Analysis Commons^™

Ruscheweyh-Goyal Derivative Of Fractional Order, Its Properties Pertaining To Pre-Starlike Type Functions And Applications, Ritu Agarwal, G. S. Paliwal

Applications and Applied Mathematics: An International Journal (AAM)

The study of the operators possessing convolution form and their properties is considered advantageous in geometric function theory. In 1975 Ruscheweyh defined operator for analytic functions using the technique of convolution. In 2005, Goyal and Goyal generalized the Ruscheweyh operator to fractional order (which we call here Ruscheweyh-Goyal differential operator) using Srivastava-Saigo fractional differential operator involving hypergeometric function. Inspired by these earlier efforts, we discuss the properties of the Ruscheweyh-Goyal derivative of arbitrary order. We define a class of pre-starlike type functions involving the Ruscheweyh-Goyal fractional derivative and obtain the inclusion relation. Further, we prove that Ruscheweyh-Goyal derivative operator preserve …

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.

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …

Memory-Modulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa

Journal of Stochastic Analysis

No abstract provided.

Some Exit Time Estimates For Super-Brownian Motion And Fleming-Viot Process, Parisa Fatheddin

Journal of Stochastic Analysis

No abstract provided.

An Improved Uniqueness Result For A System Of Sde Related To The Stochastic Wave Equation, Carl Mueller, Eyal Neuman, Michael Salins, Giang Truong

Journal of Stochastic Analysis

No abstract provided.

Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi

Q2S Enhancing Pedagogy

This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.

Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (check-ins) shall be set. With the check-ins for this assignment focus on how the group will communicate the check point and the collaboration.

The focus …

Large And Moderate Deviation Principles For Recursive Kernel Estimators For Spatial Data, Salim Bouzebda, Yousri Slaoui

Journal of Stochastic Analysis

No abstract provided.

Closed Quantum Black-Scholes: Quantum Drift And The Heisenberg Equation Of Motion, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Exit Problems For Jump-Diffusion Processes With Uniform Jumps, Mario Lefebvre

Journal of Stochastic Analysis

No abstract provided.

Ogawa Integrability And A Condition For Convergence In The Multidimensional Case, Nicolò Cangiotti, Sonia Mazzucchi

Journal of Stochastic Analysis

No abstract provided.

Mixing Coefficient For Discrete-Time Stochastic Flow, E.V. Glinyanaya

Journal of Stochastic Analysis

No abstract provided.

On A Class Of Average Preserving Semi-Martingale Laws Optimization Problems, Rémi Lassalle

Journal of Stochastic Analysis

No abstract provided.

The Semimartingale Dynamics And Generator Of A Continuous Time Semi-Markov Chain, Robert J. Elliott

Journal of Stochastic Analysis

No abstract provided.

The Isoperimetric Inequality: Proofs By Convex And Differential Geometry, Penelope Gehring

Rose-Hulman Undergraduate Mathematics Journal

The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the paper, two methods to prove this inequality will be shown and compared. First the 2-dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to prove the Brunn--Minkowski-Inequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.

Geometry Across The Curriculum, Corey Dunn

Q2S Enhancing Pedagogy

This project is designed for a multicalculus class already familiar with computing the arc length of a parameterized curve in space. The activity asks the student to first recall basic facts about arc length, and then introduces the notion of measuring lengths of vectors differently, depending on where their initial point is. This is a foundational concept in metric differential geometry, and, this activity attempts to motivate this generalization of computing lengths of vectors through this arc length activity. The activity concludes with a short discussion of basic concepts of Lorentzian geometry, including the idea that lightlike vectors have length …

Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly

Electronic Theses and Dissertations

Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …

Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu

Mathematics Faculty Research

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining R_T,n and ℛ_T,n as the basic deterministic and stochastic reproduction …

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …

Eigenvalue Statistics And Localization For Random Band Matrices With Fixed Width And Wegner Orbital Model, Benjamin Brodie

Theses and Dissertations--Mathematics

We discuss two models from the study of disordered quantum systems. The first is the Random Band Matrix with a fixed band width and Gaussian or more general disorder. The second is the Wegner $n$-orbital model. We establish that the point process constructed from the eigenvalues of finite size matrices converge to a Poisson Point Process in the limit as the matrix size goes to infinity.

The proof is based on the method of Minami for the Anderson tight-binding model. As a first step, we expand upon the localization results by Schenker and Peled-Schenker-Shamis-Sodin to account for complex energies. We …