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The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.

Ergodic theory. --- Discrete groups. --- Groups, Discrete --- Discrete mathematics --- Infinite groups --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Discrete groups

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Academic collection --- 512.54 --- Discrete groups --- Geometrical constructions --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Geometry --- Groups, Discrete --- Infinite groups --- Groups. Group theory --- Conferences - Meetings --- 512.54 Groups. Group theory --- Discrete mathematics --- Discrete groups - Congresses --- Geometrical constructions - Congresses

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This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.

Mathematics. --- Algorithms. --- Convex geometry. --- Discrete geometry. --- Operations research. --- Management science. --- Operations Research, Management Science. --- Convex and Discrete Geometry. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Geometry --- Combinatorial geometry --- Algorism --- Algebra --- Arithmetic --- Math --- Science --- Foundations --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Integer programming. --- Convex geometry .

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Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov’s Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity. The only prerequisites are a background in advanced calculus and linear algebra. Each section ends with exercises, while each chapter ends with comments covering supplementary material and historical information. Many results are new, and the whole book reflects the authors’ own experience, both in teaching and research. About the authors: Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs the Centre for Nonlinear Analysis and Its Applications and also the graduate program in Applied Mathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynamical Systems, and has received several prizes both for research and exposition. Lars Erik Persson is Professor of Mathematics at Luleå University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Luleå, a member of the Swedish National Committee of Mathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from Umeå University in 1974. Dr. Persson has published on interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has received several prizes both for research and teaching.

Convex functions --- Convex functions. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Functions, Convex --- Mathematics. --- Functional analysis. --- Functions of real variables. --- Convex geometry. --- Discrete geometry. --- Real Functions. --- Functional Analysis. --- Convex and Discrete Geometry. --- Functions of real variables --- Discrete groups. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Real variables --- Functions of complex variables --- Geometry --- Combinatorial geometry

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Discrete groups --- Isometrics (Mathematics) --- Möbius transformations --- Geometry, Hyperbolic --- Groupes discrets --- Isométrie (Mathématiques) --- Möbius, Transformations de --- Géométrie hyperbolique --- 514.16 --- Mobius transformations --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- Transformations (Mathematics) --- Groups, Discrete --- Infinite groups --- Geometries over algebras --- 514.16 Geometries over algebras --- Möbius transformations --- Isométrie (Mathématiques) --- Möbius, Transformations de --- Géométrie hyperbolique --- Discrete groups. --- Discrete mathematics