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A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô 2018 Meijo University, Tenpaku,Nagoya, Japan

A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.


A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepúlveda 2018 Portland State University

A Spacetime Dpg Method For The Wave Equation In Multiple Dimensions, Jay Gopalakrishnan, Paulina Sepúlveda

Portland Institute for Computational Science Publications

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in detail for a simple domain in arbitrary dimensions. The DPG method based on the weak formulation is then studied theoretically and numerically. Error estimates and numerical results are presented for triangular, rectangular, tetrahedral, and hexahedral meshes of ...


Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily McClung, Sam Rivas, Emma Soriano, Caelan Thomas, Hannah Highlander 2018 University of Portland

Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily Mcclung, Sam Rivas, Emma Soriano, Caelan Thomas, Hannah Highlander

Mathematics Undergraduate Publications, Presentations and Projects

Infectious diseases pose a serious threat to humans, plants, and animals. Though vaccines can help control outbreaks of infectious diseases, there is typically not enough vaccine available for the entire population. In this case, certain vaccination strategies can be employed to maximize the benefits for the entire population. Using results from graph theory and the simulation tool lONTW (Infections On NeTWorks), we investigated various vaccination strategies on certain types of so-called contact networks that model the patterns of interactions within a population. In particular, we focused on a certain class of contact networks known as small world models, where individuals ...


Reversibility Checking For Markov Chains, P. H. Brill, Chi ho Cheung, Myron Hlynka, Q. Jiang 2018 University of Windsor, Windsor, Ontario

Reversibility Checking For Markov Chains, P. H. Brill, Chi Ho Cheung, Myron Hlynka, Q. Jiang

Communications on Stochastic Analysis

No abstract provided.


Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, Stefan Koch 2018 University of Mannheim, Germany

Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, Stefan Koch

Communications on Stochastic Analysis

No abstract provided.


An Asymptotic Comparison Of Two Time-Homogeneous Pam Models, Hyun-Jung Kim, Sergey Vladimir Lototsky 2018 University of Southern California, Los Angeles, California USA

An Asymptotic Comparison Of Two Time-Homogeneous Pam Models, Hyun-Jung Kim, Sergey Vladimir Lototsky

Communications on Stochastic Analysis

No abstract provided.


Dual Perspectives On Desargues' Theorem, Carl Lienert 2018 Ursinus College

Dual Perspectives On Desargues' Theorem, Carl Lienert

Geometry

No abstract provided.


Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya 2018 Embry-Riddle Aeronautical University

Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya

Publications

“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein. Pure mathematicians study abstract entities and structures that underlie mathematics. Although their general perspective is “math for math’s sake”, sometimes even the most abstract mathematics can have unexpected applications! Come learn some of these astonishing discoveries in the history of science and mathematics! They might make you thrilled but keep in mind real-world usage is rarely the goal behind developing a new mathematical theory.

Welcome to the world of pure mathematics! In this talk, we will focus on the theory of composition operators which is a ...


An Extension Of The Method Of Brackets: Part 1, Ivan Gonzalez, Karen T. Kohl, Lin Jiu, Victor H. Moll 2018 Universidad de Valparaiso

An Extension Of The Method Of Brackets: Part 1, Ivan Gonzalez, Karen T. Kohl, Lin Jiu, Victor H. Moll

Faculty Publications

The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n 2 C, but might vanish or blow up when n 2 N. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.


Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya 2018 Embry-Riddle Aeronautical University

Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya

Soumyadip Acharyya

“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein. Pure mathematicians study abstract entities and structures that underlie mathematics. Although their general perspective is “math for math’s sake”, sometimes even the most abstract mathematics can have unexpected applications! Come learn some of these astonishing discoveries in the history of science and mathematics! They might make you thrilled but keep in mind real-world usage is rarely the goal behind developing a new mathematical theory.

Welcome to the world of pure mathematics! In this talk, we will focus on the theory of composition operators which is a ...


Bounds On The Sum Of Minimum Semidefinite Rank Of A Graph And Its Complement, Sivaram Narayan, Yousra Sharawi 2018 Central Michigan University

Bounds On The Sum Of Minimum Semidefinite Rank Of A Graph And Its Complement, Sivaram Narayan, Yousra Sharawi

Electronic Journal of Linear Algebra

The minimum semi-definite rank (msr) of a graph is the minimum rank among all positive semi-definite matrices associated to the graph. The graph complement conjecture gives an upper bound for the sum of the msr of a graph and the msr of its complement. It is shown that when the msr of a graph is equal to its independence number, the graph complement conjecture holds with a better upper bound. Several sufficient conditions are provided for the msr of different classes of graphs to equal to its independence number.


Tangent Lines, Samuel Estep 2018 Liberty University

Tangent Lines, Samuel Estep

The Kabod

In [1] Leibniz published the first treatment of the subject of calculus. An English translation can be found in [2]; he says that

to find a tangent is to draw a right line, which joins two points of the curve having an infinitely small difference, or the side of an infinite angled polygon produced, which is equivalent to the curve for us.

Today, according to [3],

a straight line is said to be a tangent line of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f (c ...


Topological Vector Spaces, Chunqing Li 2018 University of Windsor

Topological Vector Spaces, Chunqing Li

Major Papers

This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well ...


The Chapman Bone Algorithm: A Diagnostic Alternative For The Evaluation Of Osteoporosis, Elise Levesque, Anton Ketterer, Wajiha Memon, Cameron James, Noah Barrett, Cyril Rakovski, Frank Frisch 2018 Chapman University

The Chapman Bone Algorithm: A Diagnostic Alternative For The Evaluation Of Osteoporosis, Elise Levesque, Anton Ketterer, Wajiha Memon, Cameron James, Noah Barrett, Cyril Rakovski, Frank Frisch

Mathematics, Physics, and Computer Science Faculty Articles and Research

Osteoporosis is the most common metabolic bone disease and goes largely undiagnosed throughout the world, due to the inaccessibility of DXA machines. Multivariate analyses of serum bone turnover markers were evaluated in 226 Orange County, California, residents with the intent to determine if serum osteocalcin and serum pyridinoline cross-links could be used to detect the onset of osteoporosis as effectively as a DXA scan. Descriptive analyses of the demographic and lab characteristics of the participants were performed through frequency, means and standard deviation estimations. We implemented logistic regression modeling to find the best classification algorithm for osteoporosis. All calculations and ...


Microstructure Design Using Graphs, Pengfei Du, Adrian Zebrowski, Jaroslaw Zola, Baskar Ganapathysubramanian, Olga Wodo 2018 Iowa State University

Microstructure Design Using Graphs, Pengfei Du, Adrian Zebrowski, Jaroslaw Zola, Baskar Ganapathysubramanian, Olga Wodo

Mechanical Engineering Publications

Thin films with tailored microstructures are an emerging class of materials with applications such as battery electrodes, organic electronics, and biosensors. Such thin film devices typically exhibit a multi-phase microstructure that is confined, and show large anisotropy. Current approaches to microstructure design focus on optimizing bulk properties, by tuning features that are statistically averaged over a representative volume. Here, we report a tool for morphogenesis posed as a graph-based optimization problem that evolves microstructures recognizing confinement and anisotropy constraints. We illustrate the approach by designing optimized morphologies for photovoltaic applications, and evolve an initial morphology into an optimized morphology exhibiting ...


Equivalent Constructions Of Cartan Pairs, Phung Thanh Tran 2018 University of New Mexico

Equivalent Constructions Of Cartan Pairs, Phung Thanh Tran

Math Theses

Feldman and Moore [4] introduce Cartan subalgebra of the von Neumann algebra M on a separable Hilbert space H from the natural subalgebra of M(R, sigma), the twisted algebra of matrices over the relation R on a Borel space (X, B, muy). They show that if M has a Cartan subalgebra A, then M is isomorphic to M(R, sigma) where A is the twisted algebra onto the diagonal subalgebra L^inf (X, muy). The relation R is unique to isomorphism and the orbit of the two-cohomology class on R in the torus T, which is the automorphism group ...


Stranded Cellular Automaton And Weaving Products, Hao Yang 2018 Rose-Hulman Institute of Technology

Stranded Cellular Automaton And Weaving Products, Hao Yang

Mathematical Sciences Technical Reports (MSTR)

In order to analyze weaving products mathematically and find out valid weaving products, it is natural to relate them to Cellular Automaton. They are both generated based on specific rules and some initial conditions. Holden and Holden have created a Stranded Cellular Automaton that can represent common weaving and braiding products. Based on their previous findings, we were able to construct a Java program and analyze various aspects of the automaton they created. This paper will discuss the complexity of the Stranded Cellular Automaton, how to determine whether a weaving product holds together or not based on the automaton and ...


Elementary Set Theory, Richard P. Millspaugh 2018 University of North Dakota

Elementary Set Theory, Richard P. Millspaugh

Open Educational Resources

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics.


Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie 2018 Portland State University

Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.


Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez 2018 The Graduate Center, City University of New York

Studying The Space Of Almost Complex Structures On A Manifold Using De Rham Homotopy Theory, Bora Ferlengez

All Dissertations, Theses, and Capstone Projects

In his seminal paper Infinitesimal Computations in Topology, Sullivan constructs algebraic models for spaces and then computes various invariants using them. In this thesis, we use those ideas to obtain a finiteness result for such an invariant (the de Rham homotopy type) for each connected component of the space of cross-sections of certain fibrations. We then apply this result to differential geometry and prove a finiteness theorem of the de Rham homotopy type for each connected component of the space of almost complex structures on a manifold. As a special case, we discuss the space of almost complex structures on ...


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