# Analysis Commons™

## All Articles in Analysis

895 full-text articles. Page 1 of 30.

Some Graphs Determined By Their Distance Spectrum, 2018 Department of mathematics & statistics, McGill University, Montreal

#### Some Graphs Determined By Their Distance Spectrum, Stephen Drury, Huiqiu Lin

##### Electronic Journal of Linear Algebra

Let $G$ be a connected graph with order $n$. Let $\lambda_1(D(G))\geq \cdots\geq \lambda_n(D(G))$ be the distance spectrum of $G$. In this paper, it is shown that the complements of $P_n$ and $C_n$ are determined by their $D$-spectrum. Moreover, it is shown that the cycle $C_n$ ($n$ odd) is also determined by its $D$-spectrum.

Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, 2018 Sorbonne Université, Paris, France

#### Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, Michèle Thieullen, Alexis Vigot

##### Communications on Stochastic Analysis

No abstract provided.

Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, 2018 University of Kansas

#### Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, David Nualart, Raghid Zeineddine

##### Communications on Stochastic Analysis

No abstract provided.

Arratia Flow With Drift And Trotter Formula For Brownian Web, 2018 Institute of Mathematics, National Academy of Sciences of Ukraine

#### Arratia Flow With Drift And Trotter Formula For Brownian Web, Andrey A. Dorogovtsev, M. B. Vovchanskii

##### Communications on Stochastic Analysis

No abstract provided.

2018 Université Jean Monnet, Saint-Étienne, France

#### Exit-Time Of Granular Media Equation Starting In A Local Minimum, Julian Tugaut

##### Communications on Stochastic Analysis

No abstract provided.

A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, 2018 Université Mohammed Premier

#### A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, Aissa Sghir, Driss Seghir, Soukaina Hadiri

##### Communications on Stochastic Analysis

No abstract provided.

Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, 2018 ETH Zürich, Switzerland

#### Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, Peng Luo, Ludovic Tangpi

##### Communications on Stochastic Analysis

No abstract provided.

A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, 2018 Universidad Autónoma de Madrid, Spain

#### A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, Joan Bastons, Carlos Escudero

##### Communications on Stochastic Analysis

No abstract provided.

2018 Michigan Technological University

#### Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

##### Iosif Pinelis

No abstract provided.

On The Maximal Numerical Range Of Some Matrices, 2018 New York University Abu Dhabi

#### On The Maximal Numerical Range Of Some Matrices, Ali N. Hamed, Ilya M. Spitkovsky

##### Electronic Journal of Linear Algebra

The maximal numerical range $W_0(A)$ of a matrix $A$ is the (regular) numerical range $W(B)$ of its compression $B$ onto the eigenspace $\mathcal L$ of $A^*A$ corresponding to its maximal eigenvalue. So, always $W_0(A)\subseteq W(A)$. Conditions under which $W_0(A)$ has a non-empty intersection with the boundary of $W(A)$ are established, in particular, when $W_0(A)=W(A)$. The set $W_0(A)$ is also described explicitly for matrices unitarily similar to direct sums of $2$-by-$2$ blocks, and some insight into the behavior of $W_0(A)$ is provided when $\mathcal L$ has ...

New Perturbation Bounds In Unitarily Invariant Norms For Subunitary Polar Factors, 2018 Nanjing

#### New Perturbation Bounds In Unitarily Invariant Norms For Subunitary Polar Factors, Lei Zhu, Wei-Wei Xu, Hao Liu, Li-Juan Ma

##### Electronic Journal of Linear Algebra

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, 2018 Pusan National University

#### Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, Syed M. Raza Shah Naqvi, Jie Meng, Hyun-Min Kim

##### Electronic Journal of Linear Algebra

In this paper, the nonlinear matrix equation $X^p+A^TXA=Q$, where $p$ is a positive integer, $A$ is an arbitrary $n\times n$ matrix, and $Q$ is a symmetric positive definite matrix, is considered. A fixed-point iteration with stepsize parameter for obtaining the symmetric positive definite solution of the matrix equation is proposed. The explicit expressions of the normwise, mixed and componentwise condition numbers are derived. Several numerical examples are presented to show the efficiency of the proposed iterative method with proper stepsize parameter and the sharpness of the three kinds of condition numbers.

2018 DePaul University

#### United States Population Future Estimates And Long-Term Distribution, Sean P. Brogan

##### DePaul Discoveries

The population of the United States has always increased year over year. Even now with decreasing birth rates, the overall population continues to grow when looking at conventional models. The present study specifically examines what would happen to the U.S. population if we were to maintain the current birth and survival rates into the future. By 2050, our research shows that the U.S. population will become much older and cease to grow at all.

2018 Lynchburg College

#### Analysis Of 2016-17 Major League Soccer Season Data Using Poisson Regression With R, Ian D. Campbell

##### Undergraduate Theses and Capstone Projects

To the outside observer, soccer is chaotic with no given pattern or scheme to follow, a random conglomeration of passes and shots that go on for 90 minutes. Yet, what if there was a pattern to the chaos, or a way to describe the events that occur in the game quantifiably. Sports statistics is a critical part of baseball and a variety of other of today’s sports, but we see very little statistics and data analysis done on soccer. Of this research, there has been looks into the effect of possession time on the outcome of a game, the ...

Properties And Convergence Of State-Based Laplacians, 2018 University of Nebraska - Lincoln

#### Properties And Convergence Of State-Based Laplacians, Kelsey Wells

##### Dissertations, Theses, and Student Research Papers in Mathematics

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different ...

2018 The Graduate Center, City University of New York

#### Geometry And Analysis Of Some Euler-Arnold Equations, Jae Min Lee

##### All Dissertations, Theses, and Capstone Projects

In 1966, Arnold showed that the Euler equation for an ideal fluid can arise as the geodesic flow on the group of volume preserving diffeomorphisms with respect to the right invariant kinetic energy metric. This geometric interpretation was rigorously established by Ebin and Marsden in 1970 using infinite dimensional Riemannian geometry and Sobolev space techniques. Many other nonlinear evolution PDEs in mathematical physics turned out to fit in this universal approach, and this opened a vast research on the geometry and analysis of the Euler-Arnold equations, i.e., geodesic equations on a Lie group endowed with one-sided invariant metrics. In ...

On Some Geometry Of Graphs, 2018 The Graduate Center, City University of New York

#### On Some Geometry Of Graphs, Zachary S. Mcguirk

##### All Dissertations, Theses, and Capstone Projects

In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size ...

2018 The Graduate Center, City University of New York

#### The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

##### All Dissertations, Theses, and Capstone Projects

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices representing ...

Homogenization In Perforated Domains And With Soft Inclusions, 2018 University of Kentucky

#### 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 ...

Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, 2018 Soochow University

#### Determinantal Representations Of Elliptic Curves Via Weierstrass Elliptic Functions, Mao-Ting Chien, Hiroshi Nakazato

##### Electronic Journal of Linear Algebra

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass $\wp$-functions in place of Riemann theta functions. An example of this approach is given.