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Articles 1 - 30 of 95

Full-Text Articles in Analysis

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis Jul 2018

Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

Iosif Pinelis

No abstract provided.

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Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell Apr 2018

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Brandon Russell

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so-called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H^1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating, periodic, bounded, and measurable coefficients. Finally, we connect these …

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Power-Series.Pdf, Iosif Pinelis Oct 2016

Power-Series.Pdf, Iosif Pinelis

Iosif Pinelis

This a comment made on Terence Tao's blog at https://terrytao.wordpress.com/2016/10/18/a-problem-involving-power-series/

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A New Angle On An Old Construction: Approximating Inscribed N-Gons, Robert Milnikel May 2016

A New Angle On An Old Construction: Approximating Inscribed N-Gons, Robert Milnikel

Robert Milnikel

No abstract provided.

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An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench Nov 2014

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench

William F. Trench

No abstract provided.

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A Covariance Inequality With A Non-Monotone Function, Martin Egozcue Jul 2014

A Covariance Inequality With A Non-Monotone Function, Martin Egozcue

Martin Egozcue

No abstract provided.

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The Sen Limit, Adrian Clingher, Ron Donagi, Martijn Wijnholt Dec 2013

The Sen Limit, Adrian Clingher, Ron Donagi, Martijn Wijnholt

Adrian Clingher

F -theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the basis of SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a P1-bundle and a conic bundle, and the intersection yields the IIb space-time.We get a precise match between F-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread in the bulk …

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Early Investigations In Conformal And Differential Geometry, Raymond T. Walter Apr 2013

Early Investigations In Conformal And Differential Geometry, Raymond T. Walter

Raymond Walter

The present [undergraduate] honors thesis seeks to introduce fundamental notions of conformal and differ- ential geometry, especially when such notions are useful in various mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than three are Möbius transformations. The proof is nontraditional in the sense that it is based on a representation of Möbius transformations using 2x2 matrices of Clifford numbers as well as the standard Dirac operator on Euclidean space. Clifford algebras and the Dirac operator are important in other important …

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When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna Apr 2012

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Lisa D Humphreys

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

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On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton Dec 2011

On The Influence Of Damping In Hyperbolic Equations With Parabolic Degeneracy, Ralph Saxton, Katarzyna Saxton

Ralph Saxton

This paper examines the effect of damping on a nonstrictly hyperbolic 2x2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

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Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench Dec 2011

Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench

William F. Trench

No abstract provided.

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Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench Dec 2011

Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench

William F. Trench

Let $R=P \diag(\gamma_{0}I_{m_{0}}, \gamma_{1}I_{m_{1}}, \dots, \gamma_{k-1}I_{m_{k-1}})P^{-1}\in\mathbb{C}^{m\times m}$ and $S_{\sigma}=Q\diag(\gamma_{\sigma(0)}I_{n_{0}},\gamma_{\sigma(1)}I_{n_{1}}, \dots,\gamma_{\sigma(k-1)}I_{n_{k-1}})Q^{-1}\in\mathbb{C}^{n\times n}$, where $m_{0}+m_{1}+\cdots +m_{k-1}=m$, $n_{0}+n_{1}+\cdots+n_{k-1}=n$, $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$ are distinct complex numbers, and $\sigma :\mathbb{Z}_{k}\to\mathbb{Z}_{k}= \{0,1, \dots, k-1\}$. We say that $A\in\mathbb{C}^{m\times n}$ is $(R,S_{\sigma})$-commutative if $RA=AS_{\sigma}$. We characterize the class of $(R,S_{\sigma})$-commutative matrrices and extend results obtained previously for the case where $\gamma_{\ell}=e^{2\pi i\ell/k}$ and $\sigma(\ell)=\alpha\ell+\mu \pmod{k}$, $0 \le \ell \le k-1$, with $\alpha$, $\mu\in\mathbb{Z}_{k}$. Our results are independent of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$, so long as they are distinct; i.e., if $RA=AS_{\sigma}$ for some choice of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{_{k-1}}$ (all distinct), then $RA=AS_{\sigma}$ for arbitrary of …

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Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun Jun 2011

Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.

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Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench Dec 2010

Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench

William F. Trench

No abstract provided.

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The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell May 2010

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

Byron E. Bell

The 1905 wave equation of Albert Einstein is a model that can be used in many areas, such as physics, applied mathematics, statistics, quantum chaos and financial mathematics, etc. I will give a proof from the equation of A. Einstein’s paper “Zur Elektrodynamik bewegter Körper” it will be done by removing the variable time (t) and the constant (c) the speed of light from the above equation and look at the factors that affect the model in a real analysis framework. Testing the model with SDSS-DR5 Quasar Catalog (Schneider +, 2007). Keywords: direction cosine, apparent magnitudes of optical light; ultraviolet …

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From Euler To Witten: A Short Survey Of The Volume Conjecture In Knot Theory, Uwe Kaiser Mar 2010

From Euler To Witten: A Short Survey Of The Volume Conjecture In Knot Theory, Uwe Kaiser

Uwe Kaiser

No abstract provided.

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The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell Dec 2009

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

Byron E. Bell

No abstract provided.

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Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench Dec 2008

Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench

William F. Trench

No abstract provided.

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On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench Dec 2008

On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench

William F. Trench

No abstract provided.

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Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun Dec 2008

Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun

Xiao-Jun Yang

It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.

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Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench Dec 2007

Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench

William F. Trench

No abstract provided.

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Modular Invariants For Lattice Polarized K3 Surfaces, Adrian Clingher, Charles F. Doran Jan 2007

Modular Invariants For Lattice Polarized K3 Surfaces, Adrian Clingher, Charles F. Doran

Adrian Clingher

No abstract provided.

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A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell Sep 2006

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

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A New Type Of Orthogonality In Banach Spaces, Abeer Hasan Dec 2005

A New Type Of Orthogonality In Banach Spaces, Abeer Hasan

Abeer Hasan

In this Thesis we study the problem of defining orthogonality in
Banach spaces that do not possess an inner product. We present the answers
to this problem for pairs of elements. Then we handle the more general
form of the problem, by studying orthonormality of sequences.
Finally, we present a new definition of orthogonality in Banach
spaces, and study its properties

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Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench Dec 2005

Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench

William F. Trench

No abstract provided.

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Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench Dec 2005

Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench

William F. Trench

No abstract provided.

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Universal Series By Trigonometric System In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan) Dec 2005

Universal Series By Trigonometric System In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan)

Sergo Armenak Episkoposian (Yepiskoposyan)

No abstract provided.

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Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench Dec 2004

Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench

William F. Trench

No abstract provided.

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Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench Dec 2004

Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench

William F. Trench

No abstract provided.

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Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench Dec 2004

Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench

William F. Trench

No abstract provided.

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