Graham's Variety And Perverse Sheaves On The Nilpotent Cone,
2012
Louisiana State University and Agricultural and Mechanical College
Graham's Variety And Perverse Sheaves On The Nilpotent Cone, Amber Russell
LSU Doctoral Dissertations
In recent work, Graham has defined a variety which maps to the nilpotent cone, and which shares many properties with the Springer resolution. However, Graham's map is not an isomorphism over the principal orbit, and for type A in particular, its fibers have a nice relationship with the fundamental groups of the nilpotent orbits. The goal of this dissertation is to determine which simple perverse sheaves appear when the Decomposition Theorem for perverse sheaves is applied in Graham's setting for type A, and to begin to answer this question in the other types as well. In Chapter 1, we give …
Mathematical Models For Interest Rate Dynamics,
2012
Louisiana State University and Agricultural and Mechanical College
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.
Asymptotic Reliability Rheory Of K-Out-Of-N Systems,
2012
Universidad Pública de Navarra
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A nor can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0 and as t→∞) of the constituent survival probabilities. We include examples.
Integrable Models For Shallow Water With Energy Dependent Spectral Problems,
2012
Technological University Dublin
Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons
Articles
We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a Z2 reduction group. The soliton solutions are explicitly obtained.
Second Gradient Viscoelastic Fluids: Dissipation Principle And Free Energies,
2012
Universita Dini
Second Gradient Viscoelastic Fluids: Dissipation Principle And Free Energies, G. Amendola, M. Fabrizio, John Murrough Golden
Articles
We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they …
Numerical Computation Of A Certain Dirichlet Series Attached To Siegel Modular Forms Of Degree Two,
2012
Bucknell University
Numerical Computation Of A Certain Dirichlet Series Attached To Siegel Modular Forms Of Degree Two, Nathan C. Ryan, Nils-Peter Skoruppa, Fredrik Stroemberg
Faculty Journal Articles
The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.
Momcmc: An Efficient Monte Carlo Method For Multi-Objective Sampling Over Real Parameter Space,
2012
Old Dominion University
Momcmc: An Efficient Monte Carlo Method For Multi-Objective Sampling Over Real Parameter Space, Yaohang Li
Computer Science Faculty Publications
In this paper, we present a new population-based Monte Carlo method, so-called MOMCMC (Multi-Objective Markov Chain Monte Carlo). for sampling in the presence of multiple objective functions in real parameter space. The MOMCMC method is designed to address the "multi-objective sampling" problem, which is not only of interest in exploring diversified solutions at the Pareto optimal front in the function space of multiple objective functions, but also those near the front. MOMCMC integrates Differential Evolution (DE) style crossover into Markov Chain Monte Carlo (MCMC) to adaptively propose new solutions from the current population. The significance of dominance is taken into …
The Radon Transform And The Mathematics Of Medical Imaging,
2012
Colby College
The Radon Transform And The Mathematics Of Medical Imaging, Jen Beatty
Honors Theses
Tomography is the mathematical process of imaging an object via a set of finite slices. In medical imaging, these slices are defined by multiple parallel X-ray beams shot through the object at varying angles. The initial and final intensity of each beam is recorded, and the original image is recreated using this data for multiple slices. I will discuss the central role of the Radon transform and its inversion formula in this recovery process.
Iteration Digraphs,
2012
The College of Wooster
Iteration Digraphs, Hannah Roberts
Senior Independent Study Theses
No abstract provided.
Lattice Residuability,
2012
Missouri University of Science and Technology
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.
Infeasible Full-Newton-Step Interior-Point Method For The Linear Complementarity Problems,
2012
Georgia Southern University
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 …
A Numerical Investigation Of Apéry-Like Recursions And Related Picard-Fuchs Equations,
2012
Louisiana State University and Agricultural and Mechanical College
A Numerical Investigation Of Apéry-Like Recursions And Related Picard-Fuchs Equations, Maiia J. Bakhova
LSU Doctoral Dissertations
In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.
Hypercube Diagrams For Knots, Links, And Knotted Tori,
2012
Louisiana State University and Agricultural and Mechanical College
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 …
Resonance And Double Negative Behavior In Metamaterials,
2012
Louisiana State University and Agricultural and Mechanical College
Resonance And Double Negative Behavior In Metamaterials, Yue Chen
LSU Doctoral Dissertations
In this work, a generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties. We develop a rigorous method for calculating the frequency intervals where either double negative or double positive effective properties appear and show how these intervals imply the existence of propagating Bloch waves inside sub-wavelength structures. The branches of the dispersion relation associated with Bloch modes are shown to be explicitly determined by the Dirichlet spectrum of the high dielectric phase and the generalized electrostatic spectra of the complement. For numerical purposes, we consider a metamaterial constructed from a sub-wavelength …
The New Stochastic Integral And Anticipating Stochastic Differential Equations,
2012
Louisiana State University and Agricultural and Mechanical College
The New Stochastic Integral And Anticipating Stochastic Differential Equations, Benedykt Szozda
LSU Doctoral Dissertations
In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the Itô isometry that accounts for both adapted and instantly independent processes. We also present several Itô formulas for the new stochastic integral. Finally, we apply the new Itô formula to solve a linear stochastic differential equations with anticipating initial conditions.
Automated Reductions Of Markov Chain Models Of Calcium Release Site Models,
2012
College of William & Mary - Arts & Sciences
Automated Reductions Of Markov Chain Models Of Calcium Release Site Models, Yan Hao
Dissertations, Theses, and Masters Projects
Markov chain models have played an important role in understanding the relationship between single channel gating of intracellular calcium (Ca2+) channels, specifically 1,4,5-trisphosphate receptors (IP3Rs) and ryanodine receptors (RyRs), and the stochastic dynamics of Ca2+ release events, known as Ca2+ puffs and sparks. Mechanistic Ca2+ release site models are defined by the composition of single channel models whose transition probabilities depend on the local calcium concentration and thus the state of the other channels. Unfortunately, the large state space of such compositional models impedes simulation and computational analysis of the whole cell Ca2+ signaling in which the stochastic dynamics of …
Paley-Wiener Theorem For Line Bundles Over Compact Symmetric Spaces,
2012
Louisiana State University and Agricultural and Mechanical College
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 …
Stability Analysis Of Fitzhugh-Nagumo With Smooth Periodic Forcing,
2012
SUNY Geneseo
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 …
Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling,
2012
University of Texas at El Paso
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 …
A Review Of Some Subtleties Of Practical Relevance,
2012
Southern Illinois University Edwardsville
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 …
