(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, 2024 University of Engineering and Management, India

#### (Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, 2024 University of Arkansas, Fayetteville

#### Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair

*Graduate Theses and Dissertations*

We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.

Using Fibonacci Sequence In Nature, 2024 Islamic Azad University, Isfahan, 031, Iran

#### Using Fibonacci Sequence In Nature, Muhammad Hassan Hamid Al-Sultani

*Al-Qadisiyah Journal of Pure Science*

In this work, primarily focuses of the Fibonacci sequence(FS) by compute each number(N) is the total of the two preceding numbers. The quantities(N) that are associated with the Fibonacci sequence(FS) are referred to as Fibonacci numbers(FN), which are typically written as Fn. The order(S)commonly starts from 0 and 1,and presented formula for Fibonacci sequence(FS) , understand Fibonacci numbers(FN) through solved various examples. Moreover introduced connection between the Fibonacci sequence(FS) and Golden Ratio (GR),relation between Fibonacci sequence(FS) and Geometric Sequence(GS) and so comparison between Lucas Sequence And (FS).Also give applied Fibonacci sequence(FS)in nature.

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, 2024 Wilfrid Laurier University

#### Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

*Theses and Dissertations (Comprehensive)*

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Uniform Convergence Of Deep Neural Networks With Lipschitz Continuous Activation Functions And Variable Widths, 2024 Old Dominion University

#### Uniform Convergence Of Deep Neural Networks With Lipschitz Continuous Activation Functions And Variable Widths, Yuesheng Xu, Haizhang Zhang

*Mathematics & Statistics Faculty Publications*

We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias vectors together with the Lipschitz constant are provided to ensure uniform convergence of DNNs to a meaningful function as the number of their layers tends to infinity. In the framework, special results on uniform convergence of DNNs with a fixed width, bounded widths and unbounded widths are presented. In particular, as convolutional neural networks are special DNNs with weight matrices of increasing widths, we put …

Reducing Food Scarcity: The Benefits Of Urban Farming, 2023 Brigham Young University

#### Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

*Journal of Nonprofit Innovation*

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Series Expansions Of Lambert W And Related Functions, 2023 Western University

#### Series Expansions Of Lambert W And Related Functions, Jacob Imre

*Electronic Thesis and Dissertation Repository*

In the realm of multivalued functions, certain specimens run the risk of being elementary or complex

to a fault. The Lambert $W$ function serves as a middle ground in a way, being non-representable by elementary

functions yet admitting several properties which have allowed for copious research. $W$ utilizes the

inverse of the elementary function $xe^x$, resulting in a multivalued function with non-elementary

connections between its branches. $W_k(z)$, the solution to the equation $z=W_k(z)e^{W_k(z)}$

for a "branch number" $k \in \Z$, has both asymptotic and Taylor series for its various branches.

In recent years, significant effort has been dedicated to exploring …

Asymptotic Behavior Of Random Defective Parking Functions, 2023 University of Denver

#### Asymptotic Behavior Of Random Defective Parking Functions, John T. Mann, Zecheng You, Mei Yin

*DU Undergraduate Research Journal Archive*

Suppose that *m* drivers each choose a preferred parking space in a linear car park with *n* spots. In order, each driver goes to their desired spot and parks there if possible. If the spot is already occupied then the car parks in the first available spot after that; if no such spot is available then the car leaves the street without parking. When *m > n*, there will always be defects–cars that are not able to park. Building upon the work in Cameron et al. "Counting defective parking functions," we introduce a multi-shuffle construction to defective parking functions and …

The Commutant Of The Fourier–Plancherel Transform, 2023 University of Richmond

#### The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall

*Honors Theses*

One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …

(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, 2022 Pandit Deendayal Energy University

#### (R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak

*Applications and Applied Mathematics: An International Journal (AAM)*

This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, 2022 University of Science and Technology Bannu

#### (R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

*Applications and Applied Mathematics: An International Journal (AAM)*

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

Vertex-Magic Graphs, 2022 Bridgewater State University

#### Vertex-Magic Graphs, Karissa Massud

*Honors Program Theses and Projects*

In this paper, we will study magic labelings. Magic labelings were first introduced by Sedláček in 1963 [3]. At this time, the labels on the graph were only assigned to the edges. In 1970, Kotzig and Rosa defined what are now known as edge-magic total labelings, where both the vertices and the edges of the graph are labeled. Following this in 1999, MacDougall, Miller, Slamin, and Wallis introduced the idea of vertex-magic total labelings. There are many different types of magic labelings. In this paper will focus on vertex-magictotal labelings.

The Foundations Of Mathematics: Axiomatic Systems And Incredible Infinities, 2022 Bridgewater State University

#### The Foundations Of Mathematics: Axiomatic Systems And Incredible Infinities, Catherine Ferris

*Honors Program Theses and Projects*

Often, people who study mathematics learn theorems to prove results in and about the vast array of branches of mathematics (Algebra, Analysis, Topology, Geometry, Combinatorics, etc.). This helps them move forward in their understanding; but few ever question the basis for these theorems or whether those foundations are sucient or even secure. Theorems come from our foundations of mathematics, Axioms, Logic and Set Theory. In the early20th century, mathematicians set out to formalize the methods, operations and techniques people were assuming. In other words, they were formulating axioms. The most common axiomatic system is known as the Zermelo-Fraenkel axioms with …

Vertex-Magic Total Labeling On G-Sun Graphs, 2022 Bridgewater State University

#### Vertex-Magic Total Labeling On G-Sun Graphs, Melissa Mejia

*Honors Program Theses and Projects*

Graph labeling is an immense area of research in mathematics, specifically graph theory. There are many types of graph labelings such as harmonious, magic, and lucky labelings. This paper will focus on magic labelings. Graph theorists are particularly interested in magic labelings because of a simple problem regarding tree graphs introduced in the 1990’s. The problem is still unsolved after almost thirty years. Researchers have studied magic labelings on other graphs in addition to tree graphs. In this paper we will consider vertex-magic labelings on G-sun graphs. We will give vertex-magic total labelings for ladder sun graphs and complete bipartite …

(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, 2021 Cairo University

#### (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 _{4}F_{3}(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, 2021 University of Kentucky

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

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Interpolating With Outer Functions, 2021 University of Richmond

#### Interpolating With Outer Functions, Javad Mashreghi, Marek Ptak, William T. Ross

*Department of Math & Statistics Faculty Publications*

The classical theorems of Mittag-Leffler and Weierstrass show that when *(λn)n≥1* is

a sequence of distinct points in the open unit disk *D*, with no accumulation points in

*D*, and (*wn)n≥1* is any sequence of complex numbers, there is an analytic function

*ϕ* on *D* for which* ϕ(λn) = wn*. A celebrated theorem of Carleson [2] characterizes

when, for a bounded sequence* (wn)n≥1*, this interpolating problem can be solved with

a bounded analytic function. A theorem of Earl [5] goes further and shows that when

Carleson’s condition is satisfied, the interpolating function* ϕ* can be …

Fast Multipole Methods For Wave And Charge Source Interactions In Layered Media And Deep Neural Network Algorithms For High-Dimensional Pdes, 2021 Southern Methodist University

#### 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's equations and the …

Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, 2021 Utah State University

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

*All Graduate Plan B and other Reports, Spring 1920 to Spring 2023*

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.

On A Stochastic Model Of Epidemics, 2021 The University of Southern Mississippi

#### 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.