recursive Sequences And The Dilogarithm Function, Stephanie L. Harshbarger, Barton L. Willis

Applications and Applied Mathematics: An International Journal (AAM)

Using a generalized binomial transform and a novel binomial coefficient identity, we will show that the set of p-recursive sequences is closed under the binomial transform. Using these results, we will derive a new series representation for the dilogarithm function that converges on its domain of analyticity. Finally, we will show that this series representation results in a scheme for numerical evaluation of the dilogarithm function that is accurate, efficient, and stable.

Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

Access*: Interdisciplinary Journal of Student Research and Scholarship

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model ...

Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic, Yamama Shafeek, Laith Majeed, Rasha Naji

Emirates Journal for Engineering Research

Aircraft yaw movement is essential in maneuvering; it has been controlled by some methods which achieved tracking but not fast enough. This paper performs the dynamic modeling of aircraft yaw movement and develops PI and PI-like interval type-2 fuzzy logic controller for the model. The mathematical model is derived by inserting the parameters values of single-engine Navion aircraft into standard equations. Using Matlab/ Simulink platform, the controllers' effectivity is tested and verified in two different cases; system without disturbance and when system is disturbed by some wind gust to investigate the system robustness. Simulation results show that PI controller response ...

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which ...

Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing, Alexander Davis

The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences Dissertations and Theses (Open Access)

Tumor cells have heterogeneous genotypes, which drives progression and treatment resistance. Such genetic intratumor heterogeneity plays a role in the process of clonal evolution that underlies tumor progression and treatment resistance. Single-cell DNA sequencing is a promising experimental method for studying intratumor heterogeneity, but brings unique statistical challenges in interpreting the resulting data. Researchers lack methods to determine whether sufficiently many cells have been sampled from a tumor. In addition, there are no proven computational methods for determining the ploidy of a cell, a necessary step in the determination of copy number. In this work, software for calculating probabilities from ...

Some Summation Theorems For Clausen’S Hypergeometric Functions With Unit Argument, M. I. Qureshi, Mohammad Shadab

Applications and Applied Mathematics: An International Journal (AAM)

Motivated by the work on hypergeometric summation theorems, we establish new summation formula for Clausen’s hypergeometric function with unit argument in terms of pi and natural logarithms of some rational and irrational numbers. For the application purpose, we derive some new and modified summation theorems for Clausen’s hypergeometric functions using our new formula.

Some Contiguous Relation On K-Generalised Hypergeometric Function, Ekta Mittal, Sunil Joshi, Sona Kumari

Applications and Applied Mathematics: An International Journal (AAM)

In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations.

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way ...

Finite And Infinite Integral Formulas Involving The Family Of Incomplete H-Functions, Manish K. Bansal, Devendra Kumar, Jagdev Singh, Kottakkaran Sooppy Nisar

Applications and Applied Mathematics: An International Journal (AAM)

Recent research focuses on the integral representations of the various type of special functions due to their potential applicability in different disciplines. In this line, we deal with several finite and infinite integrals involving the family of incomplete H-functions. Further, we point out some known and new special cases of these integrals. Finally, we establish the integral representation of incomplete H-functions.

Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel, S. D. Purohit, N. Jolly, M. K. Bansal, Jagdev Singh, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Recently, several authors have investigated Chebyshev type inequalities for numerous fractional integral operators. Being motivated by the work done by earlier researchers and their numerous applications in probability, transform theory, numerical quadrature, statistical problems and its significance in fractional boundary value problems. We aim to evaluate Chebyshev type inequalities involving fractional integral operator containing multi-index Mittag-Leffler function in the kernel. Admissible connections of the results mentioned in this article to those associated with previously established familiar fractional integral operators have been pointed out.

Extension Of Two Parameter Gamma, Beta Functions And Its Properties, Kuldeep S. Gehlot, Kottakkaran S. Nisar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce the extension of the p-k Gamma function and the p-k Beta function. This extension of the p-k Gamma function is named as p-k-b Gamma function and an extension of the beta function is p-k-b Beta function. The new extension of the Gamma and Beta function has satisfied the usual properties. Also, we prove several identities of these functions.