Mathematics Commons^™

An Invitation To Linear Algebra, David N. Pham, Jonathon Funk, Wenjian Liu

Open Educational Resources

This is an OER textbook on linear algebra.

Numerical Approaches To A Thermoelastic Kirchhoff-Love Plate System, Zeyu Zhou

Wayne State University Dissertations

In this work, theory background of the sobolev spaces and finite element spaces are

reviewed first. Then the details of how the thermoelastic Kirchhoff-Love(KL) plates numerically established are presented. Later we approaches to the thermoelastic KL system numerically with mixed element method, H^1−Galerkin method and interior penalty discontinuous galerkin method(IP-DG).

What is more, the SIP-DG also applied to solve this KL system numerically. The well-posedness, existence, uniqueness and convergence properties are theoretical analyzed. The gain of the convergence rate is also O(h^k), that is 1 less than the observed convergence rate.

When discussing the H1-Galerkin method, the main advantages over …

Spectral Methods For Hamiltonian Systems And Their Applications, Lewei Zhao

Wayne State University Dissertations

Hamiltonian systems typically arise as models of conservative physical systems and have many applications. Our main emphasis is using spectral methods to preserve both symplectic structure and energy up to machine error in long time. An engery error estimation is given for a type of Hamiltonian systems with polynomial nonlinear part, which is numerical verified by solving a Henon-Heiles systems. Three interesting applications are presented : the first one is the N-body problems. The second one is approximation for Weyl's Law and the third one is simulating quantum cooling in an optomechanical system to study the dissipative dynamics. Moreover, nonsmooth …

Rigid Equilibriums Of A Rotating String, Teddrick Schaffer

Electronic Theses and Dissertations

This paper describes some possible equilibrium configurations of a string rotating in a certain class of force fields, which have properties motivated by the inverse square gravitational force. Specifically it is shown that for a given number n, there exists a sufficient rotational rate such that any equilibrium configuration with no more than n zeros is guaranteed to exist for any force field in the class considered.

A Study Of Several Applications Of Parallel Computing In The Sciences Using Petsc, Nicholas Stegmeier

Electronic Theses and Dissertations

The importance of computing in the natural sciences continues to grow as scientists strive to analyze complex phenomena. The dynamics of turbulence, astrophysics simulations, and climate change are just a few examples where computing is critical. These problems are computationally intractable on all computing platforms except supercomputers, necessitating the continued development of efficient algorithms and methodologies in parallel computing. This thesis investigates the use of parallel computing and mathematical modeling in the natural sciences through several applications, namely computational fluid dynamics for impinging jets in mechanical engineering, simulation of biofilms in an aqueous environment in mathematical biology, and the solution …

Practical Design Approaches For Assessing Parallelism In Dose Response Modelling, Timothy O'Brien, Jack Silcox

Mathematics and Statistics: Faculty Publications and Other Works

No abstract provided.

Basis Reduction In Lattice Cryptography, Raj Kane

Honors Theses

We develop an understanding of lattices and their use in cryptography. We examine how reducing lattice bases can yield solutions to the Shortest Vector Problem and the Closest Vector Problem.

Primes In Arithmetical Progression, Edward C. Wessel

Honors Theses

This thesis will tackle Dirichlet’s Theorem on Primes in Arithmetical Progressions. The majority of information that follows below will stem from Tom M. Apostol’s Introduction to Analytical Number Theory. This is the main source of all definitions, theorems, and method. However, I would like to assure the reader that prior knowledge of neither the text nor analytical number theory in general is needed to understand the result. A rough background in Abstract Algebra and a moderate grasp on Complex and Real Analysis are more than sufficient. In fact, my project’s intent is to introduce Dirichlet’s ideas to the mathematics student …

Ma 220 Supplement: Applied Calculus For Business & Life Sciences, Heather P. Lippert, Jan S. Collins

OER Main

The MA220 Supplement workbook is designed to support the concepts learned in MA220. There are business and life science applications for students majoring in business and/or life science. The MA220 supplement supports, but does not replace the textbook required for the MA220 course.

Gelfand-Naimark Duality For Non-Commutative C*-Algebras, Natee Pitiwan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we prove a duality between a class of non-commutative C*-algebras and projective C*-categories. After developing ideas from infinite matrices and bounded operators on Hilbert spaces, we define projective C*-categories and then define functors between the category of matrix C*-algebras and the category of projective C*-categories. Then from these functors we derive a duality between the two categories that generalizes Gelfand-Naimark duality for commutative C*-algebras. In the last chapter we discuss possibility of combining the result in this dissertation with already known results regarding sectional representations of C*-algebras to obtain a duality for a broader class of C*-algebras.

Applying Support Vector Machine With Connectivity Of Primitive Biochemical Compound Structure To Identify Target Characteristics Of Molecules, Peemapat Wongsriphisant

Chulalongkorn University Theses and Dissertations (Chula ETD)

Graph-structured data are widely used in many fields of study. For example, in cheminformatics, the data of biochemical compounds can be encoded as a compound graph where atoms are represented by vertices and chemical bonds between pairs of atoms are represented by edges. By this setting, we can predict the molecular characteristics of an unseen biochemical compound by considering the similarity between two compound graphs. This problem is called a graph classification. This study, proposes an algorithm for compound graph classification by finding primitive substructures of the compounds and encode them in a new graph form. Then, their similarities are …

Pointwise Dimension Of Archimedean Copulas, Noppawit Yanpaisan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce the pointwise dimension of a bivariate copula C at (u,v) in [0, 1]2 via its C-volume. This quantity gives a broader view of probability mass distribution than the support of a copula, the smallest closed set on which the whole mass lies. We would like to study some fundamental properties of pointwise dimension, including the equality to pointwise exponent whenever both of them exist. After that, we investigate the behavior of the pointwise dimension of copulas constructed by various methods. In the last part, we compute the pointwise dimension of Archimedean copulas, an important class …

Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, Mohsin Md Abdul Karim

Masters Theses

Classical Mechanics consists of three parts: Newtonian, Lagrangian and Hamiltonian Mechanics, where each part is a special extension of the previous part. Each part has explicit symmetries (the explicit Laws of Motion), which, in turn, generate implicit or hidden symmetries (like the Law of Conservation of Energy, etc). In this Master's Thesis, different types of hidden symmetries are considered; they are reflected in the Noether Theorem and the Poincare Recurrence Theorem applied to Lagrangian and Hamiltonian Systems respectively.

The Poincare Recurrence Theorem is also applicable to some number theory problems, which can be considered as dynamical systems. In …

Mental Imagery Practice As A Therapy For Naming Impairments: A Preliminary Study, Subhash Bhatnagar, Bridget Patek, Yasmeen Khan-Ansari, Naveen K. Bansal, Hugh Buckingham, Lotfi Hacein-Bey

Speech Pathology and Audiology Faculty Research and Publications

Background

Anomia remains one of the most recalcitrant linguistic disruptions in aphasia to treat. Developing successful interventions to address the word-finding deficits are complicated by the post-stroke symptom variability and inconsistent recovery patterns associated with anomia. Most of the current treatment methods, with a focus on specific compensating techniques and the repetitive practice of a limited set of items, have had variable success in naming treatment. However, it has not been possible to predict the gains in generalizing the learning beyond the stimuli used in practice or the controlled clinical setting. In this preliminary case study, we explore the value …

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

Teachers' Perceptions About Instructing Underachieving K-5 Students On Mathematical Word Problem-Solving, Crystal Yvette Baldwindouglas

Walden Dissertations and Doctoral Studies

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed …

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.