Physical Sciences and Mathematics Commons^™

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

Finite Extinction Time For Non-Linear Absorption-Diffusion Equations, Jacob B. Goldberg

Theses and Dissertations

In this thesis, we develop a numerical method in order to approximate the solutions of one-dimensional, non-linear absorption-diffusion equations. We test our method for accuracy against a linear diffusion equation with a solution that can be written in closed form. We then test various types of diffusion and absorption terms to determine which ones produce extinction in finite time. We also develop a numerical method to computationally solve diffusion-free equations. We compare the numerical solutions of the one-dimensional, non-linear absorption-diffusion equation and the diffusion-free equation and we find that for the cases tested, the numerical absorption-diffusion solutions are always less …

Comparing Clustering Algorithms For Use With Genomic And Proteomic Data, Rebecca A. Olson

Theses and Dissertations

The Human Genome Project and related projects have resulted in the development of a number of new experimental and analytic tools for use in genomic and proteomic research. In the area of toxicogenomics, researchers are concerned with how genes react to exposure to certain chemicals. The United States Air Force is interested in the effect of exposure to mission-essential chemicals. Although military personnel may come into contact with chemicals such as hydrazine, risk assessment is usually very limited. On the genomic level, risk assessment is a multi-stop and multi-disciplinary process. The process begins with an experiment that exposes cells to …

Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang

Mathematics Research Reports

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h^{1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.}

Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger

Mathematical Sciences Technical Reports (MSTR)

This paper develops a fast algorithm for locating one or more perfectly insulating, pair-wise disjoint, linear cracks in a homogeneous two-dimensional electrical conductor, using boundary measurements.

Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h^{1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.}

The Order At 2 Of The Odd-Partition Function, Chris Mehelich

Mathematical Sciences Technical Reports (MSTR)

Abstract. We evaluate the odd-partition function p₂(n) modulo 4 by elementary methods and analyze the asymptotic distribution of p₂(n) modulo 4. We use the theory of modular forms to obtain necessary and sufficient conditions for the order at 2 of p₂(n) to equal any given value between 0 and 4 inclusive.

Statistical Properties Of Composite Distortions In Hfc Systems And Their Effects On Digital Channels, Ron D. Katznelson

Ron D. Katznelson

The statistical properties of Composite Triple Beat (CTB) and Composite Second Order (CSO) distortion terms associated with the analog channels carried on Hybrid Fiber Coax (HFC) are presented. Both simulation and measurement results show that such distortion components falling on individual channels have amplitude Probability Density Function that is nearly Rayleigh distributed (having a Standard Deviation of 5.7 dB). It is shown that both CTB and CSO components have peak envelope power fluctuations that exceed their average (measured) power levels by more than 15 dB. The temporal statistical properties of these distortion components demonstrate peak envelope power fluctuations with characteristic …

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Yi Li

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=^N\ω is an exterior domain in ^N, ω⊂^N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈C^α_loc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|^l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=^N\ω is an exterior domain in ^N, ω⊂^N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈C^α_loc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|^l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

Nonlinear Dynamics Of Mode-Locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, J Nathan Kutz

All HMC Faculty Publications and Research

We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature …

Tournament Matrices An Overview, Russel O. Carlson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief …

Nonlinear Schrödinger Type Equations With Asymptotically Linear Terms, Francois A. Van Heerden

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We study the nonlinear Schrödinger type equation

–Δu + (λg(x) + 1)u = f(u)

on the whole space R^N. The nonlinearity f is assumed to be asymptotically linear and g(x) ≥ 0 has a potential well. We do not assume a limit for g(x) as |x| → ∞ . Using variational techniques, we prove the existence of a positive solution for λ large. In the case where f is odd we obtain multiple pairs of solutions. The limiting behavior of solutions as λ → ∞ is also considered.

Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli

CMC Faculty Publications and Research

A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.

Identifying Enlisted Stay And Leave Population Characteristics With Discriminant Analysis, Zabrina Y. Hoggard

Theses and Dissertations

The research contribution of this thesis is the first known integrated architecture and feature selection algorithm for Radial Basis Neural Networks (RBNNs). The objective is to apply the network iteratively to determine the final architecture and feature set used to evaluate a problem. Additionally, this thesis compares three different classification techniques, Discriminant Analysis (DA), Feed-Forward Neural Networks (FFN) and RBNNs against several hard to solve problems. These problems were used to evaluate general classifier performance as well as the performance of the feature selection techniques. This thesis describes the classification techniques as well as the measures used to evaluate them. …

An Analysis Of Mutually Dispersive Brown Symbols For Non-Linear Ambiguity Suppression, Matthew J. Papaphotis

Theses and Dissertations

This thesis significantly advances research towards the implementation of optimal Non-linear Ambiguity Suppression (NLS) waveforms by analyzing the Brown theorem. The Brown theorem is reintroduced with the use of simplified linear algebraic notation. A methodology for Brown symbol design and digitization is provided, and the concept of dispersive gain is introduced. Numerical methods are utilized to design, synthesize, and analyze Brown symbol performance. The theoretical performance in compression and dispersion of Brown symbols is demonstrated and is shown to exhibit significant improvement compared to discrete codes. As a result of this research a process is derived for the design of …

Selecting Salient Features In High Feature To Exemplar Ratio Conditions, Ismail Aslan

Theses and Dissertations

A key tenet to the Air Force's vision of Global Vigilance, Reach, and Power is the ability to project power via the use of aerial refueling. Scheduling of limited tanker resources is a major concern for Air Mobility Command (AMC). Currently the Combined Mating and Ranging Planning System (CMARPS) is used to plan aerial refueling operations, however due to the complex nature of the program and the length of time needed to run a scenario, the need for a simple tool that runs in much shorter time is desired. Ant colony algorithms are recently developed heuristics for finding solutions to …

Modeling And Analysis Of Multicommodity Network Flows Via Goal Programming, Matthew A. Scott

Theses and Dissertations

In this research we focused on the mobility system modeled by the AMC mobility planner's calculator (AMPCALC). We developed AMPCALC as a user-friendly tool and allow the user to easily carry out strategic airlift, air refueling and aeromedical evacuation calculations that are covered in Air Force Pamphlet 10-1403. In this study, Excel software and its macro language, Visual Basic for Application, are our two main tools. In the methodology of the thesis we examined fundamental aspects of the mobility system in AMPCALC. We discussed formulation logic of the mobility cycle. We presented ramp use optimization and tanker optimization processes. We …

A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga

Mathematics Research Reports

A new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergence at element edge centers for the regular pattern.

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

Laplace Transform Of Spherical Bessel Functions, Andrei Ludu

Andrei Ludu

No abstract provided.

Low-Cost Manufacturing Process For Nanostructured Metals And Alloys, Travis L. Brown, Srinivasan Swaminathan, Srinivasan Chandrasekar, W. Dale Compton, Alexander H. King, Kevin P. Trumble

Alexander H. King

In spite of their interesting properties, nanostructured materials have found limited uses because of the cost of preparation and the limited range of materials that can be synthesized. It has been shown that most of these limitations can be overcome by subjecting a material to large-scale deformation, as occurs during common machining operations. The chips produced during lathe machining of a variety of pure metals, steels, and other alloys are shown to be nanostructured with grain (crystal) sizes between 100 and 800 nm. The hardness of the chips is found to be significantly greater than that of the bulk material.

Resonances And Superlattice Pattern Stabilization In Two-Frequency Forced Faraday Wave, Chad M. Topaz, Mary Silber

Chad M. Topaz

We investigate the role weakly damped modes play in the selection of Faraday wave patterns forced with rationally related frequency components $m\omega$ and $n\omega$. We use symmetry considerations to argue for the special importance of the weakly damped modes oscillating with twice the frequency of the critical mode, and those oscillating primarily with the “difference frequency” $|n−m| \omega$ and the “sum frequency” $(n+m) \omega$. We then perform a weakly nonlinear analysis using equations of Zhang and Viñals [J. Fluid Mech. 336 (1997) 301] which apply to small-amplitude waves on weakly inviscid, deep fluid layers. For weak damping and forcing and …

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C^1,1 solution to the uniformly elliptic equation F(D²u) = 0 must belong to C^2,α, if the equation has the Liouville property.

Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller

Mathematics and Statistics Faculty Publications

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.

Absolutely Continuous Jacobi Operators, Steen Pedersen

Mathematics and Statistics Faculty Publications

No abstract provided.

A Recommendation For Determining The Efficacy Of Weight Removal Estimates For The Pacific Cod Longline Cdq Fishery, Anna L. Furniss

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In January 2000, the Alaska Department of Community and Economic Development contacted the National Marine Fisheries Service (NMFS) regarding concerns over the methods used to determine catch estimates for the Pacific Cod Community Development Quota (CDQ) fishery. Currently, NMFS determines catch estimates for the Pacific Cod CDQ fishery based on the data collected by observers from the North Pacific Groundfish Observer Program (NPGOP).

Observer estimates for catch are based on the random sampling methods for a longline fishing vessel as described in the North Pacific Groundfish Observer Manual. These sampling methods provide an official total catch (OTC) estimate for each …

Parameters Affecting Partitioning Of 6 Pcb Congeners In Natural Sediments, Eid A. Alkhatib, Carl Weigand

Chemistry & Physics Faculty Publications

Polychlorinated biphenyls (PCBs) released by bottom sediments were determined by experiments in which the sediments were artificially resuspended using sediment contaminated with PCBs in a particle entrainment simulator (PES). Sediment cores, spiked with PCBs, were collected from the Housatonic River in Connecticut and run in the PES at simulated shear stresses from 0 to 0.6 N m(-2). Experimental results from these simulations have shown that mean concentration of PCBs in the solid phase for sites with high volatile organic carbon (VOC) were significantly greater than samples with low VOC; the reverse was true for the water phase. In addition, on …

Explicit Multiplicative Relations Between Gauss Sums, Brian J. Murray

LSU Doctoral Dissertations

H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.

Group Automorphisms And The Decomposition Of Plancherel Measures, David Slay

LSU Doctoral Dissertations

In this paper, a natural action of the automorphisms of a group on the space of irreducible unitary representations is used to decompose the Plancherel measure on the dual space as an integral of measures on homogeneous spaces. Explicit decompositions are obtained for the cases of free 2 and 3-step nilpotent Lie groups. These results are obtained using direct integral decompositions, induced representations, the Mackey Machine, and measure theory on homogeneous spaces.