Other Mathematics Commons^™

Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

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.

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …

Developing A Comprehensive Cognitive Model Of Math Achievement, Nina Anderson

Electronic Theses and Dissertations

Recently, downward trends have been reported in U.S. children’s math performance following school disruptions during COVID-19 amidst longstanding concerns for instruction and curricula within the subject. In support of efforts to remedy these declines, the current work presents two studies dedicated to identifying cognitive factors that are most strongly related to math performance, and which therefore offer promising potential targets for assessment and intervention. Both studies use data from the Colorado Learning Disabilities Research Center, which includes participants ages 8 - 16 and multiple well-validated measures of all constructs of interest. Study 1 tests three alternative latent cognitive models of …

The Bicomplex Tensor Product And A Bicomplex Choi Theorem, Daniel Alpay, Antonino De Martino, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we extend the concept of tensor product to the bicomplex case and use it to prove the bicomplex counterpart of the classical Choi theorem in the theory of complex matrices and operators. The concept of hyperbolic tensor product is also discussed, and we link these results to the theory of quantum channels in the bicomplex and hyperbolic case.

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

Journal of Stochastic Analysis

No abstract provided.

Book Review: How To Expect The Unexpected: The Science Of Making Predictions -- And The Art Of Knowing When Not To By Kit Yates, Mark Huber

Journal of Humanistic Mathematics

Humans think about the future all the time. Prediction is a part of how we prepare for the coming of both good and bad events in our lives. Kit Yates' book, How to expect the unexpected, concentrates primarily on the question of why prediction is difficult, and what mental shortcuts people take in prediction that can lead to incorrect results. Unfortunately, a lack of concern for details and several omissions undermine the quality of the book.

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, Abdol-Reza Mansouri, Zachary Selk

Journal of Stochastic Analysis

No abstract provided.

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.

Higher Order Operator Splitting Schemes With Complex Coefficients And Applications, Arun Banjara

LSU Doctoral Dissertations

The goal of this dissertation is to apply the concept of Lie generators for linear semigroups induced by nonlinear flows, originally developed by J. R. Dorroh and J. W. Neuberger in the 1990’s [15], to approximate solutions of initial value problems like

x′(t) = F(x(t)), x(0) = x₀, (1)

where F = (F₁,··· ,F_N), and F_i : R^N ⊃ Ω -> R^N. The method, sometimes referred to as ``Bernard Koopman’s Global Linearization Method,” traces its origins back to the works of Sophus Lie in the 1890’s [30], Gerhard Kowalewski in …

The B-Chromatic Number Of Super Cycles, Blair E. Johnson

DePaul Discoveries

The b-chromatic number, a characteristic studied in graph theory, was introduced less than 25 years ago, and while some statistics have been gathered of its properties, the b-chromatic number has yet to be explored in many graphs and circumstances. Before the Undergraduate Summer Research Program, I had no exposure to graph theory, let alone b-colorings. Throughout the program, I developed a fundamental understanding of the subject and began to pursue my own research inquiries. While this objective was difficult to attain at the beginning, I learned strategies and methods to hone my ability to delve into different graphs, and soon …

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

Journal of Stochastic Analysis

No abstract provided.

Mathematical Methods For Economics And Business Syllabus, Marian Melnyk

Open Educational Resources

This syllabus outlines an online asynchronous course introducing essential mathematical tools and techniques in economics. It spans 24 sessions covering Functions, Differentiation, Limits, Integration, and Multivariable Functions, grounded in college algebra and calculus. The course utilizes Open Educational Resources (OER) for all materials, available in text and video formats on Blackboard. Continuous assessment, including quizzes, homework, two 1-hour tests, and a final exam, ensures consistent progress. Weekly online office hours provide additional support. The primary objective is to equip students with the mathematical skills necessary for economic analysis and problem-solving.

Mixed Uncertainty Analysis On Pumping By Peristaltic Hearts Using Dempster-Shafer Theory, Yanyan He, Nicholas A. Battista, Lindsay D. Waldrop

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster–Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

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.

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …