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Articles 1 - 20 of 20
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Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera
Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera
Theses and Dissertations
We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.
Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen
Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen
Theses and Dissertations
We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …
Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Theses and Dissertations
In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …
The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani
The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani
Theses and Dissertations
The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …
Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez
Contact Numbers For Packing Of Spherical Particles, Eduardo Alejandro Ramirez Martinez
Theses and Dissertations
This thesis covers packings of spherical particles. The main object of this investigation is the contact number of a packing. New bounds for contact numbers of certain families of sphere packings in dimension 3 are obtained as the outcome of this research.
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee
Theses and Dissertations
Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …
On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. …
Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao
Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational …
Non-Stationary Platform Inverse Synthetic Aperture Radar Maneuvering Target Imaging Based On Phase Retrieval, Hongyin Shi, Saixue Xia, Qi Qin, Ting Yang, Zhijun Qiao
Non-Stationary Platform Inverse Synthetic Aperture Radar Maneuvering Target Imaging Based On Phase Retrieval, Hongyin Shi, Saixue Xia, Qi Qin, Ting Yang, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
As a powerful signal processing tool for imaging moving targets, placing radar on a non-stationary platform (such as an aerostat) is a future direction of Inverse Synthetic Aperture Radar (ISAR) systems. However, more phase errors are introduced into the received signal due to the instability of the radar platform, making it difficult for popular algorithms to accurately perform motion compensation, which leads to severe effects in the resultant ISAR images. Moreover, maneuvering targets may have complex motion whose motion parameters are unknown to radar systems. To overcome the issue of non-stationary platform ISAR autofocus imaging, a high-resolution imaging method based …
Solution Of Mathematical Model For Gas Solubility Using Fractional-Order Bhatti Polynomials, Muhammad I. Bhatti, Paul Bracken, Nicholas Dimakis, Armando Herrera
Solution Of Mathematical Model For Gas Solubility Using Fractional-Order Bhatti Polynomials, Muhammad I. Bhatti, Paul Bracken, Nicholas Dimakis, Armando Herrera
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Solutions of a mathematical model for gas solubility in a liquid are attained employing an algorithm based on the generalized Galerkin B-poly basis technique. The algorithm determines a solution of a fractional differential equation in terms of continuous finite number of generalized fractional-order Bhatti polynomial (B-poly) in a closed interval. The procedure uses Galerkin method to calculate the unknown expansion coefficients for constructing a solution to the fractional-order differential equation. Caputo?s fractional derivative is employed to evaluate the derivatives of the fractional B-polys and each term in the differential equation is converted into a matrix problem which is then inverted …
A Formulation Of L-Isothermic Surfaces In Three-Dimensional Minkowski Space, Paul Bracken
A Formulation Of L-Isothermic Surfaces In Three-Dimensional Minkowski Space, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The Cartan structure equations are used to study space-like and time-like isothermic surfaces in three-dimensional Minkowski space in a unified framework. When the lines of curvature of a surface constitute an isothermal system, the surface is called isothermic. This condition serves to define a system of one-forms such that, by means of the structure equations, the Gauss-Codazzi equations for the surface are determined explicitly. A Lax pair can also be obtained from these one-forms for both cases, and, moreover, a nonhomogeneous Schrödinger equation can be associated with the set of space-like surfaces.
Preconditioning Methods For Thin Scattering Structures Based On Asymptotic Results, Josef A. Sifuentes, Shari Moskow
Preconditioning Methods For Thin Scattering Structures Based On Asymptotic Results, Josef A. Sifuentes, Shari Moskow
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We present a method to precondition the discretized Lippmann–Schwinger integral equations to model scattering of time-harmonic acoustic waves through a thin inhomogeneous scattering medium. The preconditioner is based on asymptotic results as the thickness of the third component direction goes to zero and requires solving a two dimensional formulation of the problem at the preconditioning step.
Covering A Ball By Smaller Balls, Alexey Glazyrin
Covering A Ball By Smaller Balls, Alexey Glazyrin
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.
The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin
The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are (r,R)" role="presentation">(r,R) -systems or, in other words, Delone sets of type (r,R)" role="presentation">(r,R) in d-dimensional Euclidean space. In this paper, we will …
Using Restrictions To Accept Or Reject Solutions Of Radical Equations, Eleftherios Gkioulekas
Using Restrictions To Accept Or Reject Solutions Of Radical Equations, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation. In this article, we review previous literature, establish and illustrate rigorous solution procedures for radical equations of depth 1 (i.e. equations …
Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury
Optimal Quantizers For Some Absolutely Continuous Probability Measures, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of n-means and the nth quantization errors are calculated for some positive integers n.
Cartan Frames And Algebras With Links To Integrable Systems Differential Equations And Surfaces, Paul Bracken
Cartan Frames And Algebras With Links To Integrable Systems Differential Equations And Surfaces, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Moving frames and Clifford algebras will be used to illustrate an interconnected approach to the study of integrable systems, their surfaces, and methods for producing integrable partial differential equations. After a system of one-forms is defined, moving frame equations can be integrated and the resulting equations for the surface can be obtained. Other differential equations which involve quantities relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case of constant mean curvature, they can be expressed in terms of Jacobi elliptic functions.
Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta
Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.
The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim
The Development Of Secondary Mathematics Teachers’ Pedagogical Identities In The Social Context Of Classroom Interactions, Hyung Won Kim
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, …
A Two-Dimensional Finite Element Model Of The Grain Boundary Based On Thermo-Mechanical Strain Gradient Plasticity, Yooseob Song, George Z. Voyiadjis
A Two-Dimensional Finite Element Model Of The Grain Boundary Based On Thermo-Mechanical Strain Gradient Plasticity, Yooseob Song, George Z. Voyiadjis
Civil Engineering Faculty Publications and Presentations
In this work, a two-dimensional finite element model for the grain boundary flow rule is developed based on the thermo-mechanical gradient-enhanced plasticity theory. The proposed model is temperature-dependent. A special attention is given to physical and micromechanical nature of dislocation interactions in combination with thermal activation on stored and dissipated energy. Thermodynamic conjugate microforces are decomposed into energetic and dissipative components. Correspondingly, two different grain boundary material length scales are present in the proposed model. Finally, numerical examples are solved in order to explore characteristics of the proposed grain boundary flow rule.