Analysis Commons^™

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

Institucional

En el presente libro se recopilan 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 de 2020. Publicamos estos proyectos con la intención de difundir el conocimiento y como muestra del esfuerzo y del alcance de la labor investigadora de los semilleristas de la Universidad de Cundinamarca. Esperamos que los lectores encuentren en estas propuestas caminos para resolver problemas o inspiración para construir nuevas propuestas de …

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), Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

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

Journal of Stochastic Analysis

No abstract provided.

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, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

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

UNO 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 to …

Exploring The Numerical Range Of Block Toeplitz Operators, Brooke Randell

Master's Theses

We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of the related set, \(\{W(A_0+zA_1) : z \in \partial \mathbb{D}\}\), in a specific case. We will use the theory of envelopes to explore what the boundary looks like and we will use geometric arguments to explore the number of flat portions on the boundary. We will then make a conjecture as to the number of flat …

On The Numerical Range Of Compact Operators, Montserrat Dabkowski

Master's Theses

One of the many characterizations of compact operators is as linear operators which
can be closely approximated by bounded finite rank operators (theorem 25). It is
well known that the numerical range of a bounded operator on a finite dimensional
Hilbert space is closed (theorem 54). In this thesis we explore how close to being
closed the numerical range of a compact operator is (theorem 56). We also describe
how limited the difference between the closure and the numerical range of a compact
operator can be (theorem 58). To aid in our exploration of the numerical range of
a compact …

Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by λ ∈ R. The frame in which we introduce such families is that of the evolution through Schrödinger equation (i∂/∂t−H (x))(ψ) = 0 (H (x) = −(∂2/∂x2)/2+V (x)), V being a suitable potential). If F = {(t, x) → ϕλ(t, x) ; λ ∈ R}, where ϕλ is evolved from the initial datum x → eiλx , F-supershifts will be of …

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

Construction Of The Canonical Representation From A Noncanonical Representation, Yuji Hibino

Journal of Stochastic Analysis

No abstract provided.

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Program: Senior Projects (Public)

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

New Limit Theorems For Increments Of Birth-And-Death Processes With Linear Rates, Alexander Ya. Kreinin, Vladimir V. Vinogradov

Journal of Stochastic Analysis

No abstract provided.

Backward Stochastic Differential Equations With No Driving Martingale And Pseudo-Pdes, Adrien Barrasso, Francesco Russo

Journal of Stochastic Analysis

No abstract provided.

Winning Against The Devil: A New Look Into The Angel Problem, Amelia I. Tristan

Honors Program Theses and Research Projects

The Angel Problem, first introduced in 1982, is a two-player combinatorial game played on an infinite playing field. These two players, named the angel and the devil, move around the playing field, with the devil trying to trap the angel and the angel evading capture. The problem of capturing the angel on the playing field resulted in many variants of the original game that attempt to solve this problem. In the spirit of these variants, this research focuses on a new type of angel and devil, named the duck and fox, respectively, both limited by a finite playing field, and …

Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.

The Zagreb Index Of Several Random Models, Panpan Zhang

Journal of Stochastic Analysis

No abstract provided.

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

An Intrinsic Proof Of An Extension Of Itô’S Isometry For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

Covariant Ergodic Quantum Markov Semigroups Via Systems Of Imprimitivity, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

De Finetti’S Theorem In Categorical Probability, Tobias Fritz, Tomáš Gonda, Paolo Perrone

Journal of Stochastic Analysis

No abstract provided.

A Clark-Ocone Type Formula Via Itô Calculus And Its Application To Finance, Takuji Arai, Ryoichi Suzuki

Journal of Stochastic Analysis

No abstract provided.

Calculating Infinitesimal Generators, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.

Recursive And Viterbi Estimation For Semi-Markov Chains, Robert J. Elliott, W. P. Malcolm

Journal of Stochastic Analysis

No abstract provided.

The N-Dimensional Quadratic Heisenberg Algebra As A “Non–Commutative” Sl(2,C), Luigi Accardi, Andreas Boukas, Yun-Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Rough Paths And Regularization, André O. Gomes, Alberto Ohashi, Francesco Russo, Alan Teixeira

Journal of Stochastic Analysis

No abstract provided.

Generalized Girsanov Transform Of Processes And Zakai Equation With Jumps, Masatoshi Fujisaki, Takashi Komatsu

Journal of Stochastic Analysis

No abstract provided.

On The Uniqueness Of Solutions To Martingale Problems For Diffusion Operators With Progressively Measurable Random Coefficients, Masaaki Tsuchiya

Journal of Stochastic Analysis

No abstract provided.

Particle Representation For The Solution Of The Filtering Problem. Application To The Error Expansion Of Filtering Discretizations, Dan Crisan, Thomas G. Kurtz, Salvador Ortiz-Latorre

Journal of Stochastic Analysis

No abstract provided.