Other Mathematics Commons^™

Operator Algebras Generated By Left Invertibles, Derek Desantis

Department of Mathematics: Dissertations, Theses, and Student Research

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 of the Toeplitz algebra. Of particular interest …

Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …

Distribution Spaces And A New Construction Of Stochastic Processes Associated With The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.

Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent

HMC Senior Theses

We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.

Fixed Choice Design And Augmented Fixed Choice Design For Network Data With Missing Observations, Miles Q. Ott, Matthew T. Harrison, Krista J. Gile, Nancy P. Barnett, Joseph W. Hogan

Statistical and Data Sciences: Faculty Publications

The statistical analysis of social networks is increasingly used to understand social processes and patterns. The association between social relationships and individual behaviors is of particular interest to sociologists, psychologists, and public health researchers. Several recent network studies make use of the fixed choice design (FCD), which induces missing edges in the network data. Because of the complex dependence structure inherent in networks, missing data can pose very difficult problems for valid statistical inference. In this article, we introduce novel methods for accounting for the FCD censoring and introduce a new survey design, which we call the augmented fixed choice …

Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

Communications on Stochastic Analysis

No abstract provided.

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

Communications on Stochastic Analysis

No abstract provided.

Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

Communications on Stochastic Analysis

No abstract provided.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

Communications on Stochastic Analysis

No abstract provided.

The Game Of Ur: An Exercise In Strategic Thinking And Problem Solving And A Fun Math Club Activity, Cynthia J. Huffman Ph.D.

Open Educational Resources - Math

In this Open Educational Resource activity, students learn a little about the history of the Royal Game of Ur, the first board game, and get to practice critical thinking and problem solving by playing the game. Instructions are given along with a template for the game and game pieces and tetrahedral die.

Rationality In Bargaining By Finite Automata, Jim Bell

Theses and Dissertations (Comprehensive)

Aspects of behavioral decision-making can be integrated into game-theoretic models of two-player bargaining using finite automata which can represent bargaining strategies in combination with various behavioral traits. The automata are used as bargaining agents who must jointly agree upon a fixed allocation of transferable utility in an infinite-horizon Rubinstein bargaining game. At each turn, the automata are given the opportunity to accept a proposed portion of the transferable utility, or to reject the proposal and make a counter-offer of their own. A round-robin tournament and ecological simulations were run to explore strategic dominance under different conditions. Principles of bargaining strategy …

Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta

Communications on Stochastic Analysis

No abstract provided.

Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta

Communications on Stochastic Analysis

No abstract provided.

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.

Special Issue: New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/ Off-Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/ Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we …

A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of …

Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. Ii, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

A Bipolar Fuzzy Extension Of The Multimoora Method, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Willem Brauer

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to …

Historia De Las Teorías Neutrosóficas Y Sus Aplicaciones (Actualizado), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Historia de las Teorías Neutrosóficas y sus Aplicaciones (actualizado)

Tripleta De Estructura Neutrosófica Y Tripleta De Estructura Neutrosófica Extendida, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En el presente estudio se realiza una revisión de las tripletas de estructura neutrosófica y tripleta de estructura neutrosófica extendida, con el fin de introducir nuevos conceptos a emplear en trabajos futuros.

Grado De Dependencia E Independencia De Los (Sub) Componentes De Conjuntos Borrosos Y Neutrosóficos, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia, Por tal motivo el objetivo del presente trabajo es extender el conjunto neutrosófico refinado, teniendo en cuenta la grado de dependencia o independencia de los subcomponentes …

Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier

College of Graduate Studies: Theses & Dissertations

We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound …

Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty

Graduate Theses, Dissertations, and Problem Reports (ETD)

The differential is a symbol that is common in first- and second-year calculus. It is perhaps expected that a common mathematical symbol would be interpreted universally. However, recent literature that addresses student interpretations of differentials, usually in the context of definite integration, suggests that this is not the case, and that many interpretations are possible. Reviews of textbooks showed that there was not a lot of discussion about differentials, and what interpretations there were depended upon the context in which the differentials were presented. This dissertation explores some of these issues. Since students may not have the experience necessary to …

Global Existence And Asymptotic Behaviors For Some Nonlinear Partial Differential Equations., Ismahan Dhaw Binshati

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler-Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical and we also add the friction between two fluids. In addition, we discuss the rates of decay of $L^{p}-L^{q}$ norms for a linear system. Moreover, we use the result for $L^{p}-L^{q}$ estimates to prove the decay rates for the nonlinear systems. In addition, we prove existence of heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov-Poisson systems. In the nonlinear Vlasov case with …

A Dual State Hierarchical Ensemble Kalman Filter Algorithm, William J. Cook, Jesse Johnson, Marko Maneta, Doug Brinkerhoff

Graduate Student Theses, Dissertations, & Professional Papers

Dynamic models that simulate processes across large geographic locations, such as hydrologic models, are often informed by empirical parameters that are distributed across a geographical area and segmented by geological features such as watersheds. These parameters may be referred to as spatially distributed parameters. Spatially distributed parameters are frequently spatially correlated and any techniques utilized in their calibration ideally incorporate existing spatial hierarchical relationships into their structure. In this paper, a parameter estimation method based on the Dual State Ensemble Kalman Filter called the Dual State Hierarchical Ensemble Kalman Filter (DSHEnKF) is presented. This modified filter is innovative in that …

Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Stochastic Differential Equations With Anticipating Initial Conditions, Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.