Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2009

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 31 - 60 of 223

Full-Text Articles in Applied Mathematics

The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou Nov 2009

The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),...,M*(G29),R15,R16. Here G1,...,G29 are the vertically 2-connected excluded minors for the class of projective-planar graphs and R15 and R16 are two regular matroids that we will define in the article.

Go to article

The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu Oct 2009

The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu

Physics and Astronomy Publications

We present some applications of the Lambert W function (W function) to the formalism of quantum statistics (QS). We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then present some applications of this formula including Bose–Einstein systems in d dimensions, Maxwell–Boltzmann systems, and black body radiation. We also show that for the appropriate parameter values, this formula reduces to an analytic expression in connection with Wien’s displacement law that was found in a previous study. In addition, we …

Go to article

A Radical Transformation, Michael Castelbuono Oct 2009

A Radical Transformation, Michael Castelbuono

Lake Union Herald

No abstract provided.

Go to article

A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin Oct 2009

A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin

Scholarship

Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.

Go to article

Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle Sep 2009

Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle

Conference papers

This paper discusses a new approach to ‘watermarking’ digital signals using linear frequency modulated or ‘chirp’ coding. The principles underlying this approach are based on the use of a matched filter to provide a reconstruction of a chirped code that is uniquely robust in the case of signals with very low signal-to-noise ratios. Chirp coding for authenticating data is generic in the sense that it can be used for a range of data types and applications (the authentication of speech and audio signals, for example). The theoretical and computational aspects of the matched filter and the properties of a chirp …

Go to article

On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue Sep 2009

On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue

Scholarship

Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a generalmethod to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

Go to article

Targeted Maximum Likelihood Estimation: A Gentle Introduction, Susan Gruber, Mark J. Van Der Laan Aug 2009

Targeted Maximum Likelihood Estimation: A Gentle Introduction, Susan Gruber, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This paper provides a concise introduction to targeted maximum likelihood estimation (TMLE) of causal effect parameters. The interested analyst should gain sufficient understanding of TMLE from this introductory tutorial to be able to apply the method in practice. A program written in R is provided. This program implements a basic version of TMLE that can be used to estimate the effect of a binary point treatment on a continuous or binary outcome.

Go to article

Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht Aug 2009

Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht

Publications

The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids. The basic governing equations are solved by means of a finite-volume scheme that is faithful, accurate, and conservative. Furthermore, this scheme is compatible with thermodynamics through the identification of the notions of numerical fluxes (a notion from numerics) and of excess quantities (a notion from irreversible thermodynamics). A selection of one-dimensional wave propagation problems is presented, the simulation of which exploits the designed numerical scheme. This selection of exemplary problems includes (i) waves in periodic media for weakly nonlinear waves with …

Go to article

Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne Aug 2009

Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne

Electronic Theses and Dissertations

The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain approximate solutions of the Fitzhugh Nagumo model and …

Go to article

Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel Aug 2009

Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel

COBRA Preprint Series

Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a …

Go to article

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda Aug 2009

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda

Undergraduate Research Opportunities Program (UROP)

We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.

Go to article

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, Alun L. Lloyd Aug 2009

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, Alun L. Lloyd

Mathematics and Computer Science Faculty Publications

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …

Go to article

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. Banks, Alex Capaldi, Alun Lloyd Aug 2009

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. Banks, Alex Capaldi, Alun Lloyd

Mathematics and Statistics Faculty Publications

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …

Go to article

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis Aug 2009

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis

Masters Theses & Specialist Projects

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between …

Go to article

Portfolio Selection Problem Under Uncertainty And Risk, Dimitri Nowak Aug 2009

Portfolio Selection Problem Under Uncertainty And Risk, Dimitri Nowak

All Theses

The purpose of this research is the investigation of a portfolio problem in an uncertain environment. Given possible investments with random performance depending on uncertain environmental settings the objective is to establish a methodology for construction of a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution is preferable for a least risk decision maker.

Go to article

Change-Point Analysis: Asymptotic Theory And Applications, Michael Robbins Aug 2009

Change-Point Analysis: Asymptotic Theory And Applications, Michael Robbins

All Dissertations

The problem of undocumented change-points in data sets appears in many areas of science. Mathematical fundamentals of asymptotic methods used in change-point analysis are discussed, and several important maximally selected change-point statistics are introduced. First, the likelihood ratio method is applied to abstract data models within the setting of precipitation series. Basic inference as to the legitimacy and effectiveness of asymptotic methods at detecting undocumented change-points is provided. Next, maximally selected chi-square statistics are discussed in detail and applied to data on tropical cyclone behavior, where a widely available and widely analyzed data set on Atlantic basin cyclones is studied. …

Go to article

Multiobjective Optimization For Complex Systems, Melissa Gardenghi Aug 2009

Multiobjective Optimization For Complex Systems, Melissa Gardenghi

All Dissertations

Complex systems are becoming more and more apparent in a variety of disciplines, making solution methods for these systems valuable tools. The solution of complex systems requires two significant skills. The first challenge of developing mathematical models for these systems is followed by the difficulty of solving these models to produce preferred solutions for the overall systems. Both issues are addressed by this research.
This study of complex systems focuses on two distinct aspects. First, models of complex systems with multiobjective formulations and a variety of structures are proposed. Using multiobjective optimization theory, relationships between the efficient solutions of the …

Go to article

Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich Aug 2009

Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to a rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new sub differential properties of infima! convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) sub differentials …

Go to article

Discrete Dynamics Over Finite Fields, Jang-Woo Park Aug 2009

Discrete Dynamics Over Finite Fields, Jang-Woo Park

All Dissertations

A dynamical system consists of a set V and a map f : V → V . The primary goal is to characterize points in V according to their limiting behaviors under iteration of the map f . Especially understanding dynamics of nonlinear maps is an important but difficult problem, and there are not many methods available. This work concentrates on dynamics of certain nonlinear maps over finite fields. First we study monomial dynamics over finite fields. We show that determining the number of fixed points of a boolean monomial dynamics is #P–complete problem and consider various cases in which …

Go to article

A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott Aug 2009

A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott

Department of Mathematics: Dissertations, Theses, and Student Research

Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperature-dependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate …

Go to article

Local Adaptive Smoothing In Kernel Regression Estimation, Qi Zheng Aug 2009

Local Adaptive Smoothing In Kernel Regression Estimation, Qi Zheng

All Theses

We consider nonparametric estimation of a smooth regression function of one variable. In practice it is quite popular to use the data to select one global smoothing parameter. Such global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method to select local smoothing parameters which takes into account sparseness and adapts to local curvature of the regression function. A Bayesian method allows the smoothing parameter to adapt to the local sparseness of the covariate and provides the basis for a local cross …

Go to article

Sparse Representations In Power Systems Signals, Jack Cooper Aug 2009

Sparse Representations In Power Systems Signals, Jack Cooper

All Theses

This thesis seeks to detect transient disturbances in power system signals in a sparse framework. To this end, an overcomplete wavelet packet dictionary and damped sinusoid dictionary are considered, and for each dictionary Matching Pursuit is compared with Basis Pursuit. Previous work in developing waveform dictionary theory and sparse representation is reviewed, and simulations are run on a test signal in both noisy and noiseless environments. The solutions are viewed as time-frequency plane tilings to compare the accuracy and sparsity of these algorithms in properly resolving optimal representations of the disturbances. The advantages and disadvantages of each combination of dictionary …

Go to article

Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena Aug 2009

Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena

All Theses

Over the past decades, a number of mathematical models and solution techniques have been developed to preserve reserve sites for species and their natural habitats. Two optimization models for designing spatially compact ecological reserve systems are addressed here as zero-one integer programming problems. These formulations have a bicriteria objective function that is a combination of both boundary length and distance. The two formulations cluster the sites into a relatively small number of compact groups while preserving a required number of sites that contain a certain species using a given amount of resources. Two general types of approaches have been developed …

Go to article

Variations On Graph Products And Vertex Partitions, Jobby Jacob Aug 2009

Variations On Graph Products And Vertex Partitions, Jobby Jacob

All Dissertations

In this thesis we investigate two graph products called double vertex graphs and complete double vertex graphs, and two vertex partitions called dominator partitions and rankings.
We introduce a new graph product called the complete double vertex graph and study its properties. The complete double vertex graph is a natural extension of the Cartesian product and a generalization of the double vertex graph.
We establish many properties of complete double vertex graphs, including results involving the chromatic number of a complete double vertex graph and the characterization of planar complete double vertex graphs. We also investigate the important problem of …

Go to article

Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers Aug 2009

Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers

All Dissertations

In a note in the American Mathematical Monthly in 1960, Strodt mentions a way to prove both the Euler-Maclaurin summation formula and the Boole summation formula using operators. In a 2009 article in the Monthly, Borwein, Calkin, and Manna expand on this idea. Therein, they define Strodt operators and Strodt polynomials and show that the classical Bernoulli polynomials and Euler polynomials are examples of Strodt polynomials.
It is well known that both Bernoulli polynomials and Euler polynomials on a fixed interval are asymptotically sinusoidal. Borwein, Calkin, and Manna show that a similar result holds for the uniform Strodt polynomials. We …

Go to article

Quality Representation In Multiobjective Programming, Stacey Faulkenberg Aug 2009

Quality Representation In Multiobjective Programming, Stacey Faulkenberg

All Dissertations

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along …

Go to article

Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan Aug 2009

Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan

All Dissertations

Factoring polynomials is a central problem in computational algebra and number theory and is a basic routine in most
computer algebra systems (e.g. Maple, Mathematica, Magma, etc). It has been extensively studied
in the last few decades by many mathematicians and computer scientists. The main approaches include Berlekamp's method
(1967) based on the kernel of Frobenius map, Niederreiter's method (1993) via an ordinary differential equation,
Zassenhaus's modular approach (1969), Lenstra, Lenstra and Lovasz's lattice reduction (1982), and Gao's method via a partial differential equation (2003). These methods and their recent improvements due to van Hoeij (2002) and
Lecerf et al …

Go to article

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler Jul 2009

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler

Mathematics Faculty Publications

The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works of visual art and computer programming. Two of the authors were undergraduate students in Dr. Hamburger's linear algebra class, where this technique was implemented as a special project for the students. The two students generated the images seen in this paper, and the movies that can be found on the accompanying webpage www.wku.edu/\~{\space}bruce.kessler/.

Go to article

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton Jul 2009

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

Go to article

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro Jul 2009

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro

All HMC Faculty Publications and Research

We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.

Go to article

First Prev Next Last