Mathematics Commons^™

Smoothing Parameter Selection In Nonparametric Functional Estimation, Mohamed Amezziane

Electronic Theses and Dissertations

This study intends to build up new techniques for how to obtain completely data-driven choices of the smoothing parameter in functional estimation, within the confines of minimal assumptions. The focus of the study will be within the framework of the estimation of the distribution function, the density function and their multivariable extensions along with some of their functionals such as the location and the integrated squared derivatives.

Measures Of Concordance Of Polynomial Type, Heather Edwards

Electronic Theses and Dissertations

A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations …

Asymptotic Formulas For Large Arguments Of Hypergeometric-Type Functio, Adam Heck

Electronic Theses and Dissertations

Hypergeometric type functions have a long list of applications in the field of sciences. A brief history is given of Hypergeometric functions including some of their applications. A development of a new method for finding asymptotic formulas for large arguments is given. This new method is applied to Bessel functions. Results are compared with previously known methods.

Reduction Of Jump Systems, Vadim Ponomarenko

Mathematics Faculty Research

A jump system is a set of integer lattice points satisfying an exchange axiom. We discuss an operation on lattice points, called reduction, that preserves the jump system two-step axiom. We use reduction to prove a weakened version of a matroid conjecture by Rota[3], as well as demonstrate new operations on matroids and delta-matroids.

[Introduction To] Schaum's Outline Of Programming With Java, John R. Hubbard

Bookshelf

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices …

On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He

Scholarship

By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.

[Introduction To] Data Structures With Java, John R. Hubbard, Anita Huray

Bookshelf

For a freshman/sophomore-level course in Data Structures in Computer Science. This text teaches the use of direct source code implementations and the use of the Java libraries; it helps students prepare for later work on larger Java software solutions by adhering to software engineering principles and techniques such as the UML and the Java Collections Framework (JCF). Using the spiral approach to cover such topics as linked structures, recursion, and algorithm analysis, this text also provides revealing illustrations, summaries, review questions, and specialized reference sections.

Anatomy Of A Chaotic Attractor: Subtle Model-Predicted Patterns Revealed In Population Data, Aaron A. King, R. F. Costantino, J. M. Cushing, Shandelle M. Henson, Robert A. Desharnais, Brian Dennis

Faculty Publications

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

Computational Geometry Column 45, Joseph O'Rourke

Computer Science: Faculty Publications

The algorithm of Edelsbrunner for surface reconstruction by "wrapping" a set of points in R³ is described.

A 2-Chain Can Interlock With A K-Chain, Julie Glass, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink, Jianyuan K. Zhong

Computer Science: Faculty Publications

One of the open problems posed in [3] is: what is the minimal number k such that an open, flexible k-chain can interlock with a flexible 2-chain? In this paper, we establish the assumption behind this problem, that there is indeed some k that achieves interlocking. We prove that a flexible 2-chain can interlock with a flexible, open 16-chain.

Neutrosophic Dialogues, Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

Thanks to Dr. Smarandache for his interest in Chinese culture. I cannot decline his warm request to write the preface, even with my fragments of knowledge – no insight nor wisdom, and therefore can be misleading. I have been extremely regretful for my ideological errors and mistakes in previous publications, especially those concerning Buddhism. As I mentioned in this book, I am not qualified. So please note that I am limited in my knowledge and enlightenment of the giant of Chinese heritage. I can express nothing more than my personal bias. In what aspect can Chinese culture be distinctive from …

The Quaternions With An Application To Rigid Body Dynamics, Evangelos A. Coutsias, Louis Romero

Branch Mathematics and Statistics Faculty and Staff Publications

William Rowan Hamilton invented the quaternions in 1843, in his effort to construct hypercomplex numbers, or higher dimensional generalizations of the complex numbers. Failing to construct a generalization in three dimensions (involving triplets) in such a way that division would be possible, he considered systems with four complex units and arrived at the quaternions. He realized that, just as multiplication by i is a rotation by 90o in the complex plane, each one of his complex units could also be associated with a rotation in space. Vectors were introduced by Hamilton for the first time as pure quaternions and Vector …

Advances And Applications Of Dezert-Smarandache Theory (Dsmt), Vol. 1, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning is a natural extension of the classical Dempster-Shafer Theory (DST) but includes fundamental differences with the DST. DSmT allows to formally combine any types of independent sources of information represented in term of belief functions, but is mainly focused on the fusion of uncertain, highly conflicting and imprecise quantitative or qualitative sources of evidence. DSmT is able to solve complex, static or dynamic fusion problems beyond the limits of the DST framework, especially when conflicts between sources become large and when the refinement of the frame of the problem under consideration …

Fuzzy Relational Maps And Neutrosophic Relational Maps, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature about FRE and its applications. We have given only those papers which we could access and which interested us specially. We have taken those papers which in our opinion could be transformed for neutrosophic study. The second importance of this book is that …

Basic Neutrosophic Algebraic Structures And Their Application To Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit …

Analysis Of Social Aspects Of Migrant Labourers Living With Hiv/Aids Using Fuzzy Theory And Neutrosophic Cognitive Maps, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, unknown, incompleteness, inconsistency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role in any real-world problem, was introduced first by one of the authors Florentin Smarandache. In this …

Applications Of Stochastic Calculus To Finance, Scott Stelljes

UNF Graduate Theses and Dissertations

Stochastic Calculus has been applied to the problem of pricing financial derivatives since 1973 when Black and Scholes published their famous paper "The Pricing of Options and Corporate Liabilities" in the Joumal of Political Economy. The purpose of this thesis is to show the mathematical principles underlying the methods applied to finance and to present a new model of the stock price process.

As part of this paper, we present proofs of Ito's Formula and Girsanov's Theorem which are frequently used in financial applications. We demonstrate the application of these theorems to calculating the fair price of a European call …

A Thermoviscoelastic Beam Model For Brakes, Kenneth Kuttler, J. Bajkowski, J. R. Fernandez, M. Shillor

Faculty Publications

A model for the dynamic thermomechanical behavior of a viscoelastic beam which is in frictional contact with a rigid rotating wheel is presented. It describes a simple braking system in which the wheel comes to a stop as a result of the frictional traction generated by the beam. Friction is modelled with a temperature and slip rate dependent coefficient of friction. Frictional heat generation is taken into account as well as the wheel temperature evolution, and the wear of the beam's contacting end. The model is formulated as a variational inequality. A FEM numerical scheme for the model is described, …