Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method,
2015
University of Texas at Arlington
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 …
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions,
2015
University of Southern Mississippi
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 …
Mathematical Double Dactyls,
2015
Department of Computer Science, Technische Universität Darmstadt
Mathematical Double Dactyls, Tristan Miller
Journal of Humanistic Mathematics
No abstract provided.
On Mathematicians' Eccentricity,
2015
None
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.
Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms,
2015
University of Paris
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 …
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives,
2015
University of California, Berkeley
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 …
Newton On Indivisibles,
2015
Universitat Pompeu Fabra
Newton On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.
Wallis On Indivisibles,
2015
Universitat Pompeu Fabra
Wallis On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing …
Risk Measures On Orlicz Heart Spaces,
2015
Louisiana State University
Risk Measures On Orlicz Heart Spaces, Coenraad Labuschagne, Habib Ouerdiane, Imen Salhi
Communications on Stochastic Analysis
No abstract provided.
Regular Transformation Groups Based On Fourier-Gauss Transforms,
2015
Louisiana State University
Regular Transformation Groups Based On Fourier-Gauss Transforms, Maximilian Bock, Wolfgang Bock
Communications on Stochastic Analysis
No abstract provided.
Fractional Hida-Malliavan Derivatives And Series Representations Of Fractional Conditional Expectations,
2015
Louisiana State University
Fractional Hida-Malliavan Derivatives And Series Representations Of Fractional Conditional Expectations, Sixian Jin, Qidi Peng, Henry Schellhorn
Communications on Stochastic Analysis
No abstract provided.
On P-Confidence Intervals For G-Expectations,
2015
Louisiana State University
On P-Confidence Intervals For G-Expectations, Leo Shen, Rodney C Wolff
Communications on Stochastic Analysis
No abstract provided.
Structure And Decompositions Of The Linear Span Of Generalized Stochastic Matrices,
2015
Louisiana State University
Structure And Decompositions Of The Linear Span Of Generalized Stochastic Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris
Communications on Stochastic Analysis
No abstract provided.
On Approximation Rates For Boundary Crossing Probabilities For The Multivariate Brownian Motion Process,
2015
Louisiana State University
On Approximation Rates For Boundary Crossing Probabilities For The Multivariate Brownian Motion Process, Shaun Mckinlay, Konstantin Borovkov
Communications on Stochastic Analysis
No abstract provided.
On The Fundamental Theorem Of Asset Pricing,
2015
Louisiana State University
On The Fundamental Theorem Of Asset Pricing, Abhay G Bhatt, Rajeeva L Karandikar
Communications on Stochastic Analysis
No abstract provided.
Periodic Solutions Of Discrete Generalized Schrödinger Equations On Cayley Trees,
2015
Louisiana State University
Periodic Solutions Of Discrete Generalized Schrödinger Equations On Cayley Trees, Fumio Hiroshima, József Lörinczi, Utkir Rozikov
Communications on Stochastic Analysis
No abstract provided.
Almost-Sure Explosive Solutions Of Some Nonlinear Parabolic Itô Equations,
2015
Louisiana State University
Almost-Sure Explosive Solutions Of Some Nonlinear Parabolic Itô Equations, Pao-Liu Chow, Rafail Khasminskii
Communications on Stochastic Analysis
No abstract provided.
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field,
2015
California State University - San Bernardino
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola
Electronic Theses, Projects, and Dissertations
The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order …
Non-Orientable Objects As Gaming Surfaces,
2015
Portland State University
Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais
Student Research Symposium
Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.
To receive an invitation to download the app through Google Play, contact me at [email protected]
Efficient Coupling For Random Walk With Redistribution,
2015
University of Connecticut
Efficient Coupling For Random Walk With Redistribution, Elizabeth Tripp
Honors Scholar Theses
What can be said on the convergence to stationarity of a finite state Markov chain that behaves 'locally' like a nearest-neighbor random walk on the set of integers? In this work, we looked to obtain sharp bounds for the rate of convergence to stationarity for a particular non-symmetric Markov chain. Our Markov chain is a variant of the simple symmetric random walk on the state space {0, ..., N} obtained by allowing transitions from 0 to J0 and from N to JN. We first looked at the case where J0 and JN are fixed, deterministic …
