Li Po (701-762) is considered one of the greatest poets to live during the Tang dynasty—what was considered to be the golden age for Chinese poetry. He was also the first Chinese poet to become well known in the West, and he greatly influenced many American poets during the twentieth century. Calling himself the "God of Wine" and known to his patrons as a "fallen immortal," Li Po wrote with eloquence, vividness, and often playfulness, as he extols the joys of nature, wine, and the life of a wandering recluse. Li Po had a strong social conscience, and he struggled against the hard times of his age. He was inspired by the newly blossoming Zen Buddhism and merged it with the Taoism that he had studied all his life. Though Li Po's love of wine is legendary, the translator, J. P. Seaton, includes poems on a wide range of topics—friendship and love, political criticism, poems written to curry patronage, poems of the spirit—to offer a new interpretation of this giant of Chinese poetry. Seaton offers us a poet who learned hard lessons from a life lived hard and offered his readers these lessons as vivid, lively poetry—as relevant today as it was during the Tang dynasty. Over one thousand poems have been attributed to Li Po, many of them unpublished. This new collection includes poems not available in any other editions.
There is a set-phrase in Chinese referring to the phenomenon of Li Po: "Winds of the immortals, bones of the Tao." He moved through this world with an unearthly freedom from attachment, and at the same time belonged profoundly to the earth and its process of change. However ethereal in spirit, his poems remain grounded in the everyday experience we all share. He wrote 1200 years ago, half a world away, but in his poems we see our world transformed. Legendary friends in eighth-century T'ang China, Li Po and Tu Fu are traditionally celebrated as the two greatest poets in the Chinese canon. David Hinton's translation of Li Po's poems is no less an achievement than his critically acclaimed The Selected Poems of Tu Fu, also published by New Directions. By reflecting the ambiguity and density of the original, Hinton continues to create compelling English poems that alter our conception of Chinese poetry.
An essential overview of post-deregulation market operations inelectrical power systems Until recently the U.S. electricity industry was dominated byvertically integrated utilities. It is now evolving into adistributive and competitive market driven by market forces andincreased competition. With electricity amounting to a $200 billionper year market in the United States, the implications of thisrestructuring will naturally affect the rest of the world. Why is restructuring necessary? What are the components ofrestructuring? How is the new structure different from the oldmonopoly? How are the participants strategizing their options tomaximize their revenues? What are the market risks and how are theyevaluated? How are interchange transactions analyzed and approved?Starting with a background sketch of the industry, this hands-onreference provides insights into the new trends in power systemsoperation and control, and highlights advanced issues in thefield. Written for both technical and nontechnical professionals involvedin power engineering, finance, and marketing, this must-haveresource discusses: * Market structure and operation of electric power systems * Load and price forecasting and arbitrage * Price-based unit commitment and security constrained unitcommitment * Market power analysis and game theory applications * Ancillary services auction market design * Transmission pricing and congestion Using real-world case studies, this timely survey offers engineers,consultants, researchers, financial managers, university professorsand students, and other professionals in the industry acomprehensive review of electricity restructuring and how itsradical effects will shape the market.
In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago.Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.
FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the ninth in the series of FLINS conferences cover state-of-the-art research, development, and technology for computational intelligence systems ? both from foundations and applications points-of-view.
Now available in English for the first time,?Physics and Partial Differential Equations, Volume I?bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines.? Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.?
This book focuses on the control and state estimation problems for dynamical network systems with complex samplings subject to various network-induced phenomena. It includes a series of control and state estimation problems tackled under the passive sampling fashion. Further, it explains the effects from the active sampling fashion, i.e., event-based sampling is examined on the control/estimation performance, and novel design technologies are proposed for controllers/estimators. Simulation results are provided for better understanding of the proposed control/filtering methods. By drawing on a variety of theories and methodologies such as Lyapunov function, linear matrix inequalities, and Kalman theory, sufficient conditions are derived for guaranteeing the existence of the desired controllers and estimators, which are parameterized according to certain matrix inequalities or recursive matrix equations. Covers recent advances of control and state estimation for dynamical network systems with complex samplings from the engineering perspective Systematically introduces the complex sampling concept, methods, and application for the control and state estimation Presents unified framework for control and state estimation problems of dynamical network systems with complex samplings Exploits a set of the latest techniques such as linear matrix inequality approach, Vandermonde matrix approach, and trace derivation approach Explains event-triggered multi-rate fusion estimator, resilient distributed sampled-data estimator with predetermined specifications This book is aimed at researchers, professionals, and graduate students in control engineering and signal processing.
This book consists of sixty-seven selected papers presented at the 2015 International Conference on Software Engineering and Information Technology (SEIT2015), which was held in Guilin, Guangxi, China during June 26-28, 2015. The SEIT2015 has been an important event and has attracted many scientists, engineers and researchers from academia, government laboratories and industry internationally. The papers in this book were selected after rigorous review.SEIT2015 focuses on six main areas, namely, Information Technology, Computer Intelligence and Computer Applications, Algorithm and Simulation, Signal and Image Processing, Electrical Engineering and Software Engineering. SEIT2015 aims to provide a platform for the global researchers and practitioners from both academia as well as industry to meet and share cutting-edge development in the field.This conference has been a valuable opportunity for researchers to share their knowledge and results in theory, methodology and applications of Software Engineering and Information Technology.
Since it is one of the core disciplines, every student of organic chemistry will need to cover organic synthesis at some point. This third edition of an extremely well-received and proven textbook is specially written with advanced undergraduate and graduate students in mind, although it is equally useful for research chemists, too. 50% of the text is new and includes new chapters on combinatoric chemistry, non-covalent molecular assemblies and the use of the Internet for searching chemical compounds. The authors have chosen the methods included here for their efficiency, elegance, and didactic value and have highlighted important reactions within the text. From reviews of the second edition: 'The text is very readable, and the authors are especially gifted at explaining complex concepts clearly and succinctly...This book is highly recommended reading for anyone wishing to gain an overview of organic synthesis.' J. Am. Chem. Soc. With his preface, Noble prizewinner E. J. Corey has also endorsed this already highly acclaimed work.
In a component-based approach for system design, one of the challenging problems is the way to prove the correctness of the created components. Usually, the constituent components are supposed to be correct — possessing the desirable properties and free from undesirable ones. However, the operators may destroy these properties or create new ones, resulting in an undesirable new component. Hence, every created component has to go through a new process of verification, involving a tremendous amount of effort.This book presents a component -based methodology for the creation and verification of design specifications. The methodology is formally presented as an algebra called Property-Preserving Petri Net Process Algebra (PPPA). PPPA includes five classes of operators, and the authors show that every operator of PPPA can preserve a large number of basic system properties. Therefore, if the initial set of primitive components satisfies some of these properties, the created components will also “automatically” satisfy them without the need for further verification — thus greatly saving verification efforts.
This book provides a brief introduction to some basic but important problems in celestial mechanics, and particularly in the few-body problem, such as the permissible and forbidden region of motion, the evolution of moment of inertia of a system, and the orbital stability of asteroids in the solar system. All these are based on some main results in the authors' research works, which are related to the qualitative method of celestial mechanics and nonlinear dynamics. Some of these works are interdisciplinary, involving celestial mechanics, nonlinear dynamics and other disciplines. The book covers a variety of topics for dynamics in the solar system, including the comets, asteroids, planetary rings, Trojan asteroids, etc.As a senior scientist, Professor Sun shares his research experiences in this book. Readers may find plenty of information both about the theoretical and numerical analyses in celestial mechanics, and about the applications of theories and methods to dynamical problems in astronomy.
This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of optics, optoelectronics, fiber communication, information technology and materials etc.
Production Systems Engineering (PSE) is an emerging branch of Engineering intended to uncover fundamental principles of production systems and utilize them for analysis, continuous improvement, and design. This volume is the first ever textbook devoted exclusively to PSE. It is intended for senior undergraduate and first year graduate students interested in manufacturing. The development is first principle-based rather than recipe-based. The only prerequisite is elementary Probability Theory; however, all necessary probability facts are reviewed in an introductory chapter. Using a system-theoretic approach, this textbook provides analytical solutions for the following problems: mathematical modeling of production systems, performance analysis, constrained improvability, bottleneck identification and elimination, lean buffer design, product quality, customer demand satisfaction, transient behavior, and system-theoretic properties. Numerous case studies are presented. In addition, the so-called PSE Toolbox, which implements the algorithms developed, is described. The volume includes numerous case studies and problems for homework assignment.
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.
Deals with the availability method and its application to power plant system design and energy conversion. The first part of the book describes the development and the formulation of the availability method. The second part presents its applications to energy conversion processes. Examples for each energy conversion system are introduced and there are practice problems throughout the text.
This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.
In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA
Estimation and Control of Large Scale Networked Systems is the first book that systematically summarizes results on large-scale networked systems. In addition, the book also summarizes the most recent results on structure identification of a networked system, attack identification and prevention. Readers will find the necessary mathematical knowledge for studying large-scale networked systems, as well as a systematic description of the current status of this field, the features of these systems, difficulties in dealing with state estimation and controller design, and major achievements. Numerical examples in chapters provide strong application backgrounds and/or are abstracted from actual engineering problems, such as gene regulation networks and electricity power systems. This book is an ideal resource for researchers in the field of systems and control engineering. - Provides necessary mathematical knowledge for studying large scale networked systems - Introduces new features for filter and control design of networked control systems - Summarizes the most recent results on structural identification of a networked system, attack identification and prevention
This useful volume adopts a balanced approach between technology and mathematical modeling in computer networks, covering such topics as switching elements and fabrics, Ethernet, and ALOHA design. The discussion includes a variety of queueing models, routing, protocol verification and error codes and divisible load theory, a new modeling technique with applications to grids and parallel and distributed processing. Examples at the end of each chapter provide ample material for practice. This book can serve as an text for an undergraduate or graduate course on computer networks or performance evaluation in electrical and computer engineering or computer science.
Comprehensive coverage of durability of concrete at both material and structural levels, with design related issues Links two active fields in materials science and structural engineering: the durability processes of concrete materials and design methods of concrete structures Facilitates communication between the two communities, helping to implement life-cycle concepts into future design methods of concrete structures Presents state-of-the-art information on the deterioration mechanism and performance evolution of structural concrete under environmental actions and the design methods for durability of concrete structures Provides efficient support and practical tools for life-cycle oriented structural design which has been widely recognized as a new generation of design philosophy for engineering structures The author has long experience working with the topic and the materials presented have been part of the author's current teaching course of Durability and Assessment of Engineering Structures for graduate students at Tsinghua University The design methods and approaches for durability of concrete structures are developed from newly finished high level research projects and have been employed as recommended provisions in design code including Chinese Code and Eurocode 2
The aim of this book is to provide some useful methods to improve the spectrum sensing performance in a systematic way, and point out an effective method for the application of cognitive radio technology in wireless communications. The book gives a a state-of-the-art survey and proposes some new cooperative spectrum sensing (CSS) methods attempting to achieve better performance. For each CSS, the main idea and corresponding algorithm design are elaborated in detail. This book covers the fundamental concepts and the core technologies of CSS, especially its latest developments. Each chapter is presented in a self-sufficient and independent way so that the reader can select the chapters interesting to them. The methodologies are described in detail so that the readers can repeat the corresponding experiments easily. It will be a useful book for researchers helping them to understand the classifications of CSS, inspiring new ideas about the novel CSS technology for CR, and learning new ideas from the current status of CSS. For engineers, it will be a good guidebook to develop practical applications for CSS.
This book offers a comprehensive introduction to advanced methods for image and video analysis and processing. It covers deraining, dehazing, inpainting, fusion, watermarking and stitching. It describes techniques for face and lip recognition, facial expression recognition, lip reading in videos, moving object tracking, dynamic scene classification, among others. The book combines the latest machine learning methods with computer vision applications, covering topics such as event recognition based on deep learning,dynamic scene classification based on topic model, person re-identification based on metric learning and behavior analysis. It also offers a systematic introduction to image evaluation criteria showing how to use them in different experimental contexts. The book offers an example-based practical guide to researchers, professionals and graduate students dealing with advanced problems in image analysis and computer vision.
This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.
The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science. Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric–Magnetohydrodynamic Equations References
This book introduces advanced mathematical methods and techniques for analysis and simulation of models in mathematical epidemiology. Chronological age and class-age play an important role in the description of infectious diseases and this text provides the tools for the analysis of this type of partial differential equation models. This book presents general theoretical tools as well as large number of specific examples to guide the reader to develop their own tools that they may then apply to study structured models in mathematical epidemiology. The book will be a valuable addition to the arsenal of all researchers interested in developing theory or studying specific models with age structure.
This book aims at providing cases with inspiring findings for global researchers in capacity allocation and reservation. Capacity allocation mechanisms are introduced in the book, as well as the measures to build models and the ways to achieve supply chain coordination. In addition, it illustrates the capacity reservation contract and quantity flexible contract with comparisons and some numerical studies. The book is divided into 7 chapters. Chapter 1 introduces the background and the latest development of the research. Chapter 2 introduces how to manage downstream competition through capacity allocation in symmetric market, including proportional mechanism and lexicographic mechanism. Demand competition is introduced in Chapter 3 as well as the uniform allocation mechanism and the comparisons among three different mechanisms. In Chapter 4, we give information about demand competition with fixed factor allocation, and the comparison with other allocations. Chapter 5 provides the optimal strategies under fixed allocation with multiple retailers and the impacts of fixed proportions. Chapter 6 illustrates how to achieve supply chain coordination through capacity reservation contract and its comparison with the quantity flexibility contract, and in Chapter 7 we describe outsourcing decisions and order policies in different systems with some numerical studies. We sincerely hope that this book can provide some useful suggestions and inspirations for scholars around the world who have the same interests in this field.
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.
This book presents a study in educational sociology, exploring the function of rural schools, which are a symbol of the state in rural society, in a time characterized by local cultural transition. The book begins with an investigation of the status quo, background and history of a representative rural school, Fengning Hope Elementary School, and gives a definition of “the ‘states’ in villages.” Subsequently, on the basis of research on the teachers, an analysis of the courses taught, and comparison to other rural elementary schools of the same type, it reveals the dual status of rural schools and their relation with social development in rural areas. Based on thorough fieldwork and empirical research, the book provides a new vision of the interactive relation between the state and rural society, particularly focusing on the role of rural education in that relation. In addition, it explores the reshaping of Chinese culture and the part that intellectuals play in the process of today’s cultural transition. For English-language readers and Western professionals, this translated version will offer an essential window into Chinese studies from a local point of view.
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
This clearly written, comprehensively indexed, and reader-friendly manual contains more than 350 monographs -- each describing the functions, indications, combinations, and applications of commonly used Chinese Materia Medica. Comprehensive monographs contain: details of main ingredients, taste and nature, channels entered, functions and indications, common dosage, precautions and contraindications. Unique tabular format lists provide "at-a-glance" accessibility. Summary tables in each chapter help you obtain quick overviews of the material covered. Unique coverage on toxicity and legal status. Comprehensive list of appendices and indices -- listings are by pinyin, pharmaceutical, and English names for easy reference.
The purpose of this book is to provide the reader with a self-contained treatment of fundamen tal solid state and semiconductor device physics. The material presented in the text is based upon the lecture notes of a one-year graduate course sequence taught by this author for many years in the ·Department of Electrical Engineering of the University of Florida. It is intended as an introductory textbook for graduate students in electrical engineering. However, many students from other disciplines and backgrounds such as chemical engineering, materials science, and physics have also taken this course sequence, and will be interested in the material presented herein. This book may also serve as a general reference for device engineers in the semiconductor industry. The present volume covers a wide variety of topics on basic solid state physics and physical principles of various semiconductor devices. The main subjects covered include crystal structures, lattice dynamics, semiconductor statistics, energy band theory, excess carrier phenomena and recombination mechanisms, carrier transport and scattering mechanisms, optical properties, photoelectric effects, metal-semiconductor devices, the p--n junction diode, bipolar junction transistor, MOS devices, photonic devices, quantum effect devices, and high speed III-V semiconductor devices. The text presents a unified and balanced treatment of the physics of semiconductor materials and devices. It is intended to provide physicists and mat erials scientists with more device backgrounds, and device engineers with a broader knowledge of fundamental solid state physics.
Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
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