Other Mathematics Commons^™

The Stationary Phase Method For Real Analytic Geometry, Domenico Napoletani, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove that the existence of isolated solutions of systems of equations of analytical functions on compact real domains in R^p, is equivalent to the convergence of the phase of a suitable complex valued integral I(h) for h→∞. As an application, we then use this result to prove that the problem of establishing the irrationality of the value of an analytic function F(x) at a point x₀ can be rephrased in terms of a similar phase convergence.

The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni

MPP Published Research

The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …

Solving A Class Of Linear Skorokhod Stochastic Differential Equations, Karl-Heinz Fichtner, Steffen Klaere, Volkmar Liebscher

Communications on Stochastic Analysis

No abstract provided.

Two-Dimensional 1-Meixner Random Vectors And Their Semi-Quantum Operators, Gabriela Popa, Aurel I Stan

Communications on Stochastic Analysis

No abstract provided.

A Poisson Shot-Noise Process Of Pulses And Its Scaling Limits, Mine Çaglar

Communications on Stochastic Analysis

No abstract provided.

On The Lévy-Khinchin Decomposition Of Generating Functionals, Uwe Franz, Malte Gerhold, Andreas Thom

Communications on Stochastic Analysis

No abstract provided.

Doob's Decomposition Theorem For Near-Submartingales, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Stochastic Tidal Dynamics Equation, Murugan Suvinthra, Sivaguru S Sritharan, Krishnan Balachandran

Communications on Stochastic Analysis

No abstract provided.

White Noise Analysis For The Canonical Lévy Process, Rolando D Navarro Jr., Frederi G Viens

Communications on Stochastic Analysis

No abstract provided.

Krylov-Veretennikov Formula For Functionals From The Stopped Wiener Process, Georgii V Riabov

Communications on Stochastic Analysis

No abstract provided.

In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty

Applications and Applied Mathematics: An International Journal (AAM)

This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had …

Manzanar Murakami As Radical Mathematician, Logan Bishop-Van Horn

Scholarly Undergraduate Research Journal at Clark (SURJ)

In Karen Tei Yamashita’s Tropic of Orange, characters attempt to make meaning of the many complex structures in which they are situated. In his unique meaning-making process, Manzanar Murakami, a homeless Sansei, “conducts” the Los Angeles traffic with a silver baton from atop a highway overpass. In conducting his music, Murakami per- forms complex mathematics, finding meaning in connection by mapping the rhythmic flow of humans, machines, and goods. Through his baton, to the sounds of a beautiful orchestra, he translates precisely the relationships he sees before him. Murakami’s music and Yamashita’s fantastic images constitute a “mathematical realism,” a lens …

Some Quantum Dynamical Semi-Groups With Quantum Stochastic Dilation, Lingaraj Sahu, Preetinder Singh

Communications on Stochastic Analysis

No abstract provided.

Singular Equations Driven By An Additive Noise And Applications, Nicolas Marie

Communications on Stochastic Analysis

No abstract provided.

On The Regularity Of One Parameter Transformation Groups In Barreled Locally Convex Topological Vector Spaces, Maximilian Bock

Communications on Stochastic Analysis

No abstract provided.

Stochastic Dynamics Of Determinantal Processes By Integration By Parts, Laurent Decreusefond, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi

Communications on Stochastic Analysis

No abstract provided.

Hidden Markov Change Point Estimation, Robert J Elliott, Sebastian Elliott

Communications on Stochastic Analysis

No abstract provided.

Revisiting A Theorem Of L. A. Shepp On Optimal Stopping, Philip A Ernst, Larry A Shepp

Communications on Stochastic Analysis

No abstract provided.

Theoretical And Numerical Analysis Of An Optimal Execution Problem With Uncertain Market Impact, Kensuke Ishitani, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.

Some New Connections Between Brownian Bridges And Brownian Motions, Estate V Khmaladze

Communications on Stochastic Analysis

No abstract provided.

Geometric Constructions From An Algebraic Perspective, Betzabe Bojorquez

Electronic Theses, Projects, and Dissertations

Many topics that mathematicians study at times seem so unrelated such as Geometry and Abstract Algebra. These two branches of math would seem unrelated at first glance. I will try to bridge Geometry and Abstract Algebra just a bit with the following topics. We can be sure that after we construct our basic parallel and perpendicular lines, bisected angles, regular polygons, and other basic geometric figures, we are actually constructing what in geometry is simply stated and accepted, because it will be proven using abstract algebra. Also we will look at many classic problems in Geometry that are not possible …

On Dedekind’S “Über Die Permutationen Des Körpers Aller Algebraischen Zahlen", Joseph Jp Arsenault Jr

Electronic Theses and Dissertations

We provide an analytic read-through of Richard Dedekind's 1901 article “Über die Permutationen des Körpers aller algebraischen Zahlen," describing the principal results concerning infinite Galois theory from both Dedekind's point of view and a modern perspective, noting an apparently uncorrected error in the supplement to the article in the Collected Works. As there is no published English-language translation of the article, we provide an annotated original translation.

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …

Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)

Idaho Conference on Undergraduate Research

With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …

Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica

Dissertations

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …

Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo

STAR Program Research Presentations

This report examines a new methodology in solving Partial Differential Equations (PDEs) numerically. The report also studies the accuracy of this new method as a PDE solver. This new Fourier Continuation (FC) method is one of a few that avoids the well-known Gibbs Phenomenon, which is the overestimation or underestimation of a function. These estimations are oscillations around a “jump” when a non-periodic function is expressed in terms of sines and cosines. Instead, the FC algorithm creates a smooth, periodic extension of a function over a general domain, as demonstrated by the many examples presented here. The FC algorithm was …

Mathematical Double Dactyls, Tristan Miller

Journal of Humanistic Mathematics

No abstract provided.

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.

Linear Algebra, Daniel Scully

Math Faculty Publications

Table of Contents:

1. Systems of Linear Equations and Matrices

• Systems of Linear Equations
• Elementary Row Operations
• Row Reduction and Reduced Row-Echelon Form
• Solutions of Systems of Linear Equations
• Matrix Operations
• Matrix Inverses

2. Euclidean 2-Space and 3-Space

• Vectors in the Plane and in Space
• The Dot Product
• Cross Product
• Lines in Space
• Planes in Space

3. Determinants

• The Definition of Determinant
• Elementary Row Operations and the Determinant
• Elementary Matrices and the Determinant
• Applications of the Determinant

4. Vector Spaces and Subspaces

• Vector Spaces
• Subspaces
• Linear Dependence and Independence
• Basis and Dimension

5. Linear Transformations

• Definition of Linear Transformation
• The …

Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu

MPP Published Research

This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …