The Binomial Transform Of P-Recursive Sequences And The Dilogarithm Function,
2020
University of Nebraska at Kearney
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,
2020
University of Washington, Tacoma
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, and test …
Controlling Aircraft Yaw Movement By Interval Type-2 Fuzzy Logic,
2020
University of Technology, Iraq
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,
2020
University of Pittsburgh
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 marks the …
Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing,
2020
The University of Texas MD Anderson Cancer Center UTHealth Graduate School of Biomedical Sciences
Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing, Alexander Davis
Dissertations & 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 Contiguous Relation On K-Generalised Hypergeometric Function,
2020
IIS (deemed to be University)
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.
Some Summation Theorems For Clausen’S Hypergeometric Functions With Unit Argument,
2020
Jamia Millia Islamia (A Central University)
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.
Symbolic Construction Of Matrix Functions In A Numerical Environment,
2020
Georgia Southern University
Symbolic Construction Of Matrix Functions In A Numerical Environment, Evan D. Butterworth
Honors College Theses
Within the field of Computational Science, the importance of programs and tools involving systems of differential equations cannot be overemphasized. Many industrial sites, such as nuclear power facilities, are unable to safely operate without these systems. This research explores and studies matrix differential equations and their applications to real computing structures. Through the use of software such as MatLab, I have constructed a toolbox, or collection, of programs that will allow any user to easily calculate a variety of matrix functions. The first tool in this collection is a program that computes the matrix exponential, famously studied and presented by …
Teaching And Learning Of Fluid Mechanics,
2020
Montclair State University
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 to arrange information so …
Certain Mathieu-Type Series Pertaining To Incomplete H-Functions,
2020
Malaviya National Institute of Technology
Certain Mathieu-Type Series Pertaining To Incomplete H-Functions, Nidhi Jolly, Manish K. Bansal, Devendra Kumar, Jagdev Singh
Applications and Applied Mathematics: An International Journal (AAM)
In the present article, we derive closed integral form expressions for a family of convergent Mathieu type a-series along with its alternating variants, whose terms contain incomplete H-functions, which are a notable generalization of familiar H-function. The results established herewith are very general in nature and provide an exquisite generalization of closed integral form expressions of aforementioned series whose terms contain H-function and Fox-Wright function, respectively. Next, we present some new and interesting special cases of our main results.
Chebyshev Type Inequalities Involving The Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function In The Kernel,
2020
Rajasthan Technical University
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.
Class Of Integrals Involving Generalized Hypergeometric Function,
2020
Wollo University
Class Of Integrals Involving Generalized Hypergeometric Function, D. L. Suthar, Teklay Hailay, Hafte Amsalu, Jagdev Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we establish some definite integrals involving generalized hypergeometric function, product of algebraic functions, Jacobi function, Legendre function and general class of polynomials. Certain special cases of the main results are also pointed out.
Finite And Infinite Integral Formulas Involving The Family Of Incomplete H-Functions,
2020
Government Engineering College
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.
Extension Of Two Parameter Gamma, Beta Functions And Its Properties,
2020
JNV University Jodhpur
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.
Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions,
2020
Jamia Millia Islamia (A Central University)
Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, M. I. Qureshi, M. Kashif Khan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we construct four summation formulas for terminating Gauss’ hypergeometric series having argument “two" and with the help of our summation formulas. We establish two quadratic transformations for Gauss’ hypergeometric function in terms of finite summation of combination of two Clausen hypergeometric functions. Further, we have generalized our quadratic transformations in terms of general double series identities as well as in terms of reduction formulas for Kampé de Fériet’s double hypergeometric function. Some results of Rathie-Nagar, Kim et al. and Choi-Rathie are also obtained as special cases of our findings.
Generalized Hermite-Based Apostol-Euler Polynomials And Their Properties,
2020
Amity University
Generalized Hermite-Based Apostol-Euler Polynomials And Their Properties, Aparna Chaturvedi, Prakriti Rai, S. Ahmad Ali
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynomials with three parameters. We have shown that there is an intimate connection between these polynomials and established their elementary properties. We also established some identities by applying the generating functions and deduce their special cases and applications.
Phylogenetic Networks And Functions That Relate Them,
2020
The University of Akron
Phylogenetic Networks And Functions That Relate Them, Drew Scalzo
Williams Honors College, Honors Research Projects
Phylogenetic Networks are defined to be simple connected graphs with exactly n labeled nodes of degree one, called leaves, and where all other unlabeled nodes have a degree of at least three. These structures assist us with analyzing ancestral history, and its close relative - phylogenetic trees - garner the same visualization, but without the graph being forced to be connected. In this paper, we examine the various characteristics of Phylogenetic Networks and functions that take these networks as inputs, and convert them to more complex or simpler structures. Furthermore, we look at the nature of functions as they relate …
Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions,
2019
Sur University College
Q-Sumudu Transforms Pertaining To The Product Of Family Of Q-Polynomials And Generalized Basic Hypergeometric Functions, V. K. Vyas, Ali A. Al –Jarrah, S. D. Purohit
Applications and Applied Mathematics: An International Journal (AAM)
The prime objective of commenced article is to determine q-Sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analog of Fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-Sumudu transform of general class of q-polynomials and q-Sumudu transforms of the basic analogs of Fox’s H-function and I-functions.
Certain Quadruple Hypergeometric Series And Their Integral Representations,
2019
Aden University- Khormaksar
Certain Quadruple Hypergeometric Series And Their Integral Representations, Maged Bin-Saad, Jihad Younis
Applications and Applied Mathematics: An International Journal (AAM)
While investigating the Exton's list of twenty one hyper-geometric functions of four variables and the Sharma's and Parihar's list of eighty three hyper-geometric functions of four variables, we noticed existence of new hyper-geometric series of four variables. The principal object of this paper is to introduce new hyper-geometric series of four variables and present a natural further step toward the mathematical integral presentation concerning these new series of four variables. Integral representations of Euler type and Laplace type involving Appell's hyper-geometric functions and the Horn's series of two variables, Exton's and Lauricella's triple functions and Sharma and Parihar hyper-geometric functions …
A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method,
2019
Ferhat Abbas Sétif University 1
A New Method To Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method, Ali Khalouta, Abdelouahab Kadem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature.
