Pricing Variance Swaps For The Discrete Bn-S Model, 2024 School of Computing and Data Science, Wentworth Institute of Technology, Boston MA, 02115, USA

#### Pricing Variance Swaps For The Discrete Bn-S Model, Semere Gebresilasie

*Journal of Stochastic Analysis*

No abstract provided.

(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.

Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, 2024 Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea

#### Errata: The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saito

*Journal of Stochastic Analysis*

No abstract provided.

Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, 2024 University of Teacher Education Fukuoka

#### Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, Toshio Nakata, Hosam Mahmoud

*Journal of Stochastic Analysis*

No abstract provided.

Probabilistic Frames And Concepts From Optimal Transport, 2024 Clemson University

#### Probabilistic Frames And Concepts From Optimal Transport, Dongwei Chen

*All Dissertations*

As the generalization of frames in the Euclidean space $\mathbb{R}^n$, a probabilistic frame is a probability measure on $\mathbb{R}^n$ that has a finite second moment and whose support spans $\mathbb{R}^n$. The p-Wasserstein distance with $p \geq 1$ from optimal transport is often used to compare probabilistic frames. It is particularly useful to compare frames of various cardinalities in the context of probabilistic frames. We show that the 2-Wasserstein distance appears naturally in the fundamental objects of frame theory and draws consequences leading to a geometric viewpoint of probabilistic frames.

We convert the classic lower bound estimates of 2-Wasserstein distance \cite{Gelbrich90, …

Short-Time Fourier Transform And Superoscillations, 2024 Chapman University

#### Short-Time Fourier Transform And Superoscillations, Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory behavior by taking the limit. It turns out that these computations lead to interesting connections with various features of time-frequency analysis such as Gabor spaces, Gabor kernels, Gabor frames, 2D-complex Hermite polynomials, and polyanalytic functions. We treat different cases depending on the …

Stochastic Solutions For Hyperbolic Pde, 2024 Queen's University - Kingston, Ontario

#### Stochastic Solutions For Hyperbolic Pde, Abdol-Reza Mansouri, Zachary Selk

*Journal of Stochastic Analysis*

No abstract provided.

Uniformly Distributing Points On A Sphere, 2024 Institute of Analysis and Number Theory

#### Uniformly Distributing Points On A Sphere, Flavio Arrigoni

*Rose-Hulman Undergraduate Mathematics Journal*

In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.

Monotone Functions On General Measure Spaces, 2024 Western University

#### Monotone Functions On General Measure Spaces, Alejandro Santacruz Hidalgo

*Electronic Thesis and Dissertation Repository*

Given a measure space and a totally ordered collection of measurable sets, called an ordered core, the notion of a core decreasing function is introduced and used to generalize monotone functions to general measure spaces. The least core decreasing majorant construction, the level function construction, and the greatest core decreasing minorant, already known for functions on the real line, are extended to this general setting. A functional description of these constructions is provided and is shown to be closely related to the pre-order relation of functions induced by integrals over the ordered core.

For an ordered core, the down space …

Analytic Properties Of Quantum States On Manifolds, 2024 The University of Western Ontario

#### Analytic Properties Of Quantum States On Manifolds, Manimugdha Saikia

*Electronic Thesis and Dissertation Repository*

The principal objective of this study is to investigate how the Kahler geometry of a classical phase space influences the quantum information aspects of the quantum Hilbert space obtained from geometric quantization and vice versa. We associated states with subsets of a product of two integral Kahler manifolds using a quantum line bundle in a particular manner. We proved that the states associated this way are separable when the subset is a finite union of products. We presented an asymptotic result for the average entropy over all the pure states on the Hilbert space H^{0}(M_{1},L_{1 …}

Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition, 2024 University of Toronto, Toronto, Canada

#### Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition, Alexander Kreinin, Vladimir V. Vinogradov

*Journal of Stochastic Analysis*

No abstract provided.

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, 2024 Louisiana State University and Agricultural and Mechanical College

#### Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

*LSU Doctoral Dissertations*

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Holomorphic Functional Calculus Approach To The Characteristic Function Of Quantum Observables, 2024 Volterra Center, Roma

#### Holomorphic Functional Calculus Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

*Journal of Stochastic Analysis*

No abstract provided.

The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, 2024 Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea

#### The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

*Journal of Stochastic Analysis*

No abstract provided.

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, 2024 NMIMS Deemed to be University

#### (R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

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

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, 2024 Sardar Vallabhbhai National Institute of Technology

#### (R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh

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

In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …

Pt-Symmetry And Eigenmodes, 2024 Portland State University

#### Pt-Symmetry And Eigenmodes, Tamara Gratcheva

*University Honors Theses*

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (*PT*) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (*P*) symmetric configuration of three smaller disks containing gain and loss media, which does not have *PT*-symmetry. In the second case, we study a *PT*-symmetric configuration …

Matrix Approximation And Image Compression, 2024 California Polytechnic State University, San Luis Obispo

#### Matrix Approximation And Image Compression, Isabella R. Padavana

*Master's Theses*

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some …

Exploring The Mandelbrot Set, 2024 Stephen F. Austin State University

#### Exploring The Mandelbrot Set, James Shirley

*Electronic Theses and Dissertations*

The Mandelbrot set is a mathematical mystery. Finding its home somewhere be-

tween holomorphic dynamics and complex analysis, the Mandelbrot set showcases

its usefulness in fields across the many realms of math—ranging from physics to nu-

merical methods and even biology. While typically defined in terms of its bounded

sequences, this thesis intends to illuminate the Mandelbrot set as a type of param-

eterization of connectivity itself, specifically that of complex-valued rational maps

of the form z → z² + c. This fully illustrated guide to the Mandelbrot set merges

the worlds of intuition and theory with a series of …

How To Explain Allen-Manandhar’S Method To Beginner Mathematicians : A Convergence Analysis Of A Hybrid Method For Variable-Coefficient Boundary Value Problems, 2024 The University of Southern Mississippi

#### How To Explain Allen-Manandhar’S Method To Beginner Mathematicians : A Convergence Analysis Of A Hybrid Method For Variable-Coefficient Boundary Value Problems, Rebecca Scariano

*Honors Theses*

In this project, analogies are employed to make complex math concepts approachable to beginners who may only have a basic understanding of calculus and linear algebra. Serving as the focal point of this project, Allen-Manandhar’s method solves an equation, known as an ordinary differential equation (ODE). The mentioned equation with its coefficients is comparable to a pie recipe with ingredients. With the outcome to a recipe seen as its solution, the solution to our pie recipe is a perfectly baked pie, as in without error. The chosen method for baking a pie then classifies as its baking approach that when …