61. Convex Convex is a Maple package for convex geometry. It can deal with polytopes and,more generally, with all kinds of polyhedra of (in principle) arbitrary http://www-fourier.ujf-grenoble.fr/~franz/convex/

Convex - a Maple package for convex geometry Current version: 1.1.1 (Sep 29 2004) Matthias Franz Convex is a Maple package for convex geometry. It can deal with polytopes and, more generally, with all kinds of polyhedra of (in principle) arbitrary dimension. The only restriction is that all coordinates must be rational. The integration into the computer algebra system Maple makes Convex particularly suited for "applied" problems where polyhedra arise together with other mathematical structures. Examples we had in mind while writing the package were toric varieties (which are defined by fans) and moment polytopes related to representation theory. But of course the package is not restricted to these kinds of applications. On the other hand, if you want to break the current record for dualising polytopes, you will probably choose a different program. The main design principles of Convex are as follows: Easy to use One quickly learns how to use it. (See the example .) Part of this strategy is some kind of "object-oriented approach": functions accept different types as input and automatically choose the right subroutine. Moreover, Convex is very easy to install (if you have already installed Maple). Full generality No restrictions are imposed on the polyhedra (apart from being rational). They may be unbounded or even contain lines. They may also be empty or not full-dimensional or live in 0-dimensional space. This is important in applications where one wants to apply functions to (many) polyhedra that are the result of previous calculations.

62. Convex Manual: Introduction Convex is a Maple package for computations in rational convex geometry.Here rational means that all coordinates must be rational numbers. http://www-fourier.ujf-grenoble.fr/~franz/convex/doc/current/intro.html

Contents Introduction What is Convex? Convex is a Maple package for computations in rational convex geometry. Here "rational" means that all coordinates must be rational numbers. The package provides functions for "linear" as well as "affine" convex geometry. In the affine setting, the basic objects are polyhedra, which are intersections of finitely many (affine) halfspaces. Polyhedra can also be described as the convex hull of finitely many points and rays. A bounded polyhedron is also called a polytope. In the Convex package, polyhedra are represented by the type POLYHEDRON and polytopes by the subtype POLYTOPE . A POLYHEDRON may contain lines and may not be full-dimensional. The most important functions to define a POLYHEDRON are convhull and intersection The linear setting is based on cones, which are intersections of finitely many linear halfspaces (i.e., whose boundary contains the origin). Cones are generated by finitely many rays. In the Convex package, cones are represented by the type CONE . They may contain lines and may not be full-dimensional. A CONE can be created from either description with the functions poshull and intersection , respectively.

63. Neeb: On The Complex And Convex Geometry Of Ol'shanskii Semigroups on D^ is locally convex. So far the arguments are purely geometric. To obtainthe converse, we need some COMPLEX AND convex geometry OF OL SHANSKII http://www.numdam.org/numdam-bin/item?id=AIF_1998__48_1_149_0

64. Publications Of Károly Böröczky, Jr. K. Böröczky, Jr. Approximation of smooth convex bodies by circumscribed polytopes In Combinatorial convex geometry and Toric Varieties, (G. Ewald, http://www.renyi.hu/~carlos/carlospub.html

. (in Hungarian) preprint. Typical faces of best approximating three-polytopes . submitted. Approximation of smooth convex bodies by circumscribed polytopes with respect to the surface area . preprint. Convex bodies of minimal volume, surface area and mean width with respect to thin shells . submitted. Covering the crosspolytope by equal balls . submitted. Polytopes of minimal volume with respect to a shell - another characterization of the octahedron and the icosahedron . submitted. Note on an inequality of Wegner . submitted. Extremal mean width when covering the one-skeleton . submitted. Finite lattice packings and the Wulff-shape . Mathematika, accepted. Finite coverings in the hyperbolic plane . Discrete and Computational Geometry, 33 (2005), 165-180. The stability of the Rogers-Shepard inequality . Adv. Math., 190 (2005), 47-76. Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes . Annals of Applied Prob., 14 (2004), 239-273. Cyclic polytopes, hyperplanes, and codes . J. Geometry, 78 (2003), 25-49. Finite packing and covering by congruent convex domains . Discrete and Computational Geometry, 30 (2003), 185-193.

65. Algebra, Convexity And Optimization We will focus on Gröbner bases from the point of view of convex geometry (thecourse will contain a complete course in the basics of convex geometry) and http://home.imf.au.dk/niels/aco.html

Introduction Messages Calendar Exercises ... Projects Algebra, Convexity and Optimization Niels Lauritzen Monday 9-11, Wednesday 12-14 in Aud. D3 Updates: Last update: Monday, 07-Feb-2005 23:04:45 CET. Notes ( ps pdf ) on regular triangulations by Bjarke Roune. Notes ( ps pdf Notes ( ps pdf ) on counting integral points in polytopes by Mathias Neelen. Notes ( ps pdf ) on Brions theorem by Michael Knudsen. There will be no lectures on April 5 and April 7. Projects updated. Classes February 25 in Koll A4, 11-13. Calendar updated.

66. CDSAGENDA V.5 School On Commutative Algebra And Interactions With Algebraic Geom Toric ring and discrete convex geometry (1). 01h00 . lecture_notes. W.Bruns Universität Osnabrück, Germany. 1515 1545. Break. 30 . 1545 1645 http://cdsagenda5.ictp.trieste.it/full_display.php?smr=0&ida=a0344

67. ConvGeomToolbox The convex geometry toolbox is a Matlab toolbox designed to provide useful toolsin Convex 4) Details of the functions of the convex geometry toolbox http://www.lama.univ-savoie.fr/~oudet/ConvGeomToolbox/ConvGeomToolbox.html

The Convex Geometry toolbox The Convex Geometry toolbox is a Matlab toolbox designed to provide useful tools in Convex Geometry optimization. This toolbox is based on the very efficient "qhull" library developped by the The Geometry Center of Minneapolis 1) Installation You first have to install and compile the sources of the C "qhull" library which can be freely downloaded at the following adress : http://www.qhull.org/ The toolbox can be downloaded here 2) Compilation You just have to check the adress of the library in the compil_mexfile.m and run the mex instructions. 3) Two examples Example of bigest balls inscribed in a given polytop Example of steiner symetrization 4) Details of the functions of the Convex Geometry toolbox compil_mexfile.m : Compile the mex files of the toolbox. compute_normals.m : Computes the normal vectors of the convex polytop defined as the hull of the input points. dodec.m : Computes the normal vectors of a dodecahedron. edges_matlab.m : Computes the edges of the convex polytop defined as the hull of the input points. inscribe_ball.m

68. [PS] Geometric Tomography There is a large overlap between geometric tomography and convex geometry. V.Soltan keeps a useful list of convex geometry people. http://www.ac.wwu.edu/~gardner/research.html

Geometric Tomography In recent years my research has been in a new field called geometric tomography, an area of mathematics dealing with the retrieval of information about a geometric object from data concerning its projections ("shadows") on planes and/or sections by planes. The subject has connections with convex geometry, stereology, geometric probing in robotics, computerized tomography, and other areas. My book "Geometric Tomography" was published by Cambridge University Press (New York) in 1995. It is designed to be somewhat accessible even to advanced undergraduate students, and contains 70 computer-generated pictures, 72 open problems, and over 500 references. A SECOND EDITION has been prepared (preliminary draft) and will be submitted to the publisher in September, 2005. Corrections and recent results (last updated August 18, 2004 and will not be further updated before the second edition appears, probably in 2006). Related Links Workshop on Geometric Tomography , Alicante, Spain, October 5 to 10, 2004. Click on the icon to view my power point presentation at this workshop

69. Annex I To The Contract 3) Geometry of Banach spaces, convex geometry Develop the aspects of the geometry of Find new applications to analysis, convex geometry and statistical http://www.amsta.leeds.ac.uk/pure/analysis/network/annex1.html

EU Research Training Network ANNEX I LIST OF PARTICIPANTS AND DESCRIPTION OF WORK Network title: Classical analysis, Operator theory, Geometry of Banach spaces, their interplay and their applications Network short title: Analysis and Operators PART A - The participants The principal contractor and the members listed below shall be jointly and severally liable in the execution of work defined in part B of this annex: The principal contractor The members Vrije Universiteit, Amsterdam, established in the Netherlands Universitat Autonoma de Barcelona, established in Spain University College Dublin, established in Ireland University of Leeds, established in the United Kingdom The Norwegian University of Science and Technology, established in Norway Vienna University of Technology, established in Austria Tel Aviv University, established in Israel St Petersburg department of the V.A. Steklov Mathematical Institute, established in Russia The principal contractor and the members are referred to jointly as ``the participants'' PART B - The joint programme of work 1. Project objectives

70. Publication Info. convex geometry and Semiflows in P/T nets. A Comparative Study of Algorithms forComputation of Minimal PsemiflowsBibTeX. Authors, JM Colom and M. Silva http://webdiis.unizar.es/GISED/gised/php/show_publication.php?publication=RP-91-

71. Publication Info. convex geometry and semiflows in P/T nets. A comparative study of algorithms forcomputation of minimal psemiflowsBibTeX. Authors, JM Colom and M. Silva http://webdiis.unizar.es/GISED/gised/php/show_publication.php?publication=RP-89-

72. UNIVERSITY OF JYVÄSKYLÄ Center For Mathematical And Computational Modeling This mapping enables us to use methods of convex geometry in statistics. We willpresent results of using such methods in problems of risk measurement and http://www.stat.jyu.fi/cmcmsem/sem310303.htm

UNIVERSITY OF JYVÄSKYLÄ Center for Mathematical and Computational Modeling Gleb A. Koshevoy (Russian Academy of Sciences) "A piece of convex geometry in statistics." Abstract Welcome. Pasi Koikkalainen Laboratory of Data Analysis

73. Department Of Mathematics - University Of Idaho picture of curved plane. convex geometry and Discrete Optimization.Mark Nielsen (also see the web page on Dr. Nielsen s research interests) http://www.uidaho.edu/math/research/geometry.htm

Convex Geometry and Discrete Optimization Mark Nielsen (also see the web page on Dr. Nielsen's research interests

74. Convolution Inequalities In Convex Geometry Convolution Inequalities in convex geometry. 900945, Thursday, July 4, 2002Math Annex 1100, UBC. Watch or hear lecture now http://www.pims.math.ca/science/2002/aga/convexityvideos/ball/

The Pacific Institute for the Mathematical Sciences launched a new web site on March 31, 2005. If there is any discrepancy between the information on this page and the new site, the information on the new site should be used. Thematic Programme on Aymptotic Geometric Analysis: Conference on Convexity and Asymptotic Theory of Normed Spaces Keith Ball University College London Convolution Inequalities in Convex Geometry 9:00-9:45, Thursday, July 4, 2002 Math Annex 1100, UBC Watch or hear lecture now using the Real Player software. View abstract in PDF format. This talk was part of the Thematic Programme on Aymptotic Geometric Analysis: Conference on Convexity and Asymptotic Theory of Normed Spaces An file of this lecture can be downloaded here The complete archive of online lectures available from PIMS is available here Pacific Institute for the Mathematical Sciences Last Modified: Monday, 19-Aug-2002 03:45:14 PDT

75. Librairie Ellipse.ch [Fourier Analysis In Convex Geometry] Translate this page Fourier Analysis in convex geometry. Fourier Analysis in convex geometry. Auteur(s).Koldobsky. Editeur. American Mathematical Society. Catégories http://www.ellipse.ch/Produit.aspx?Produit=1142115

76. Geometric And Convex Combinatorics Geometric and convex combinatorics. origin in various fields of mathematics,such as Geometry of Numbers, convex geometry, Algebra, or Number Theory. http://www.math.uni-magdeburg.de/institute/imo/research/geometry_html/geometry.h

Next: References Geometric and convex combinatorics Methods for the solution of problems in integer programming have their origin in various fields of mathematics, such as Geometry of Numbers Convex Geometry Algebra , or Number Theory . The reason for this is the fact that the study of relations between discrete structures (lattices) and continuous sets (convex bodies, cones) is of fundamental importance for all of them. In this project we are trying to utilize current methods and results from the fields mentioned above for integer programming, and to contribute to a better understanding of lattice structures in connection with convex sets. The individual projects can be classified as follows: Geometry of Numbers Crepant Resolutions of Toric Singularities Test Sets in Integer Programming Packings and Coverings of Convex Bodies Geometry of Numbers Authors: Martin Henk, Robert Weismantel Cooperations: Support: Gerhard-Hess-Preis of the Deutschen Forschungsgemeinschaft, awarded to Robert Weismantel (We 1462/2-1) In 1896 Minkowski laid the foundation of what is today called the Geometry of Numbers , when he solved problems in number theory using geometric methods and interpretations. Today it is an independent field of research with close ties to other mathematical disciplines, for example coding theory and integer programming.

77. Semi-infinite Optimization are opened up in the last years, first of all in convex geometry. or embeddings in convex geometry can be described by semiinfinite systems and http://www.math.uni-magdeburg.de/institute/imo/research/semiinfinite_html/semiin

Next: About this document ... Semi-infinite Optimization Authors: Friedrich Juhnke Staff Members: Cooperations: Semi-infinite Optimization deals with the problem of minimizing (maximizing) a real-valued objective function of a finite number of variables with respect to an (possibly and generally) infinite number of constraints. There is a great variety of (classical) applications of semi-infinite optimization, including problems in approximation theory (with respect to polyhedral norms), operation research, optimal control, boundary value problems and others. These applications and appealing theoretical properties of semi-infinite problems gave rise to intensive (and up to now undiminished) research activities in this field since its inceptive appearing in the 1960s. Recent applications of semi-infinite optimization techniques to geometric extremal problems are opened up in the last years, first of all in convex geometry. Describing an n-dimensional convex body by its Minkowski support function, there occur in a very natural way systems of (infinitely many) linear inequalities with a finite number of variables. Additionally, any inclusion of two convex bodies can equivalently be formulated by the inequality for all directions , where h k are the support functions of C K , respectively. So the feasible regions of extremum problems corresponding to coverings or embeddings in convex geometry can be described by semi-infinite systems and semi-infinite optimization techniques turn out to be an appropriate tool for handling them.

78. AMS-UMI 2002 : Special Sessions 4) Analytic Aspects of convex geometry S. Campi (University of Modena)campi@unimo.it R. Gardner (Western Washington University) Richard.Gardner@wwu.edu http://www.dm.unipi.it/~meet2002/english/session04.html

Special Sessions - Abstracts "Analytic Aspects of Convex Geometry" S. Campi (University of Modena) campi@unimo.it R. Gardner (Western Washington University) Richard.Gardner@wwu.edu E. Lutwak (Polytechnic University Brooklyn) elutwak@duke.poly.edu A. Volcic (University of Trieste) volcic@univ.trieste.it Abstracts (tex format) Abstracts (ps format) Abstracts (dvi format) Special Sessions

79. Category Browsing Results One aim of this Handbook is to survey convex geometry, Problems in discretegeometry, convexity and combinatorial geometry are examined in this volume. http://opamp.com/cf/browse.cfm?Main=MATHEMATICS&Sub1=GEOMETRY

80. Spring School 2001 - List Of The Talks Smolikova HighDimensional convex geometry (1), Karl Koehler High-Dimensionalconvex geometry (3). Dirk Mueller High-Dimensional convex geometry (2) http://kam.mff.cuni.cz/~spring/2001/talks.html

Spring School on Combinatorics 2001 - List of the Talks See also: Spring School homepage List of the participants Study texts Day Morning session Evening session April 17, Tuesday Daniel Kral : Tree Decomposition Algorithms (1) Zdenek Dvorak : Tree Decomposition Algorithms (2) April 18, Wednesday Petra Smolikova : High-Dimensional Convex Geometry (1) Karl Koehler : High-Dimensional Convex Geometry (3) Dirk Mueller : High-Dimensional Convex Geometry (2) Jochen Alber : Parametrized Algorithms April 19, Thursday Tomas Chudlarsky : Set-pair method (1) Ondrej Pangrac : Small Worlds Robert Samal : Set-pair method (2) Jan Foniok : Distance in Small Worlds April 20, Friday Stephan Held : Small Worlds and the Web Ulrich Brenner : Approximations of Steiner tree problem (2) Martin Mares : Approximations of Steiner tree problem (1) April 21, Saturday Diana Piguetova : Set-pair method (3) Martin Pergel : Convex holes Jan Kara : Erdos-Szekeres Theorem April 22, Sunday Jana Maxova : High-Dimensional Spheres April 23, Monday Jakub Cerny : High-Dimensional Convex Geometry (4) Omer Gimenez : Probablity and Computation (1) Robert Babilon : High-Dimensional Convex Geometry (5) April 24, Tuesday

Page 4     61-80 of 89    Back | 1  | 2  | 3  | 4  | 5  | Next 20