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The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions.

Functions of complex variables -- Congresses. --- Mathematical analysis -- Congresses. --- Functions of complex variables --- Riemann surfaces --- Topology --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Differential equations, partial. --- Partial differential equations --- Riemann surfaces. --- Topology.

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Conceptually, a database consists of objects and relationships. Object Relationship Notation (ORN) is a simple notation that more precisely defines relationships by combining UML multiplicities with uniquely defined referential actions. This volume shows how ORN can be used in UML class diagrams and database definition languages (DDLs) to better model and implement relationships and thus more productively develop database applications. For the database developer, it presents many examples of relationships modeled using ORN-extended class diagrams and shows how these relationships are easily mapped to an ORN-extended SQL or Object DDL. For the DBMS developer, it presents the specifications and algorithms needed to implement ORN in a relational and object DBMS. This book also describes tools that can be downloaded or accessed via the Web. These tools allow databases to be modeled using ORN and implemented using automatic code generation that adds ORN support to Microsoft SQL Server and Progress Object Store. Object Relationship Notation (ORN) for Database Applications: Enhancing the Modeling and Implementation of Associations is written for research scientists, research libraries, professionals, and advanced-level students in computer science. .

Functions of complex variables --Congresses. --- Mathematical analysis --Congresses. --- Relational databases --Design and construction. --- Relational databases --- Engineering & Applied Sciences --- Computer Science --- Design and construction --- Database design. --- Functions of complex variables. --- Complex variables --- Data base design --- -Mathematical analysis --- -Advanced calculus --- -517.1 Mathematical analysis --- -Analysis--?<061.3> --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Computer science. --- Data structures (Computer science). --- Database management. --- Data mining. --- Information storage and retrieval. --- Artificial intelligence. --- Computer graphics. --- Computer Science. --- Data Structures, Cryptology and Information Theory. --- Database Management. --- Data Mining and Knowledge Discovery. --- Information Storage and Retrieval. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Artificial Intelligence (incl. Robotics). --- Numerical solutions of differential equations --- 519.6 --- 681.3*G17 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Functions of complex variables --- Mathematical analysis --- 517 <061.3> --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- 517.1 Mathematical analysis --- Congresses --- Complex analysis --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Informatics --- Science --- Digital techniques --- 517.1 --- Congresses. --- Elliptic functions --- Functions of real variables --- System design --- Data structures (Computer scienc. --- Information storage and retrieva. --- Computer vision. --- Data Structures and Information Theory. --- Artificial Intelligence. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Information storage and retrieval systems. --- Computer Science, general. --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval --- Optical data processing. --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment --- Langages de programmation --- Programming languages (Electronic computers) --- Analyse numérique --- Fonctions d'une variable complexe --- Fonctions de plusieurs variables complexes --- Langages de programmation.