Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, 2019 University of Nebraska-Lincoln

#### Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

*Dissertations, Theses, and Student Research Papers in Mathematics*

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_{D} which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_{D} shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a ...

Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, 2019 University of Nebraska-Lincoln

#### Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, Mitchell A. Hamidi

*Dissertations, Theses, and Student Research Papers in Mathematics*

In 2015, E. Katsoulis and C. Ramsey introduced the construction of a non-self-adjoint crossed product that encodes the action of a group of automorphisms on an operator algebra. They did so by realizing a non-self-adjoint crossed product as the subalgebra of a C*-crossed product when dynamics of a group acting on an operator algebra by completely isometric automorphisms can be extended to self-adjoint dynamics of the group acting on a C*-algebra by ∗-automorphisms. We show that this extension of dynamics is highly dependent on the representation of the given algebra and we define a lattice structure for an ...

An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, 2019 Bowdoin College

#### An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, Kevin Chen

*Honors Projects*

No abstract provided.

Minimal Principal Series Representations Of Sl(3,R), 2019 William & Mary

#### Minimal Principal Series Representations Of Sl(3,R), Jacopo Gliozzi

*Undergraduate Honors Theses*

We discuss the properties of principal series representations of SL(3,R) induced from a minimal parabolic subgroup. We present the general theory of induced representations in the language of fiber bundles, and outline the construction of principal series from structure theory of semisimple Lie groups. For SL(3,R), we show the explicit realization a novel picture of principal series based on the nonstandard picture introduced by Kobayashi, Orsted, and Pevzner for symplectic groups. We conclude by studying the K-types of SL(3,R) through Frobenius reciprocity, and evaluate prospects in developing simple intertwiners between principal series representations.

An Anatomical And Functional Analysis Of Digital Arteries, 2019 University of Lynchburg

#### An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith

*Student Scholar Showcase*

Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the ...

Making The Cut: Receivers Of The National Football League, 2019 Louisiana Tech University

#### Making The Cut: Receivers Of The National Football League, Anthony Kent Davis

*Mathematics Senior Capstone Papers*

In this paper the prospects of the National Football League, or NFL, are studied in order to determine the relationships between past college statistics, other “measurables,” and how they translate to successful careers in the league. When referring to measurables, this consists of all of the numerical data from each player that should, in theory, help teams get an idea of the players strengths or weaknesses. The data being used comes from an annual scouting combine for NFL teams that is held prior to each season. Information about the player’s college statistics and pre-draft measurables are being compared to ...

The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, 2019 Boise State University

#### The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe

*Mathematics Undergraduate Theses*

The hyperreal number system *ℝ forms an ordered field that contains ℝ as a subfield as well as infinitely many large and small numbers. A number is defined to be infinitely large if |* ω*| >

*n*for all

*n*= 1, 2, 3, ... and infinitely small if |ε| < 1/

*n*for all

*n*= 1, 2, 3... This number system is built out of the real number system analogous to Cantor’s construcion of ℝ out of ℚ. The new entities in *ℝ and the relationship between the reals and hyperreals provides an appealing alternate approach to real (standard) analysis referred to as nonstandard ...

A General Weil-Brezin Map And Some Applications, 2019 William & Mary

#### A General Weil-Brezin Map And Some Applications, Benjamin Bechtold

*Undergraduate Honors Theses*

We recall a theory generalizing the Heisenberg group on $\R$ to an analogous structure using a locally compact abelian group $G$. Then, using our new, general Heisenberg groups, we generalize the classical Weil-Brezin map, from an operator on $L^2(\R )$ and develop a theory of that generalized Weil-Brezin map on $L^2(G)$ for some locally compact abelian group $G$. We then apply our generalized Weil-Brezin map to recover the Poisson Summation Formula as well as the Plancherel Theorem.

On The Continuation Of The Hartogs Series With Holomorphic Coefficients, 2019 National University of Uzbekistan

#### On The Continuation Of The Hartogs Series With Holomorphic Coefficients, Takhir Tuychiev, Jurabay Tishabaev

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.

On A Control Problem Associated With Fast Heating Of A Thin Rod, 2019 National University of Uzbekistan

#### On A Control Problem Associated With Fast Heating Of A Thin Rod, Shavkat Alimov, Farrukh Dekhkonov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In this work, we consider boundary control problem associated with a parabolic equation on a interval. On the part of the border of the considered segment, the value of the solution with control parameter is given. Restrictions on the control are given in such a way that the average value of the solution in some part of the considered interval gets a given value. The auxiliary problem is solved by the method of separation of variables, while the problem in consideration is reduced to the Volterra integral equation of the second kind. The control parameter is defined on one. The ...

Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, 2019 Air Force Institute of Technology

#### Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands

*Theses and Dissertations*

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were ...

Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, 2019 University of Nebraska at Omaha

#### Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

*Student Research and Creative Activity Fair*

**Description**: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general ...

Some Properties Of The Inhomogeneous Panjer Process, 2019 Department of Industrial Engineering, Pontificia Universidad Javeriana, Bogotá D.C., Colombia

#### Some Properties Of The Inhomogeneous Panjer Process, Ana María Beltrán Cortés, José Alfredo Jiménez Moscoso

*Communications on Stochastic Analysis*

No abstract provided.

A Nonlocal Approach To The Quantum Kolmogorov Backward Equation And Links To Noncommutative Geometry, 2019 Investec Bank PLC, 30 Gresham Street, London EC2V 7QP, United Kingdom

#### A Nonlocal Approach To The Quantum Kolmogorov Backward Equation And Links To Noncommutative Geometry, Will Hicks

*Communications on Stochastic Analysis*

No abstract provided.

Second Order Stochastic Partial Integro Differential Equations With Delay And Impulses, 2019 Department of Mathematics, UCEK, JNTUK, Kakinada, A.P. -533003, India

#### Second Order Stochastic Partial Integro Differential Equations With Delay And Impulses, M.V.S.S.B.B.K. Sastry, G.V.S.R. Deekshitulu

*Communications on Stochastic Analysis*

No abstract provided.

On The Adjoint Markov Policies In Stochastic Differential Games, 2019 University of Minnesota, Minneapolis, MN 55455, USA

#### On The Adjoint Markov Policies In Stochastic Differential Games, Nicolai V. Krylov

*Communications on Stochastic Analysis*

No abstract provided.

Regularity Of The Local Time Of Diffusions On The Positive Real Line With Reflection At Zero, 2019 University of the Ryukyus, Department of Mathematical Sci- ences, Faculty of Science, Nishihara-cho, Okinawa 903-0213, Japan

#### Regularity Of The Local Time Of Diffusions On The Positive Real Line With Reflection At Zero, Masafumi Hayashi

*Communications on Stochastic Analysis*

No abstract provided.

On The Spectrum Of Self-Adjoint Lévy Generators, 2019 School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, England

#### On The Spectrum Of Self-Adjoint Lévy Generators, David Applebaum

*Communications on Stochastic Analysis*

No abstract provided.

On A Stochastic 2d Cahn-Hilliard-Navier-Stokes System Driven By Jump Noise, 2019 Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, USA

#### On A Stochastic 2d Cahn-Hilliard-Navier-Stokes System Driven By Jump Noise, G. Deugoué, T. Tachim Medjo

*Communications on Stochastic Analysis*

No abstract provided.

Operator Algebras Generated By Left Invertibles, 2019 University of Nebraska - Lincoln

#### Operator Algebras Generated By Left Invertibles, Derek Desantis

*Dissertations, Theses, and Student Research Papers in Mathematics*

Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. Representations of such algebras encode the dynamics of orthonormal sets in a Hilbert space.We instigate a research program on concrete operator algebras that model the dynamics of Hilbert space frames.

The primary object of this thesis is the norm-closed operator algebra generated by a left invertible $T$ together with its Moore-Penrose inverse $T^\dagger$. We denote this algebra by $\mathfrac{A}_T$. In the isometric case, $T^\dagger = T^*$ and $\mathfrac{A}_T$ is a representation ...