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This book presents a comprehensive description of theory, algorithms and software for solving nonconvex mixed integer nonlinear programs (MINLP). The main focus is on deterministic global optimization methods, which play a very important role in integer linear programming, and are used only recently in MINLP. The presented material consists of two parts. The first part describes basic optimization tools, such as block-separable reformulations, convex and Lagrangian relaxations, decomposition methods and global optimality criteria. Some of these results are presented here for the first time. The second part is devoted to algorithms. Starting with a short overview on existing methods, deformation, rounding, partitioning and Lagrangian heuristics, and a branch-cut-and-price algorithm are presented. The algorithms are implemented as part of an object-oriented library, called LaGO. Numerical results on several mixed integer nonlinear programs are reported to show abilities and limits of the proposed solution methods. The book contains many illustrations and an up-to-date bibliography. Because of the emphasis on practical methods, as well as the introduction into the basic theory, it is accessible to a wide audience and can be used both as a research as well as a graduate text.

Nonconvex programming. --- Nonlinear programming. --- Integer programming. --- Programming (Mathematics) --- Global optimization --- Non-convex programming --- Nonconvex programming --- Nonlinear programming --- Integer programming --- Computer science. --- Mathematics. --- Algorithms. --- Math Applications in Computer Science. --- Applications of Mathematics. --- Computational Science and Engineering. --- Programming Techniques. --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Informatics --- Foundations --- Computer science—Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Computer programming. --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Computer mathematics --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Programming

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It is not an exaggeration that much of what people devote in their hfe re­ solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve­ ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro­ gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.

Integer programming. --- Nonlinear programming. --- Programming (Mathematics) --- Integer programming --- Nonlinear programming --- Mathematical optimization. --- Operations research. --- Computer science. --- Optimization. --- Operations Research/Decision Theory. --- Operations Research, Management Science. --- Mathematical Modeling and Industrial Mathematics. --- Mathematics of Computing. --- Math Applications in Computer Science. --- Informatics --- Science --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Decision making. --- Management science. --- Mathematical models. --- Computer science—Mathematics. --- Models, Mathematical --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Decision making --- Acqui 2006 --- Programmation non lineaire

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This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

Finite element method. --- Méthode des éléments finis --- Finite element method --- Méthode des éléments finis --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Computer science—Mathematics. --- Partial differential equations. --- Computer mathematics. --- Analysis. --- Applications of Mathematics. --- Math Applications in Computer Science. --- Partial Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Mathematical and Computational Engineering. --- Computer mathematics --- Electronic data processing --- Mathematics --- Partial differential equations --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Éléments finis, Méthode des --- Acqui 2006 --- Éléments finis, Méthode des.

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Learning spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, learning spaces as well as knowledge spaces (which made the title of the first edition) generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises, and an extensive bibliography.

Mathematics. --- Intelligent tutoring systems --- Artificial intelligence --- Grading and marking (Students) --- Education --- Engineering & Applied Sciences --- Social Sciences --- Applied Mathematics --- Theory & Practice of Education --- Educational applications --- Intelligent tutoring systems. --- Educational applications. --- Graded schools --- Marking (Students) --- Grading and marking --- Computer science --- Multimedia information systems. --- Artificial intelligence. --- Applied mathematics. --- Engineering mathematics. --- Mathematics --- Applications of Mathematics. --- Artificial Intelligence (incl. Robotics). --- Multimedia Information Systems. --- Math Applications in Computer Science. --- Computers and Education. --- Mathematics Education. --- Data processing. --- Study and teaching. --- Students --- Educational tests and measurements --- Examinations --- School reports --- ICAI (Computer-assisted instruction) --- Intelligent computer-assisted instruction --- ITS (Computer-assisted instruction) --- Knowledge-based tutoring systems --- Tutoring systems, Intelligent --- Computer-assisted instruction --- Expert systems (Computer science) --- Interpretation --- Rating of --- Data processing --- Artificial intelligence - Educational applications

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Heavy metals always pose serious ecological risks when released into the environment due to their elemental non-degradable nature, regardless of their chemical form. This calls for the development of efficient and low-cost effluent treatment and metal recuperation technologies for contaminated waste water, not only because regulatory limits need to be met but also because the waste itself can be a resource for certain precious metals.   Biosorption is a general property of living and dead biomass to rapidly bind and abiotically concentrate inorganic or organic compounds from even very diluted aqueous solutions. As a specific term, biosorption is a method that utilizes materials of biological origin – biosorbents formulated from non-living biomass - for the removal of target substances from aqueous solutions. Recent research on biosorption provides a solid understanding of the mechanism underlying microbial biosorption of heavy metals and related elements.   This book gathers review articles analyzing current views on the mechanism and (bio)chemistry of biosorption,  the performance of bacterial, fungal and algal biomass, and the practical aspects of biosorbent preparation and engineering.  It also reviews the physico-chemical evaluations of biosorbents and modelling of the process as well as the importance of biosorption during heavy metal removal using living cells. It is a reference work for scientists, environmental safety engineers and R&D specialists who wish to further promote biosorption research and use the accumulated knowledge to develop and build industrial applications of biosorption in heavy metal separation technologies.  .

Bioremediation. --- Metal ions -- Absorption and adsorption. --- Pollutants -- Absorption and adsorption. --- Toxic Actions --- Microbiological Phenomena --- Environmental Remediation --- Waste Management --- Inorganic Chemicals --- Sanitary Engineering --- Chemicals and Drugs --- Environmental Pollution --- Phenomena and Processes --- Chemical Actions and Uses --- Sanitation --- Public Health --- Environment and Public Health --- Health Care --- Microbiological Processes --- Biodegradation, Environmental --- Environmental Pollutants --- Metals --- Civil & Environmental Engineering --- Biology --- Engineering & Applied Sciences --- Health & Biological Sciences --- Environmental Engineering --- Microbiology & Immunology --- Pollutants --- Metal ions --- Absorption and adsorption. --- Chemical pollutants --- Contaminants, Environmental --- Environmental contaminants --- Environmental pollutants --- Environmental biotechnology --- Life sciences. --- Biotechnology. --- Microbiology. --- Chemometrics. --- Environmental engineering. --- Water pollution. --- Life Sciences. --- Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution. --- Environmental Engineering/Biotechnology. --- Applied Microbiology. --- Math. Applications in Chemistry. --- Chemicals --- Pollution --- Biodegradation --- Environmental pollution. --- Chemistry --- Mathematics. --- Chemical engineering --- Genetic engineering --- Chemical pollution --- Contamination of environment --- Environmental pollution --- Contamination (Technology) --- Asbestos abatement --- Bioremediation --- Environmental engineering --- Environmental quality --- Factory and trade waste --- Hazardous waste site remediation --- Hazardous wastes --- In situ remediation --- Lead abatement --- Refuse and refuse disposal --- Microbial biology --- Microorganisms --- Environmental aspects --- Chemistry, Analytic --- Analytical chemistry --- Environmental control --- Environmental effects --- Environmental stresses --- Engineering --- Environmental health --- Environmental protection --- Sustainable engineering --- Aquatic pollution --- Fresh water --- Fresh water pollution --- Freshwater pollution --- Inland water pollution --- Lake pollution --- Lakes --- Reservoirs --- River pollution --- Rivers --- Stream pollution --- Water contamination --- Water pollutants --- Water pollution --- Waste disposal in rivers, lakes, etc. --- Mathematics --- Measurement --- Statistical methods