Analysis Commons^™

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

Secondary Features Of Importance For A Url Ranking, Atajan Abdyyev

Dissertations and Theses

This paper investigates the impact of secondary ranking factors on webpage relevance and rankings in the context of Search Engine Optimization (SEO), focusing on the jewelry domain within the United States e-commerce market. By generating a keyword list related to jewelry and retrieving top URLs from Google's search results, the study employs machine learning models including XGBoost, CatBoost, and Linear Regression to identify key features influencing webpage relevance and rankings.The findings highlight specific optimal ranges for features like Outlinks, Unique Inlinks, Flesch Reading Ease Score, and others, indicating their significant impact on better rankings. Notably, Random Forest model performed best …

Bayesian Optimization With Switching Cost: Regret Analysis And Lookahead Variants, Peng Liu, Haowei Wang, Wei Qiyu

Research Collection Lee Kong Chian School Of Business

Bayesian Optimization (BO) has recently received increasing attention due to its efficiency in optimizing expensive-to-evaluate functions. For some practical problems, it is essential to consider the path-dependent switching cost between consecutive sampling locations given a total traveling budget. For example, when using a drone to locate cracks in a building wall or search for lost survivors in the wild, the search path needs to be efficiently planned given the limited battery power of the drone. Tackling such problems requires a careful cost-benefit analysis of candidate locations and balancing exploration and exploitation. In this work, we formulate such a problem as …

Concentration Theorems For Orthonormal Sequences In A Reproducing Kernel Hilbert Space, Travis Alvarez

All Dissertations

Let H be a reproducing kernel Hilbert space with reproducing kernel elements {Kx} indexed by a measure space {X,mu}. If H can be embedded in L2(X,mu), then H can be viewed as a framed Hilbert space. We study concentration of orthonormal sequences in such reproducing kernel Hilbert spaces.

Defining different versions of concentration, we find quantitative upper bounds on the number of orthonormal functions that can be classified by such concentrations. Examples are shown to prove sharpness of the bounds. In the cases that we can add "concentrated" orthonormal vectors indefinitely, the growth rate of doing so is shown.

Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce

All Dissertations

Quadratically constrained quadratic programs (QCQPs) are a set of optimization problems defined by a quadratic objective function and quadratic constraints. QCQPs cover a diverse set of problems, but the nonconvexity and unboundedness of quadratic constraints lead to difficulties in globally solving a QCQP. This thesis covers properties of unbounded quadratic constraints via a description of the asymptotic cone of a set defined by a single quadratic constraint. A description of the asymptotic cone is provided, including properties such as retractiveness and horizon directions.

Using the characterization of the asymptotic cone, we generalize existing results for bounded quadratically defined regions with …

Stability Of Cauchy's Equation On Δ+., Holden Wells

Electronic Theses and Dissertations

The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …

Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs

All Dissertations

Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …

A Dilation Theoretic Approach To Approximation By Inner Functions, Daniel Alpay, Tirthankar Bhattacharyya, Abhay Jindal, Poornendu Kumar

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using results from the theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction and the realization formula for functions in the unit ball of . We first prove a generalization of a result of Carathéodory. This generalization has many applications. A uniform approximation result for matrix-valued holomorphic functions which extend continuously to the unit circle is proved using the Potapov factorization. This generalizes a theorem due to Fisher. Approximation results are proved for matrix-valued …

Study On Port Service Capacity Along The 21st Century Maritime Silk Road : Taking Container Ports As An Example, Rujin Fu

World Maritime University Dissertations

No abstract provided.

Study On The Construction Of Public Information Platform For International Multimodal Transport : A Case Study Of Shanghai, Yijie Chen

World Maritime University Dissertations

No abstract provided.

Study On Overcapacity Of Liner Shipping : On The Transpacific Routes, Yuxin Pu

World Maritime University Dissertations

No abstract provided.

Analysis On The Fluctuations In Port Demand Caused By The Change In International Trade Of The Countries Along The 21st Century Maritime Silk Road : Take The Asean Countries For Example, Ziyi Shu

World Maritime University Dissertations

No abstract provided.

Research On Investment Risk And Decision Making In Dry Bulk Ships : Case Study Nijie Shipping World Limited, Mingyu Xu

World Maritime University Dissertations

No abstract provided.

The Attempt And Operation Of Container Sharing Platform In The Yangtze River Delta : Efficient Transfer Of Empty Containers And Resources Sharing, Yifei Wei

World Maritime University Dissertations

No abstract provided.

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez

LSU Doctoral Dissertations

This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.

The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.

The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …

The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations, Stephanie Walker

Rose-Hulman Undergraduate Mathematics Journal

This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, …

Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.

Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.