Applied Mathematics Commons^™

Shock-Associated Noise Generation In Curved Coanda Turbulent Wall Jets, Caroline P. Lubert, Richard J. Shafer

Department of Mathematics and Statistics - Faculty Scholarship

Curved three-dimensional turbulent Coanda wall jets are present in a multitude of natural and engineering applications. The mechanism by which they form a shock-cell structure is poorly understood, as is the accompanying shock-associated noise (SAN) generation. This paper discusses these phenomena from both a modeling and experimental perspective. The Method of Characteristics is used to rewrite the governing hyperbolic partial differential equations as ordinary differential equations, which are then solved numerically using the Euler predictor-corrector method. The effects of complicating factors -- such as radial expansion and streamline curvature -- on the prediction of shock-cell location are then discussed. This …

Cooper’S Hawk Nest Site Characteristics In The Pineywoods Region, Richard R. Schaefer, D. Craig Rudolph, Josh B. Pierce, Jesse F. Fagan

Faculty Publications

Early accounts describe the Cooper’s Hawk (Accipiter cooperi) as a species in decline in much of North America during the early twentieth century (Bent 1937), particularly when in close proximity to humans (Eaton 1914). This decreasing population trend continued to be recognized later in the century in both Texas (Oberholser 1974) and Louisiana (Lowery 1974). Shooting and trapping during the first half of the 1900s, and pesticide use (especially DDT) after World War II are suggested as primary causes of the decline (Henny and Wight 1972, Bednarz et al. 1990). The Migratory Bird Treaty Act of 1972 and the ban …

A Time Series Approach To Electric Load Modelling, Matthias Benjamin Noller

Masters Theses

"With resources becoming more and more scarse [sic] as well as increasing competition caused by the liberalisation of the energy markets electric load modelling becomes ever more important for proper resource allocation.

This work tries to bridge the gap between long-term modelling done mainly via econometric approaches and short-term modelling in which time series models are more commonplace by focussing [sic] on pure time series modelling [sic] and exploring its limits in the process. Due to various seasonalities present in the data the approach chosen starts with a subdivision of the time axis in different time frames: A model for …

Problems In Gps Accuracy, Michael Thomas Vodhanel

CGU Theses & Dissertations

Improving and predicting the accuracy of positioning estimates derived from the global positioning system (GPS) continues to be a problem of great interest. Dependable and accurate positioning is especially important for navigation applications such as the landing of commercial aircraft. This subject gives rise to many interesting and challenging mathematical problems. This dissertation investigates two such problems. The first problem involves the study of the relationship between positioning accuracy and satellite geometry configurations relative to a user's position. In this work, accuracy is measured by so-called dilution of precision (DOP) terms. The DOP terms arise from the linear regression model …

On Greenberg's Question: An Algebraic And Computational Approach, David H. Chapman

LSU Doctoral Dissertations

Greenberg asked whether arithmetically equivalent number fields share the same Iwasawa invariants. In this dissertation it is shown that the problem naturally breaks up into four cases, depending on properties of Galois groups. This analysis is then used to give a positive answer to Greenberg’s question in some nontrivial examples.

Algebraic Structures Using Super Interval Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

This book has seven chapters. Chapter one is introductory in nature, just introducing the super interval matrices or interval super matrices. In chapter two essential operations on super interval matrices are defined. Further in this chapter algebraic structures are defined on these super interval matrices using these operation. Using these super interval matrices semirings and semivector spaces …

Studies In Sampling Techniques And Time Series Analysis, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

This book has been designed for students and researchers who are working in the field of time series analysis and estimation in finite population. There are papers by Rajesh Singh, Florentin Smarandache, Shweta Maurya, Ashish K. Singh, Manoj Kr. Chaudhary, V. K. Singh, Mukesh Kumar and Sachin Malik. First chapter deals with the problem of time series analysis and the rest of four chapters deal with the problems of estimation in finite population. The book is divided in five chapters as follows: Chapter 1. Water pollution is a major global problem. In this chapter, time series analysis is carried out …

Algebraic Structures Using Natural Class Of Intervals, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Authors in this book introduce a new class of intervals called the natural class of intervals, also known as the special class of intervals or as natural intervals. These intervals are built using increasing intervals, decreasing intervals and degenerate intervals. We say an interval [a, b] is an increasing interval if a < b for any a, b in the field of reals R. An interval [a, b] is a decreasing interval if a > b and the interval [a, b] is a degenerate interval if a = b for a, b in the field of reals R. The natural class of intervals consists of the collection of increasing intervals, decreasing intervals and the degenerate intervals. Clearly R is contained in the natural …

Study Of Natural Class Of Intervals Using (–∞,∞) And (∞, –∞), Florentin Smarandache, W.B. Vasantha Kandasamy, D. Datta, H.S. Kushwaha, P.A. Jadhav

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors study the properties of natural class of intervals built using (–∞, ∞) and (∞, –∞). These natural class of intervals behave like the reals R, as far as the operations of addition, multiplication, subtraction and division are concerned. Using these natural class of intervals we build interval row matrices, interval column matrices and m × n interval matrices. Several properties about them are defined and studied. Also all arithmetic operations are performed on them in the usual way. The authors by defining so have made it easier for operations like multiplication, addition, finding determinant and …

Dsm Super Vector Space Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which …

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly …

Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

No abstract provided.

Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk

Mathematics & Statistics Faculty Publications

Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics …

Dea With A Perfect Object: Analytical Solutions, Alexander Vaninsky

Publications and Research

For the main DEA models, adding a Perfect Object—that is, a virtual object that has the smallest inputs and greatest outputs—to a collection of actual objects permits obtaining solutions analytically. The paper derives formulas for the solutions and demonstrates that computations with them comprise simple operations with ratios of inputs and outputs while avoiding the use of linear programming (LP) algorithms. A numerical example illustrates the utility of the approach.

A Sparse Representation Technique For Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. In order to find such sparse linear representation, we implement an l₁-minimization algorithm. This methodology overcomes the lack of robustness with respect to outliers. In contrast to other classification …

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …

Currency Trading Using The Fractal Market Hypothesis, Jonathan Blackledge, Kieran Murphy

Articles

We report on a research and development programme in financial modelling and economic security undertaken in the Information and Communications Security Research Group (ICSRG, 2011) which has led to the launch of a new company - Currency Traders Ireland Limited - funded by Enterprise Ireland. Currency Traders Ireland Limited (CTI, 2011) has a fifty year exclusive license to develop a new set of indicators for analysing currency exchange rates (Forex trading). We consider the background to the approach taken and present examples of the results obtained to date.

A Generalized Nonlinear Model For The Evolution Of Low Frequency Freak Waves, Jonathan Blackledge

Articles

This paper presents a generalized model for simulating wave fields associated with the sea surface. This includes the case when `freak waves' may occur through an effect compounded in the nonlinear (cubic) Schrodinger equation. After providing brief introductions to linear sea wave models, `freak waves' and the linear and nonlinear Schrodinger equations, we present a unified model that provides for a piecewise continuous transition from a linear to a nonlinear state. This is based on introducing a fractional time derivative to develop a fractional nonlinear partial differential equation with a stochastic source function. In order to explore the characteristics of …

Nonlinear Behaviour Of Sea Surface Waves Based On Low-Gradient Phase-Only Scattering Effects, Jonathan Blackledge, Eugene Coyle, Derek Kearney

Conference papers

Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid …

Analytical And Experimental Investigations Of Ships Impact Interaction With One-Sided Barrier, Ihab M. Grace

Wayne State University Dissertations

This study deals with impact interaction of ships with one-sided ice barrier during roll dynamics. An analytical model of ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, brings to the attention the fact that the impact dynamics may have qualitatively different response characteristics to different …

Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren

Mathematics & Statistics Faculty Publications

We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u'(t) + ∫0 β (t - s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space, and β (t) is locally integrable, nonnegative, nonincreasing, convex, and -β'(t) is convex. We establish stability of the method under these hypotheses on β(t). Thus, …

Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez

Open Access Theses & Dissertations

Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.

In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both …

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

Short-Term Facilitation May Stabilize Parametric Working Memory Trace, Vladimir Itskov, David Hansel, Misha Tsodyks

Department of Mathematics: Faculty Publications

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the …

Extremal Problems For Independent Set Enumeration, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

The study of the number of independent sets in a graph has a rich history. Recently, Kahn proved that disjoint unions of Kr,r’s have the maximum number of independent sets amongst r-regular bipartite graphs. Zhao extended this to all r-regular graphs. If we instead restrict the class of graphs to those on a fixed number of vertices and edges, then the Kruskal-Katona theorem implies that the graph with the maximum number of independent sets is the lex graph, where edges form an initial segment of the lexicographic ordering. In this paper, we study three related questions. Firstly, we …

An Entropy Proof Of The Kahn-Lovasz Theorem, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

Bregman [2], gave a best possible upper bound for the number of perfect matchings in a balanced bipartite graph in terms of its degree sequence. Recently Kahn and Lovasz [8] extended Bregman’s theorem to general graphs. In this paper, we use entropy methods to give a new proof of the Kahn-Lovasz theorem. Our methods build on Radhakrishnan’s [9] use of entropy to prove Bregman’s theorem.

Specification Of Structural Viewer And Analytical Tool (Jecp/Svat), Xingzhong Li

Nebraska Center for Materials and Nanoscience: Faculty Publications

Java Electron Crystallography Package (JECP) is a collection of programs for crystallography and electron diffraction analysis. The package is designed and written by Dr. X.Z. Li. The software can be used as a research tool as well as a teaching aid. The need of a structural viewer/an analytical tool, using the same input data format as the JECP and proJECT software, becomes obvious with the growth of the JECP and proJECT programs and users. There exist many programs for structural design and/or display in various levels developed by individual, research group or software company. Some of them are expensive software …

A Dynamic System Model Of Biogeography-Based Optimization, Daniel J. Simon

Electrical and Computer Engineering Faculty Publications

We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely …

Modular And Graceful Edge Colorings Of Graphs, Ryan Jones

Dissertations

Abstract attached as separate file.

Hamiltonicity And Connectivity In Distance-Colored Graphs, Kyle C. Kolasinski

Dissertations

Abstract attached as separate file.