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Siegel Modular Forms
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Dynamics and Control of Energy Systems
This book presents recent advances in dynamics and control of different types of energy systems. It covers research on dynamics and control in energy systems from different aspects, namely, combustion, multiphase flow, nuclear, chemical and thermal. The chapters start from the basic concepts so that this book can be useful even for researchers with very little background in the area. A dedicated chapter provides an overview on the fundamental aspects of the dynamical systems approach. The book will be of use to researchers and professionals alike.
L-Functions and Automorphic Forms
This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.
Irreducible Almost Simple Subgroups of Classical Algebraic Groups
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
Drying of Complex Fluid Drops
Understanding the phenomena of complex fluid drops with respect to drying is important for technology and a lot of research in academia and industry is poured into this topic. This book addresses this industrially important area and provides a thorough grounding to the field.
DECODING STARLIGHT: AN ELEMENTARY TALE OF GENESIS
Our Universe is majestic, magnificent in its splendour and deeply mysterious at the same time. Throughout this book, we shall try to act as Cosmic Detectives. Through careful observation of some very elementary clues scattered across the sky, we try to gradually discover some of the deepest and darkest secrets or mysteries of the Universe. From our familiar shoreline on the Earth, we dare to venture into the harrowing depths of vast unknown Cosmic abyss. Believe me, it will be a fascinating journey indeed!
Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.
Advances in Knowledge Discovery and Data Mining
The two-volume set LNAI 12084 and 12085 constitutes the thoroughly refereed proceedings of the 24th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2020, which was due to be held in Singapore, in May 2020. The conference was held virtually due to the COVID-19 pandemic. The 135 full papers presented were carefully reviewed and selected from 628 submissions. The papers present new ideas, original research results, and practical development experiences from all KDD related areas, including data mining, data warehousing, machine learning, artificial intelligence, databases, statistics, knowledge engineering, visualization, decision-making systems, and the emerging applicati...
Analysis of the Hodge Laplacian on the Heisenberg Group
The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
SSC Reasoning (Verbal & Non-Verbal) Guide for CGL/ CHSL/ MTS/ GD Constable/ Stenographer
The book 'SSC Reasoning (Verbal & Non-Verbal) Guide for CGL/ CHSL/ MTS/ GD Constable/ Stenographer' has been designed considering the latest patterns of the SSC exams. The book has 2 parts - Verbal and Non-Verbal Reasoning. The Verbal part contains 22 chapters whereas the Non-Verbal part contains 7 chapters. Further a Question Bank of past SSC Questions and 8 Practice Sets have been provided for the SSC exams. Each chapter of this book contains theory with Solved Examples. The chapter's Exercise part has been sub-divided into four sections on the basis of the difficulty level of the questions, i.e. • Concept Applicator: Easy • Concept Builder: Easy –Moderate • Concept Cracker: Modera...
