Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics

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This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions. The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Normed Spaces and Banach Spaces Contents: Normed Spaces and Banach Spaces Hilbert Spaces Finite Dimensional Hilbert Spaces Hilbert Space L₂(Ω) Hilbert Space ℓ₂(II) Fourier Transform Wavelets Holomorphic Entire Functions and Hilbert Space Generalized Functions Quantum Mechanics Readership: Advanced undergraduate, graduate and post-graduate students in mathematics and theoretical physics. The book is also suitable for those taking courses in functional analysis and quantum theory.

Foundations of Linear and Generalized Linear Models (1版)

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<內容簡介> A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. ●An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods ●An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems ●Numerous examples that use R software for all text data analyses ●More than 400 exercises for readers to practice and extend the theory, methods, and data analysis ●A supplementary website with datasets for the examples and exercises <章節目錄> 1 Introduction to Linear and Generalized Linear Models 2 Linear Models: Least Squares Theory 3 Normal Linear Models: Statistical Inference 4 Generalized Linear Models: Model Fitting and Inference 5 Models for Binary Data 6 Multinomial Response Models 7 Models for Count Data 8 Quasi-Likelihood Methods 9 Modeling Correlated Responses 10 Bayesian Linear and Generalized Linear Modeling 11 Extensions of Generalized Linear Models Appendix A Supplemental Data Analysis Exercises Appendix B Solution Outlines for Selected Exercises 商品描述(中文翻譯) 內容簡介 《線性與廣義線性模型基礎》是一本對統計建模中最重要的概念和結果提供寶貴概述的書籍。這本書由一位經驗豐富的作者撰寫，清晰而全面地介紹了線性統計模型的關鍵概念和結果。本書通過討論模型背後的理論、R軟體應用和精心設計的模型示例，提供了最常用的統計模型的廣泛而深入的概述，以闡明關鍵思想並促進實際模型建立。 本書首先介紹了線性模型的基礎知識，例如模型擬合如何將數據投影到模型向量子空間上，以及數據的正交分解如何提供有關解釋變量效應的信息。隨後，本書介紹了最流行的廣義線性模型，包括用於分類數據的二項和多項羅吉斯回歸，以及用於計數數據的泊松和負二項對數線性模型。 本書還包括以下內容： - 弱分佈假設下的拟似然方法介紹，例如廣義估計方程方法 - 線性混合模型和帶有隨機效應的廣義線性混合模型，用於處理聚類相關數據、貝葉斯建模以及處理高維問題等問題的擴展 - 使用R軟體進行所有文本數據分析的眾多示例 - 超過400個練習題，供讀者練習和擴展理論、方法和數據分析能力 - 附帶網站提供示例和練習的數據集 無需翻譯的部分已移除。