A First-Passage Problem For Exponential Integrated Diffusion Processes, 2022 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada

#### A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre

*Journal of Stochastic Analysis*

No abstract provided.

Introduction To Mathematical Analysis I - 3rd Edition, 2022 Portland State University

#### Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

*PDXOpen: Open Educational Resources*

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels ...

Proving Dirichlet's Theorem On Arithmetic Progressions, 2022 Western University

#### Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma

*Undergraduate Student Research Internships Conference*

First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.

Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, 2022 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

*Journal of Stochastic Analysis*

No abstract provided.

The Art Of Analysis, 2022 Connecticut College

#### The Art Of Analysis, Christopher Hammond

*Open Educational Resources*

Christopher Hammond, Professor of Mathematics at Connecticut College, has written an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply a ...

On The Thom Isomorphism For Groupoid-Equivariant Representable K-Theory, 2022 Dartmouth College

#### On The Thom Isomorphism For Groupoid-Equivariant Representable K-Theory, Zachary J. Garvey

*Dartmouth College Ph.D Dissertations*

This thesis proves a general Thom Isomorphism in groupoid-equivariant KK-theory. Through formalizing a certain pushforward functor, we contextualize the Thom isomorphism to groupoid-equivariant representable K-theory with various support conditions. Additionally, we explicitly verify that a Thom class, determined by pullback of the Bott element via a generalized groupoid homomorphism, coincides with a Thom class defined via equivariant spinor bundles and Clifford multiplication. The tools developed in this thesis are then used to generalize a particularly interesting equivalence of two Thom isomorphisms on TX, for a Riemannian G-manifold X.

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), 2022 Claremont Colleges

#### Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat

*Journal of Humanistic Mathematics*

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?

The Construction And Estimation Of Hidden Semi-Markov Models, 2022 University of Sulaimani, Sulaymaniyah, Iraq

#### The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek

*Journal of Stochastic Analysis*

No abstract provided.

Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, 2022 DePaul University

#### Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, Harshita Bali, Enrico Au-Yeung

*DePaul Discoveries*

Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type ...

Propuestas Y Resultados De Investigación Transmoderna, Translocal Y Digital Desde Jóvenes Semilleristas, 2022 Universidad de Cundinamarca

#### Propuestas Y Resultados De Investigación Transmoderna, Translocal Y Digital Desde Jóvenes Semilleristas, Xiomara Gonzalez Gaitan

*Institucional*

En el presente libro intitulado Propuestas y resultados de investigación transmoderna, translocal y digital desde jóvenes semilleristas, se encuentran compilados las propuestas, avances y resultados de los proyectos en curso de los Semilleros de Investigación de la Universidad de Cundinamarca, Colombia, que se presentaron en el “II encuentro de semilleros de investigación: ciencia, tecnología e innovación en la era digital” en su versión 2020. Hacemos la labor de publicar estos proyectos con la intensión de difundir el conocimiento y como muestra del esfuerzo y alcance de la labor investigativa de los semilleristas de la Universidad de Cundinamarca. Esperamos que lo ...

The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, 2022 University of Mazandaran, Babolsar, Iran

#### The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, O.K. Kazemi, A. Pourdarvish, J. Sadeghi

*Journal of Stochastic Analysis*

No abstract provided.

Quantization Of The Poisson Type Central Limit Theorem (1), 2022 Università di Bari, n.4, Via E. Orabona, 70125 Bari, Italy

#### Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu

*Journal of Stochastic Analysis*

No abstract provided.

Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, 2022 Louisiana State University and Agricultural and Mechanical College

#### Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage

*LSU Doctoral Dissertations*

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an essential role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Grudsky and Vasilevski showed in 2002 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra $\mathcal{T}^G$, while Esmeral and Maximenko showed that $C^*$-algebra $\mathcal{T}^G$ is isometrically isomorphic to the $C ...

A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, 2022 Heinrich Heine University, Düsseldorf, Germany

#### A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, Peter Kern, Christian Müller

*Journal of Stochastic Analysis*

No abstract provided.

Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, 2022 Ursinus College

#### Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam

*Analysis*

No abstract provided.

An Optimal Transportation Theory For Interacting Paths, 2022 University of Massachusetts Amherst

#### An Optimal Transportation Theory For Interacting Paths, Rene Cabrera

*Doctoral Dissertations*

In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing stronger conditions, we characterize the minimizers by relating them to an auxiliary Monge-Kantorovich problem of the more standard kind. With this notion of how particles interact and travel along paths, we produce a dual problem. The main novelty here is to incorporate an interaction effect to the optimal path transport problem. This covers for instance, *N*-body dynamics when the underlying measures are discrete. Lastly ...

Self-Repelling Elastic Manifolds With Low Dimensional Range, 2022 University of Rochester, Rochester, NY 14627, USA

#### Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

*Journal of Stochastic Analysis*

No abstract provided.

Induced Matrices: Recurrences And Markov Chains, 2022 Southern Illinois University, Carbondale, Illinois 62901, USA

#### Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver

*Journal of Stochastic Analysis*

No abstract provided.

Unomaha Problem Of The Week (2021-2022 Edition), 2022 University of Nebraska at Omaha

#### Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

*Student Research and Creative Activity Fair*

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding ...

(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, 2022 Muş Alparslan University

#### (R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir

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

In this manuscript, we investigate the asymptotical stability of solutions of Riemann-Liouville fractional neutral systems associated to multiple time-varying delays. Then, we use the linear matrix inequality (LMI) and the Lyapunov-Krasovskii method to obtain sufficient conditions for the asymptotical stability of solutions of the system when the given delays are time dependent and one of them is unbounded. Finally, we present some examples to indicate the efficacy of the consequences obtained.