Mathematics Commons^™

Supershift Properties For Nonanalytic Signals, Fabrizio Colombo, Irene Sabadini, Daniele Carlo Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this perspective, this is a notion that might have significant applications. This paper will provide an up to date report on the complex connections between the concept of supershift and that of analyticity.

An Analysis On The Time Effectiveness Of Speeding While Driving A Vehicle, Joy Skaggs

ATU Scholars Symposium

Speeding is responsible for roughly a third of all crashes, often coming at a deadly cost. The National Highway Traffic Safety Administration reports many negative consequences, such as a greater likelihood of loss of vehicle control, reduced protection equipment effectiveness, increased stopping distance, crash severity, and fuel consumption (National Highway Traffic Safety Administration, n.d.). Yet despite these costs, drivers continue to speed. In fact, in our fast paced world, speeding is so normalized that it’s uncommon to encounter a driver following the speed limit. Hawaiian psychology professor Leon James explains it best: people have twisted their definitions of speeding to …

Analyticity And Supershift With Regular Sampling, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the interval. In this paper, we study the relation between supershift and real analyticity. We use a classical result due to Serge Bernstein to show that real analyticity for a complex-valued function implies a strong form of supershift. On the other hand, we use a parametric version of a result by Leonid Kantorovitch to show that the converse is not true. …

My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo

Journal of Stochastic Analysis

No abstract provided.

Perencanaan Bauran Pembangkit Listrik Energi Terbarukan Di Indonesia: Pendekatan Optimasi Program Linier Berbasis Wilayah, Annisa Garmaisa, Uka Wikarya

Jurnal Kebijakan Ekonomi

Indonesia has renewable energy potential spread across various islands. However, limited interconnection between regions is an obstacle to energy distribution. The purpose of this study is to analyze the planning of renewable energy (RE) power plants covering eight types: Geothermal Power Plants (PLTP), Solar Power Plants (PLTS), Wind Power Plants (PLTB), Biomass Power Plants (PLTBm), Biogas Power Plants (PLTBg), and Waste Power Plants (PLTSa). The analysis was conducted in four main system regions in Indonesia, namely Java-Bali, Sumatra, Kalimantan, and Sulawesi, which are currently not interconnected. The study is based on the availability of renewable energy potential, production forecasts, and …

A Study Of The Sum Of Divisors, Henry M. Willie

Miners Solving for Tomorrow Research Conference

No abstract provided.

Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

An In-Depth Analysis Of The Bellarmine University Student Athlete Experience, Mattingly E. Spalding

Undergraduate Theses

The goal of this thesis is to improve the student athlete experience at Bellarmine University through direct feedback from our current student athletes. By defining what parts of the student athlete experience they value most, Bellarmine can reflect on the support currently provided in these areas. Additionally, if it is concluded through the response that high valued areas are not being satisfied, Bellarmine can work to improve the support in these areas. Or, if there is abundant support in a low-valued area, Bellarmine could think to shift resources into a more needed concentration. Through the design sample, data was accumulated …

On Regularity And Convergence Of Solutions To The Boltzmann-Enskog Equations, Christian Ennis

LSU Doctoral Dissertations

The Boltzmann equation describes the time evolution of the density function in position-velocity space for a classical particle subjected to possible collisions by other particles in a diluted gas that expands in vacuum for a given initial distribution. While many authors have studied the probabilistic interpretation of the spatially homogeneous Boltzmann equation, there is a dearth of articles on the stochastic framework of the full (that is, spatially inhomogeneous) Boltzmann equation. In this thesis, we examine a stochastic process, developed by S. Albevario, B. Ruediger, and P. Sundar, whose law is a weak solution to a mollified Boltzmann equation. This …

Stochastic Analysis And White Noise Calculus Of Nonlinear Wave Equations With Application To Laser Generation And Propagation, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

An Operator Information Quantity Of A Semigroup And Associated Differential Equations, Kimiaki Saito, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih

Journal of Stochastic Analysis

No abstract provided.

American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah

Journal of Stochastic Analysis

No abstract provided.

About Fixed Points Of Quantum Channels, Raffaella Carbone

Journal of Stochastic Analysis

No abstract provided.

Stochastic Bundles, New Classes Of Gaussian Processes And White Noise-Space Analysis Indexed By Measures, Daniel Alpay, Palle Jorgensen

Mathematics, Physics, and Computer Science Faculty Articles and Research

Starting from a fixed measure space (X,F,μ), with μ a positive sigma-finite measure defined on the sigma-algebra F, we continue here our study of a generalization W(μ) of Brownian motion, and introduce a corresponding white-noise process. In detail, the generalized Brownian motion is a centered Gaussian process W^(μ), indexed by the elements A in F of finite μ measure, and with covariance function μ(A ∩ B). The purpose of our present paper is to make precise and study the corresponding whitenoise process, i.e., a point-wise process which is indexed by X, and which arises …

Analysis Of Systematic Trade-Offs Between Military And Healthcare Expenditure Alongside Gdp Growth Of Select Asian And Western Exporting Economies In The 21st Century, Rahul Balamurugan, Carlos Gershenson, Preethi Nanjundan, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study explores the complexity in the trade-offs between military expenditure, healthcare expenditure, and GDP growth across select Asian nations and major weapon-exporting countries, examining how nations allocate finite resources between national security and human well-being over the past two decades. Using a systems science approach, the research integrates Granger causality testing to analyze temporal and directional relationships among GDP growth, military expenditure, and healthcare expenditure, uncovering their dynamic interdependencies. The methodology includes trend and slope analysis, Granger causality testing, outlier detection, and clustering to identify heterogeneity in resource allocation strategies. Developed, weapon-exporting nations exhibit complementary trends, with strong causality …

(Si14-12) Some Novel Fractional Discrete Inequalities Of Gronwall-Bellman Type And Their Applications To Fractional Difference Equations, Subhash Kendre, Nagesh Kale, Dimplekumar Chalishajar

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we develop multiple power nonlinear generalizations of Gronwall-Bellman type fractional discrete inequalities and fractional sum inequalities through combining functions with powered unknown functions.We have employed technique of reducing power non-linearity into linearity to furnish these refinements. These novel findings present a broader framework for dealing with wider range of nonlinear fractional difference equations and fractional sum-difference equations. The utilization of these inequalities enables to study certain crucial classes of fractional difference equations that arise in the realm of fractional difference calculus, both quantitatively and qualitatively. Several illustrations are provided to examine the boundedness of initial value problems …

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

The Operator Algebras Mentor Network: Impact Of Community-Based Mentoring, Anna Duwenig, Kari Eifler, Priyanga Ganesan, Lara Ismert, Viviana Meschitti, Sarah Plosker, Karen Strung

Journal of Humanistic Mathematics

The Operator Algebras Mentor Network (OAMN) is an international mentoring initiative that offers support in small groups to women and minority genders in the particularly male-dominated field of operator algebras (OA) in mathematics. Expected advantages of membership include raising awareness of the lack of gender diversity in this field, providing advice to mentees by mentors (e.g., pertaining to career or work/life balance), broadening one’s network in OA, etc. In this project, we set out to determine if membership within the OAMN is beneficial to its members. To this end we sent a questionnaire to OAMN members and a control group …

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.

On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

Kroger Post-Pandemic Customer Segmentation, Mario Mata, Joey Truitt, Renn Spigelmyer, Dhanuja Kasturiratna, Lisa Holden, Nitish Baidya, Hanna Tafari

Posters-at-the-Capitol

The grocery retail industry landscape has changed greatly in the wake of the pandemic. Specifically, delivery and pickup services have become more popular and customer buying habits have evolved. At the same time, improvements in data collection and analysis have allowed grocery marketing strategies to become highly individualized.

We worked with 84.51, an analytics firm, to identify customer segments for the Kroger Company based on data from 2023. Using clustering techniques, we organized customers into groups, or segments, based on similar characteristics. We identified and profiled four distinct groups of customers. Three segments were characterized by high frequency and spending …

Malliavin Calculus On The Clifford Algebra, Takayoshi Watanabe

Journal of Stochastic Analysis

No abstract provided.

Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary Vs Non-Unitary Time Evolution, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Long-Time Asymptotics For The Kadomtsev–Petviashvili I Equation With Small Initial Data, Samir Donmazov

Theses and Dissertations--Mathematics

We study the initial value problem for the Kadomtsev--Petviashvili I (KP I) equation (u_t + 6uu_x + u_xxx)_x = 3u_yy with small initial data belonging to a subspace of the energy space for the KP I equation. We establish the long-time asymptotics for solutions of the KP I equation using the inverse scattering transform formalism developed by Zhou. Within this framework, the inverse problem for the KP I equation is formulated as a nonlocal Riemann--Hilbert problem (RHP) in two spatial dimensions. As part of the asymptotic analysis, we determine the long-time behavior of the …

The Anatomy Of A Reconstruction: From Fourier Space To Image Recovery In Computed Tomography, Charlotte P. Maurer

Honors Theses

This thesis develops the mathematical foundations of computed tomography (CT) reconstruction through the lens of harmonic analysis. Beginning with the Schwartz class, we introduce the Fourier transform and its role in expressing the Radon transform and its inversion via a fractional Laplacian. After constructing the Radon transform in general dimension R^d, we specialize to the cases d = 2 and d = 3, demonstrating explicit inversion formulas and the associated instability in lower dimensions. For its computational advantages, we study filtered back-projection using classical low-pass filters (Ram-Lak, Shepp–Logan, Cosine, Gaussian) and formulate a discrete reconstruction algorithm grounded in …

Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan

Honors Theses

In this thesis, we classify the pointwise behavior of finite-range random walks on finitely generated abelian groups in terms of local limit theorems. Random walks are central objects of research in probability theory, and the theory has found applications in statistics, physics, and even card shuffling. One significant topic in this line of study is random walks on finitely generated groups. Starting from the pioneering work of G. Pólya and H. Kesten, random walks on finitely generated groups have been studied extensively. However, many notable results on the subject (local limit theorems, for example) make assumptions about periodicity and irreducibility …