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Applied Mathematics

2012

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Articles 331 - 351 of 351

Full-Text Articles in Physical Sciences and Mathematics

Lattice Residuability, Philip Theodore Thiem Jan 2012

Lattice Residuability, Philip Theodore Thiem

Masters Theses

"Residuated lattices form the basis of certain kinds of logical interpretations. Also, complete commutative integral zero-bounded residuated lattices are used as a set of truth values for fuzzy logic values, Which are more general than the traditional bounded interval introduced by Zadeh. At times, it is important to know whether or not the lattice can be residuated in the first place. This thesis reviews the literature in lattice residuability and adds more observations. Specifically, (1) bounded chains and top-residuated lattices are show [sic] to be residuable, and (2) additional conditions necessary for residuability are established"--Abstract, page iii.

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Infeasible Full-Newton-Step Interior-Point Method For The Linear Complementarity Problems, Antré Marquel Drummer Jan 2012

Infeasible Full-Newton-Step Interior-Point Method For The Linear Complementarity Problems, Antré Marquel Drummer

Electronic Theses and Dissertations

In this tesis, we present a new Infeasible Interior-Point Method (IPM) for monotone Linear Complementarity Problem (LPC). The advantage of the method is that it uses full Newton-steps, thus, avoiding the calculation of the step size at each iteration. However, by suitable choice of parameters the iterates are forced to stay in the neighborhood of the central path, hence, still guaranteeing the global convergence of the method under strict feasibility assumption. The number of iterations necessary to find -approximate solution of the problem matches the best known iteration bounds for these types of methods. The preliminary implementation of the method …

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Lifetime Prediction And Confidence Bounds In Accelerated Degradation Testing For Lognormal Response Distributions With An Arrhenius Rate Relationship, Steven Michael Alferink Jan 2012

Lifetime Prediction And Confidence Bounds In Accelerated Degradation Testing For Lognormal Response Distributions With An Arrhenius Rate Relationship, Steven Michael Alferink

Doctoral Dissertations

"Determining the lifetime of a product is an important component of quality assurance. Traditional life testing methods are infeasible for products that have been designed to have a very long lifetime because they require a lengthy testing period. An alternative method is accelerated degradation testing, where a response variable determining the usability of the product is measured over time under multiple accelerating stress levels. The resulting data are then used to predict the life distribution of the product under the design stress level. In this dissertation, several methods are proposed and studied for obtaining prediction bounds for the lifetime of …

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Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek Jan 2012

Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek

Open Access Theses & Dissertations

In this work we will present a self-contained introduction to the option pricing problem. We will introduce some basic ideas from the probability theory and stochastic differential equations. Later we will move to the partial differential equations since the option pricing problem arising in financial mathematics when asset is driven by a stochastic volatility process and assumed presence of transaction cost leads to solving non-linear partial dif- ferential equation. We will also present the complete process from deriving the desired partial differential equation to the proof of existence of a solution and also the numerical simulations. Using techniques form stochastic …

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A Review Of Some Subtleties Of Practical Relevance, Keqin Gu Jan 2012

A Review Of Some Subtleties Of Practical Relevance, Keqin Gu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The …

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The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu Jan 2012

The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological …

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Stability Analysis Of Fitzhugh-Nagumo With Smooth Periodic Forcing, Tyler Massaro, Benjamin F. Esham Jan 2012

Stability Analysis Of Fitzhugh-Nagumo With Smooth Periodic Forcing, Tyler Massaro, Benjamin F. Esham

Faculty Publications and Other Works -- Mathematics

Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propagation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later by Jin-Ichi Nagumo who created a tunnel diode circuit based upon FitzHugh’s work. The resulting differential model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics (Izhikevich, 2010). We begin by providing a thorough grounding in the physiology behind the equations, then continue by introducing some …

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Hypercube Diagrams For Knots, Links, And Knotted Tori, Ben Mccarty Jan 2012

Hypercube Diagrams For Knots, Links, And Knotted Tori, Ben Mccarty

LSU Doctoral Dissertations

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. Finally, there is a generalization of cube …

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Paley-Wiener Theorem For Line Bundles Over Compact Symmetric Spaces, Vivian Mankau Ho Jan 2012

Paley-Wiener Theorem For Line Bundles Over Compact Symmetric Spaces, Vivian Mankau Ho

LSU Doctoral Dissertations

We generalize a Paley-Wiener theorem to homogeneous line bundles $L_\chi$ on a compact symmetric space U/K with $\chi$ a nontrivial character of K. The Fourier coefficients of a $\chi$-bi-coinvariant function f on U are defined by integration of f against the elementary spherical functions of type $\chi$ on U, depending on a spectral parameter $\mu$, which in turn parametrizes the $\chi$-spherical representations $\pi$ of U. The Paley-Wiener theorem characterizes f with sufficiently small support in terms of holomorphic extendability and exponential growth of their $\chi$-spherical Fourier transforms. We generalize Opdam's estimate for the hypergeometric functions in a bigger domain with …

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Mathematical Models For Interest Rate Dynamics, Xiaoxue Shan Jan 2012

Mathematical Models For Interest Rate Dynamics, Xiaoxue Shan

LSU Master's Theses

We present a study of mathematical models of interest rate products. After an introduction to the mathematical framework, we study several basic one-factor models, and then explore multifactor models. We also discuss the Heath-Jarrow- Morton model and the LIBOR Market model. We conclude with a discussion of some modified models that involve stochastic volatility.

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On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton Dec 2011

On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton

Ralph Saxton

This paper examines the effect of damping on a nonstrictly hyperbolic 2x2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

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On The Strengthening Of Topological Signals In Persistent Homology Through Vector Bundle Based Maps, E. Hanson, F. Motta, C. Peterson, Lori Ziegelmeier Dec 2011

On The Strengthening Of Topological Signals In Persistent Homology Through Vector Bundle Based Maps, E. Hanson, F. Motta, C. Peterson, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

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Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel Dec 2011

Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel

Tamas Lengyel

Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1,X2,...,Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased estimators and present the best estimators.

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General Allee Effect In Two-Species Population Biology, Saber Elaydi Dec 2011

General Allee Effect In Two-Species Population Biology, Saber Elaydi

Saber Elaydi

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator-prey models. The study is restricted to the strong Allee effect caused by an interspecific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a "phase space core" of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar …

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On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel Dec 2011

On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel

Tamas Lengyel

We analyze some 2 adic properties of the sequence defined by the recurrence Z(1) =1; Z(n) = n−1 k=1 S(n, k) Z(k), n ≥ 2, which counts the number of ultra-dissimilarity relations, i.e., ultra-metrics on an n-set. We prove the 2 adic growth property v2 (Z(n) ≥ log 2 n - 1) and present conjectures on the exact values.

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Eulerian Polynomials And B-Splines, Tian-Xiao He Dec 2011

Eulerian Polynomials And B-Splines, Tian-Xiao He

Tian-Xiao He

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, B-splines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann-zeta function values at odd integers are given. The relation between Eulerian numbers and B-spline values at knot points are also discussed.

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Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu Dec 2011

Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu

Andrei Ludu

No abstract provided.

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Excel Calculator For Assignment/Article "Compound Interest And The Power Of Saving", Richard H. Serlin Dec 2011

Excel Calculator For Assignment/Article "Compound Interest And The Power Of Saving", Richard H. Serlin

Richard H. Serlin

No abstract provided.

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A Remark On "A Nonlinear Mathematical Model Of The Corneal Shape", Ji-Huan He Dec 2011

A Remark On "A Nonlinear Mathematical Model Of The Corneal Shape", Ji-Huan He

Ji-Huan He

An analytical method using Taylor series is proposed to solve a nonlinear two-point boundary problem arising in corneal shape. The solution process makes it extremely easy to obtain a relatively accurate solution. The pencil-and-paper solution procedure can be extended to other boundary value problems.

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Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski Dec 2011

Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski

Wojciech Budzianowski

Oxy-reforming is emerging as an interesting alternative to conventional methods of hydrogen generation. The current article characterises this process through analysis of individual reactions: SMR (steam methane reforming), WGS (water gas shift) and CPO (catalytic partial oxidation). Analyses relate to optimisation of thermal conditions thus enabling cost-effectivenes of the process.

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Syllabus Of Intermediate Macroeconomics (Master's Course), Reza Moosavi Mohseni Dr. Dec 2011

Syllabus Of Intermediate Macroeconomics (Master's Course), Reza Moosavi Mohseni Dr.

Reza Moosavi Mohseni

No abstract provided.

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