Physical Sciences and Mathematics Commons^™

Environmental Acoustic Transfer Functions And Filtering Acoustic Signals, Brandon P. Dias

Theses and Dissertations

Signal processing is the method of taking a given signal and extracting useful information, usually by a means of a transformation of some kind. Acoustic signals are functions of time in which the output is a pressure or a velocity potential response. An acoustic signal is affected by the environment in which it propagates, so one can attempt to remove the environmental effects to extract the useful information, in this case the original signal. This thesis will derive, in a mathematical framework, the process of filtering extraneous signals in a way that yields the original signal, and will then apply …

Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …

Noise Estimation In The Presence Of Bpsk Digital Burst Transmissions, Susan E. Bettison

Theses and Dissertations

This research explores noise estimation techniques in an attempt to improve upon a previously developed digital burst transmission Binary Phase Shift Keyed (BPSK) demodulator. The demodulator success is dependent on the accuracy of the estimate of Power Spectral Density (PSD) of the unknown noise. Given a discrete time signal transformed into the frequency domain, the research seeks to determine if it is possible to effectively estimate the PSD of the unknown noise. The demodulator was developed using a new signal model for digital burst transmissions based on linear spectral subspace theory. Using this model and the redundancy properties of BPSK …

Laser Wakefield Acceleration By Petawatt Ultrashort Laser Pulses, Leonid M. Gorbunov, Serguei Y. Kalmykov, Patrick Mora

Serge Youri Kalmykov

An ultrashort (about 30 fs) petawatt laser pulse focused with a wide focal spot (about 100 mm) in a rarefied plasma (n_0 ~ 10^{17} cm^{−3}) excites a nonlinear plasma wakefield which can accelerate injected electrons up to GeV energies without any pulse channeling. Under these conditions, propagation of the laser pulse with an overcritical power for relativistic self-focusing is almost the same as in vacuum. The nonlinear quasiplane plasma wave, whose amplitude and phase velocity vary along the laser path, effectively traps and accelerates injected electrons with a wide range of initial energies. Electrons accelerated over two Rayleigh lengths (about …

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.

Balanced Scaling Vectors Using Linear Combinations Of Existing Scaling Vectors, Bruce Kessler

Mathematics Faculty Publications

The majority of the research done into creating balanced multiwavelets has involved establishing a series of conditions on the mask of the new scaling vector by solving a large nonlinear system. The result is a completely different new function vector solution to the dilation equation with the new matrix coefficients. The research presented here will show a way to use previously-constructed orthonormal scaling vectors to generate equivalent orthonormal scaling vectors that are balanced up to the approximation order of the previous scaling vector. The technique uses linear combinations of the integer translates of the previous-constructed scaling vector.

Cluster Analysis Of Genomic Data With Applications In R, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper, we provide an overview of existing partitioning and hierarchical clustering algorithms in R. We discuss statistical issues and methods in choosing the number of clusters, the choice of clustering algorithm, and the choice of dissimilarity matrix. In particular, we illustrate how the bootstrap can be employed as a statistical method in cluster analysis to establish the reproducibility of the clusters and the overall variability of the followed procedure. We also show how to visualize a clustering result by plotting ordered dissimilarity matrices in R. We present a new R package, hopach, which implements the hybrid clustering method, …

Multiple Testing Procedures And Applications To Genomics, Merrill D. Birkner, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

This chapter proposes widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; van der Laan et al., 2004a,b; Pollard and van der Laan, 2004; Pollard et al., 2005). Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of Type I errors, V_n, and rejected hypotheses, R_n. These error rates include: …

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models, Larry Leon, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are …

Internal Design Of Uniform Shear Rate Dies, Thomas J. Awe, M. B. M. Eligindi, R. W. Langer, University Of Wisconsin - Eau Claire, Department Of Mathematics

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

An Introduction To Sdr's And Latin Squares, Jordan Bell, Carleton University, School Of Mathematics And Statistics

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

A Survey Of The Quadratic Assignment Problem, With Applications, Clayton W. Commander

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Implementing Lazy Streams In C++, David Renz, Mike Borowczak

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Reversals And Transpositions Over Finite Alphabets, A. J. Radcliffe, A. D. Scott, E. L. Wilmer

Department of Mathematics: Faculty Publications

Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, or signed reversal distance between two strings over a finite alphabet is NP-hard, while for “dense” instances we give a polynomial-time approximation scheme. We also give a number of extremal results, as well as investigating the distance between random strings and the problem of sorting a string over a finite alphabet.

Weak Solutions To The Cauchy Problem Of A Semilinear Wave Equation With Damping And Source Terms, Petronela Radu

Department of Mathematics: Faculty Publications

In this paper we prove local existence of weak solutions for a semilinear wave equation with power-like source and dissipative terms on the entire space ℝⁿ. The main theorem gives an alternative proof of the local in time existence result due to J. Serrin, G. Todorova and E. Vitillaro, and also some extension to their work. In particular, our method shows that sources that are not locally Lipschitz in L² can be controlled without any damping at all. If the semilinearity involving the displacement has a “good” sign, we obtain global existence of solutions.

Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi

Mathematics Faculty Research Publications

In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.

A Posteriori Estimate For Tikhonov Regularization Parameter, S. Abbasbandy

Saeid Abbasbandy

This paper deals the numerical solution of integral equations of the first kind with using regularization method. There are many stopping rules based on discrepancy principle or discussed in [3]. Here a new stopping rule is described which uses SVD (Singular Value Decomposition) and condition number of matrices. Finally, we give a number of numerical examples showing that the method works well in practice.

A Method For Solving Fuzzy Linear Systems, S. Abbasbandy, M. Alavi

Saeid Abbasbandy

In this paper we present a method for solving fuzzy linear systems by two crisp linear systems. Also necessary and sufficient conditions for existence of solution are given. Some numerical examples illustrate the efficiency of the method.

A New Method For Solving Symmetric Fuzzy Linear Systems, S. Abbasbandy, M. Alavi

Saeid Abbasbandy

In this paper we represent a new method for solving a symmetric fuzzy linear system by two crisp linear systems. Also necessary and sufficient conditions for the solution existence are given.

Rebuild Of King Fang 40 Bc Musical Scales, Ji-Huan He

Ji-Huan He

No abstract provided.

Mathematical Modeling Of The Hypothalamic-Pituitary-Adrenal System Activity, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Mechanism Of Structural Transformation In Bismuth Titanate, Sudhanshu Mallick, Keith J. Bowman, Alexander H. King

Alexander H. King

Sodium-doped bismuth titanate undergoes a transformation from Bi4Ti3O12 to Na0.5Bi4.5Ti4O15 on heating in air at temperatures exceeding 800 °C. This transformation proceeds through the intermediate Na0.5Bi8.5Ti7O27 structure which is an intergrowth phase of the two. High-resolution transmission electron microscopy was used to study this transformation. From the Moiré pattern that was obtained, the crystallographic orientation of the transformation front has been determined and a mechanism is proposed for this structural transformation.

Dislocation-Indenter Interaction In Nanoindentation, M. Ravi Shankar, Alexander H. King, Srinivasan Chandrasekar

Alexander H. King

A formulation of dislocation-indenter interaction in two-dimensional, isotropic elasticity is presented. A significant dislocation-indenter interaction is predicted when dislocations are nucleated very close to the indenter. This interaction is expected to have an important influence on dislocation motion and multiplication. Upon nucleation close to the indenter, the dislocations are shown to modify the load, load distribution, and moment acting on the indenter. This effect is seen to vary with the indentation contact length. Further away from the indenter, the indenter-dislocation interaction is shown to be negligible.

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Yi Li

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

Stability Properties Of Linear Volterra Integrodifferential Equations With Nonlinear Perturbation, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

A Lyapunov functional is employed to obtain conditions that guarantee stability, uniform stability and uniform asymptotic stability of the zero solution of a scalar linear Volterra integrodifferential equation with nonlinear perturbation.

Boundedness And Stability In Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam, Ernest Yankson

Mathematics Faculty Publications

In this paper we study stability and boundedness of the nonlinear difference equation

x(t+1)=a(t)x(t)+c(t)Δx(t−g(t))+q(x(t),x(t−g(t))).

In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.

The Harmony Of The World, Chris Arthur

Faculty publications

Experimental music with mathematics and astronomy is discussed. Chord-like pitch arrangements are determined with geometric proportions arising in planetary movements. Rudimentary digital audio with Fourier series and the JPL on-line ephemeris is developed as a software solution. Computer musicians may listen to and select harmonies by specifying a date in time. A study and application of the ideas in The Harmony of the World by Johannes Kepler is presented with a software demonstration.

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

On Cographic Matroids And Signed-Graphic Matroids, Dan Slilaty

Mathematics and Statistics Faculty Publications

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-planar graphs, then the cographic matroids of G1, . . . , G29 are among the forbidden minors for the class of bias matroids …

A Geometric Characterization: Complex Ellipsoids And The Bochner-Martinelli Kernel, Michael Bolt

University Faculty Publications and Creative Works

Boas' characterization of bounded domains for which the Bochner-Martinelli kernel is self-adjoint is extended to the case of a weighted measure. For strictly convex domains, this equivalently characterizes the ones whose Leray-Aǐzenberg kernel is self-adjoint with respect to weighted measure. In each case, the domains are complex linear images of a ball, and the measure is the Fefferman measure. The Leray-Aǐzenberg kernel for a strictly convex hypersurface in ℂn is shown to be Möbius invariant when defined with respect to Fefferman measure. © 2005 University of Illinois.