21. ACM Guide Subject Index 3, An APL package for convex geometry Richard A. Vitale , Alan J. Tarr Proceedingsof seventh international conference on APL June 1975 The package of APL http://portal.acm.org/subjects.cfm?part=subject&row=H&idx=Hierarchy and geometri

22. [math/9211216] A Low-technology Estimate In Convex Geometry From Greg Kuperberg greg@math.ucdavis.edu Date Sun, 1 Nov 1992000000 GMT (3kb) A lowtechnology estimate in convex geometry. http://arxiv.org/abs/math.MG/9211216

Mathematics, abstract math.MG/9211216 A low-technology estimate in convex geometry Authors: Greg Kuperberg (U Chicago) Comments: The abstract is adapted from the Math Review by Keith Ball, MR 93h:52010 Report-no: Kuperberg migration 5/2002 Subj-class: Metric Geometry; Functional Analysis Journal-ref: Internat. Math. Res. Notices, 1992 (1992), no. 9, 181-183 Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv math find abs

23. Convexity.html Jeffrey C. Lagarias convex geometry papers. Other papers related toconvexity can be found in the list of packing and tiling papers. http://www.research.att.com/~jcl/convexity.html

Jeffrey C. Lagarias: Convex geometry papers Other papers related to convexity can be found in the list of packing and tiling papers. Sets Uniquely Determined by Projection I. Continuous Case P. C. Fishburn, J. C. Lagarias, J. A. Reeds and L. A. Shepp, SIAM J. Applied Math. 50 (1990), pp. 288-306. Sets Uniquely Determined by Projections II. Discrete Case P. C. Fishburn, J. C. Lagarias, J. A. Reeds and L. A. Shepp, Discrete Math. 91 (1991), pp. 141-151. Singularities of minimal surfaces and networks and related extremal problems in Minkowski space Z. Furedi, J. C. Lagarias and F. Morgan, in: DIMACS Geometry Year (R. Pollack, ed.), DIMACS Series Vol. 6, AMS: Providence 1991, pp. 95-109. Self-packing of Centrally Symmetric Convex Bodies in R^2 P. G. Doyle, J. C. Lagarias and D. S. Randall, 8 (1992), PP. 171-189. Keller's Cube Tiling Conjecture is False in High Dimensions Jeffrey C. Lagarias and Peter W. Shor, Bull. Amer. Math. Soc. 27 (1992), pp. 279-283. Cube Tilings in R^n and Nonlinear Codes J. C. Lagarias and P. W. Shor

24. Convex Geometry And Semiflows In P/T Nets. A Comparative Study Of Algorithms For The Petri Nets Bibliography convex geometry and Semiflows in P/T Nets. AComparative convex geometry and Semiflows in P/T Nets. A Comparative http://www.informatik.uni-hamburg.de/TGI/pnbib/c/colom_j_m3.html

For the most recent entries see the Petri Nets Newsletter Convex Geometry and Semiflows in P/T Nets. A Comparative Study of Algorithms for Computation of Minimal P-Semiflows. Colom, J.M. Silva, M. In: Proceedings of the 10th International Conference on Application and Theory of Petri Nets, 1989, Bonn, Germany , pages 74-95. 1989. Also: Universidad de Zaragoza, departamento de ingenieria electrica e informatica, Research Report 89-01, January 1989. Also in: Rozenberg, G.: Lecture Notes in Computer Science, Vol. 483; Advances in Petri Nets 1990 , pages 79-112. Berlin, Germany: Springer-Verlag, 1991. Abstract: P-semiflows are nonnegative left annullers of a net's flow matrix. The concept of minimal p-semiflow is known in the context of mathematical programming under the name `extremal direction of a cone'. The algorithms known in the domain of P/T nets for computing elementary semi-flows are basically improvements of the basic Fourier-Motzkin method. One of the fundamental problems of these algorithms is their complexity. Various methods and rules for mitigating this problem are examined. As a result, the paper presents two improved algorithms which are more efficient and robust when handling `real-life' nets. Keywords: convex geometry (and) semiflows (in) place/transition net(s); minimal p-semiflows computation; Fourier-Motzkin method; complexity reduction.

25. Geometry Algebraic topology Computational geometry convex geometry Differential geometryFractals General topology Knot theory Manifolds Polytopes convex geometry. http://felix.unife.it/ /ma-ge

26. Felix.unife.it/Root/d-Mathematics/d-Geometry/b-Convex-geometry W. Coppel Foundations of convex geometry. Cambridge UP 1998, 220p. 10279 PeterGruber/Joerg Wills (ed.) Handbook of convex geometry. 2 volumes. http://felix.unife.it/Root/d-Mathematics/d-Geometry/b-Convex-geometry

27. Kutateladze's Curriculum Vitae and explicit solution in Alexandrov surface area measures of isoperimetricalproblems with arbitrary constraints on mixed volumes in convex geometry. http://www.math.nsc.ru/LBRT/g2/english/ssk/cv.html

CURRICULUM VITAE Kutateladze Semën Samsonovich Born at St. Petersburg (Leningrad) on October 2, 1945 Graduated with Honors from Novosibirsk State University the Chair of Computational Mathematics in 1968 Degrees PhD in 1970 from the United Scientific Council of the Siberian Division of the RAS for the thesis “Related Topics of Geometry and Mathematical Programming” ScD in 1978 from St. Petersburg State University for the thesis “Linear Problems of Convex Analysis” Positions Sobolev Institute of Mathematics of the Siberian Division of the RAS postgraduate junior researcher senior researcher 1986-by now head of the laboratory of functional analysis Novosibirsk State University assistant professor associate professor 1980 by now professor vice-chair of mathematical analysis Main Areas of Research functional analysis nonstandard methods of analysis nonsmooth analysis and optimization theory convex geometry Main Results Tools for parametrization and explicit solution in Alexandrov surface area measures of isoperimetrical problems with arbitrary constraints on mixed volumes in convex geometry.

28. Convex Geometry: Mixed Volumes And Related Concepts Convex...... Dr. Markus Kiderlen, Universität Karlsruhe, Germany. convex geometryMixed volumes and related concepts. Abstract/ http://www.imf.au.dk/events/calendar/events/2173.html

Department of Theoretical Statistics University of Aarhus Ny Munkegade * 8000 Aarhus C * Denmark STATISTICS SEMINAR Thursday, 22 March, 2001 at 14:15 in H2.28 Convex Geometry: Mixed volumes and related concepts Abstract/Description: The purpose of the talk is to give an accessible introduction to notions like 'Steiner formula', 'intrinsic volumes' and 'Minkowki's inequality'. All these concepts naturally arise if the volume of the vector-sum of two or more compact convex sets is considered. We will mainly restrict ourselves to the planar case ($d=2$) and only mention higher dimensional generalizations. We will also consider applications in Stochastic Geometry, such as randomly translated convex sets or contact distributions of germ-grain models. Contact person: Eva B. Vedel Jensen Announced by Helle Damgaard on March 12, 2001 at 13:32:48 and can only be removed by this person.

29. Convex Geometry: convex geometry Definitions convex polygon a polygon is convex ifyou can choose any two points from the interior of the polygon http://www.stetson.edu/departments/mathcs/students/research/math/steph/tsld009.h

Convex Geometry: Definitions convex polygon: a polygon is convex if you can choose any two points from the interior of the polygon and draw a line such that that entire line is inside the polygon. S= ,where li is the length of the side i of a polygon and n is the number of sides of the polygon. Previous slide Next slide Back to first slide View graphic version

30. Convex Geometry: First Previous Next Last Index Text. Slide 9 of 22. http://www.stetson.edu/departments/mathcs/students/research/math/steph/sld009.ht

First Previous Next Last ... Text Slide 9 of 22

31. Description Of Courses convex geometry and Optimization. Compare the schedule at the beginnof the term for hours and rooms. Responsible Instructor Bokowski. http://www.mathematik.tu-darmstadt.de/Math-Net/Lehrveranstaltungen/SS1999/Haupts

Third Year and Upwards Offered in the Summersemester 1999 Convex Geometry and Optimization Go backward to Functional analysis and integral equations Go up to Lectures and exercise courses which only require first and second year courses Go forward to History of mathematics: Analysis from Euler to Riemann Convex Geometry and Optimization Compare the schedule at the beginn of the term for hours and rooms Responsible Instructor: Bokowski Group Targeted: Students in mathematics Prerequisites: Basic knowledge of linear algebra Contents: The objective of the course is an introduction to the theory of convex bodies with special emphasis on linear optimization. When optimizing an objective funktion under linear constraints the admissable sets under consideration are convex cones or convex polytopes of in general high dimension. A deaper insight of algorithmical aspects in optimization requires first a study of convex polytopes and related concepts, like supporting hyperplane, facet, k-face, supporting function, distance function, face lattice, k-skeletons etc. During the lecture these concepts will be developped along a Graduate Text in Mathematics, Arne Broendsted, An Introduction to Convex Polytopes. Also nonpolytopal convex sets play a role.

32. Veranstaltungen - Arbeitsgruppe 7 Programme. Workshop Discrete convex geometry . 2. 4. February 2003 in honourof Jürgen Bokowski's 60th birthday. convex geometry and Knots . 4.45 - 5.15 pm. http://www.mathematik.tu-darmstadt.de/ags/ag7/Workshops/Programm2_en.html

About us Secretary's Office Members Research ... How to find us Programme Workshop "Discrete Convex Geometry" Conference office open 12.00 - 5.30 p.m. 3 rd floor, room 310 , Secretary Ursula Roeder Sunday, February Venue: Department of Mathematics, Schlossgartenstr. 7, 1 st floor, room 134 12.00 - 2.00 p.m. arrival Office room, Ursula Roeder: 310 Bernd Sturmfels, Berkeley, USA "The Geometry of Nash Equilibria" 3.00 - 3.30 p.m. B r e a k st floor 3.30 - 4.00 p.m. Horst Martini, Chemnitz "Location Problems in Minkowski Spaces" 4.00 - 4.30 p.m. Tudor Zamfirescu, Dortmund "Acute Triangulations" 4.30 - 5.00 p.m. B r e a k st floor 5.00 - 5.30 p.m. Simon King, Darmstadt "On a Topological Representation Theorem for Oriented Matroids" Phillippe Cara, Brussels, Belgium, (at present: USA) "Spherical Designs in 4 Dimensions" 6.00 - 6.30 p.m. Michel Las Vergnas, Paris, France "Linear Programming in Oriented Matroids and the Tutte Polynomial" Monday, February, 3 : 9.00 - 10.00 a.m. "Some New Construction Techniques For 4-Dimensional Polytopes" 10.00 - 10.30 a.m. B r e a k 10.30 - 11.00 a.m.

33. Abteilung Für Analysis - Research Main research. convex geometry, In convex geometry, geometric and analyticmethods are used to study convex sets and convex functions. http://osiris.tuwien.ac.at/~analysis/research.html

Research A-1040 Wien, Austria Main research Convex Geometry In Convex Geometry, geometric and analytic methods are used to study convex sets and convex functions. Therefore Convex Geometry is situated between Analysis and Geometry.  At the Department of Analysis especially the following problems are studied: Approximation of convex bodies by polytopes Properties of typical convex bodies in the sense of Baire categories Characterization of special convex bodies Valuations on the space of convex bodies Geometric Probabilities The Theory of Geometric Probabilities, Integral Geometry and Stochastic Geometry are situated between Geometry and Probability Theory. At the Department of Analysis especially the following problems are studied: Approximation of convex bodies by random polytopes Questions on the geometric structure of random polytopes Geometry of Numbers Geometry of Numbers forms a bridge between convexity, Diophantine approximation and the theory of quadratic forms. Today it is an independent problem-oriented field of mathematics having relations with coding theory, numerical integration, computational geometry and optimization. Geometry of Numbers has a long tradition in Vienna and at the Department of Analysis the following problems are studied: Diophantine approximation Products of inhomogeneous linear forms Inverting Minkowski's theorem on linear forms Algorithmic aspects of geometry of numbers Test sets and integer programming TU Wien Homepage webmaster Last modified: Wed Oct 31 19:49:50 CET 2001

34. 68U: Computer Graphics And Computational Geometry Subject Classifications, computational topics primarily focused on geometry are classifiedin sections 51 Geometry and 52 convex geometry and their subareas http://www.math.niu.edu/~rusin/known-math/index/68U05.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 68U: Computer graphics and computational geometry Introduction At present there is really nothing here regarding computer graphics per se; this is primarily focused on computational geometry. In keeping with the general pattern of use of the Mathematics Subject Classifications, computational topics primarily focused on geometry are classified in sections 51: Geometry and 52: Convex Geometry and their subareas such as 52B: Polygons and polyhedra . This classification is intended for topics whose geometric aspects are fairly straightforward, but for which the main questions involve efficient, accurate computation. Many geometric questions arise involving large sets of points (e.g. which of these points are closest together?) which are arguably combinatorics or statistics , but we have included them here. History Applications and related fields Some problems (e.g. finding the best circle passing through some points) are considered Statistics.

35. CMIS Research - Image Analysis - Applications/Work Overview - Hyperspectral Imag scene). Fig. 2 Toy example of convex geometry model (M = 3) with noiseendmembers lie at the vertices of the triangle. The leading http://www.cmis.csiro.au/iap/RecentProjects/hyspec_eg.htm

Image Analysis Application Areas Biotechnology Health Asset Monitoring Exploration/Mining ... Other Areas Skills Segmentation Statistical Analysis Stereo Vision Image Motion ... Staff Image Analysis Current Research In Hyperspectral Imaging What is Spectroscopy? What is Hyperspectral Imaging? What are the Major Processing and Analysis Challenges for Hyperspectral Image Data? How are These Problems Currently Addressed? (a) (b) Fig. 1: (a) 54 AVIRIS shortwave infrared images of Oatman, Arizona (courtesy of NASA JPL). (b) "Stackplot" of spectra at 6 pixels in the Oatman Image. Please click on the images for an enlarged view. Fig. 2: Toy example of convex geometry model (M = 3) with noise: endmembers lie at the vertices of the triangle The leading hyperspectral image analysis package, ENVI , has a method which finds the "pointiest" pixels (i.e. near vertices) using the "Pixel Purity Index". Clusters of such points are identified interactively as likely endmember clusters. More sophisticated methods include those of Craig (1994) which finds the simplex of minimum volume with a given number of vertices and completely enclosing the data "cloud"; and the N-FINDR algorithm of Winter (1999), which finds the simplex of maximum volume whose vertices are constrained to be a subset of the data points. N-FINDR is in commercial use. The Craig and Winter solutions for the toy example are shown in Fig. 3 (in pink and blue respectively). Note that Craig's solution is too large in the presence of noise, while Winter's will be too small if some materials in the scene are not represented by whole pixels.

36. DEPARTMENT OF MATHEMATICS UNIVERSITY OF CRETE Knossos Ave, GR- Apostolos Giannopoulos, Associate Professor (DIVISION Analysis) convex geometry;Emmanuil Katsoprinakis, Associate Professor and Chair (DIVISION Analysis http://www.math.uoc.gr/dept/people.html

D EPARTMENT OF M ATHEMATICS ... RETE Knossos Ave, GR-714 09 Iraklio, Greece. Tel: +30 2810393801 Fax +30 2810393881 Faculty Emeriti Fellows Visiting Faculty ... Everybody's Picture Faculty Jannis Antoniadis Professor DIVISION Algebra - Geometry) Number Theory Christos Athanasiadis Assistant Professor DIVISION Algebra - Geometry) Combinatorics, Discrete Geometry Ioannis Athanasopoulos Professor DIVISION Applied Math - Statistics) Partial Differential Equation, Free Boundary Problems Konstantin Athanasopoulos Associate Professor DIVISION Algebra - Geometry) Dynamical Systems Apostolos Giannopoulos Associate Professor DIVISION Analysis) Convex Geometry Emmanuil Katsoprinakis Associate Professor and Chair DIVISION Analysis) Harmonic Analysis, Complex Variables Vassilis Klonias Associate Professor DIVISION Applied Math - Statistics) Statistics Mihalis Kolountzakis Associate Professor DIVISION Analysis) Harmonic Analysis, Combinatorial Problems, Computation Georgios Kossioris Associate Professor DIVISION Applied Math - Statistics) Nonlinear PDE and applications Christos Kourouniotis Assistant Professor DIVISION Algebra - Geometry) Geometry Alexandros Kouvidakis Associate Professor and Division Director DIVISION Algebra - Geometry) Algebraic Geometry Doukissa Kritikou Lecturer DIVISION Applied Math - Statistics) Statistics Michael Lambrou Associate Professor and Division Director DIVISION Analysis) Functional Analysis Paris Pamfilos Associate Professor DIVISION Algebra - Geometry) Geometry Ioannis Papadakis Professor and Director IACM DIVISION Applied Math - Statistics) Differential Equations

37. DEPARTMENT OF MATHEMATICS UNIVERSITY OF CRETE Apostolos Giannopoulos, Assistant Professor (DIVISION Analysis) convex geometry. NikosDafnis. Marianna Hartzoulaki, PhD Candidate convex geometry. http://www.math.uoc.gr/~www-old/2000-01/people.html

D EPARTMENT OF M ATHEMATICS ... Graduate Students Faculty Jannis Antoniadis Professor DIVISION Algebra - Geometry) Number Theory Ioannis Athanasopoulos Professor DIVISION Applied Math - Statistics) Partial Differential Equation, Free Boundary Problems Konstantin Athanasopoulos Assistant Professor DIVISION Algebra - Geometry) Dynamical Systems Constantine Callias Professor (until June 28, 2001) DIVISION Applied Math - Statistics) Mathematical Physics Apostolos Giannopoulos Assistant Professor DIVISION Analysis) Convex Geometry Apostolos Hadjidimos Professor DIVISION Applied Math - Statistics) Numerical Analysis Emmanuil Katsoprinakis Associate Professor DIVISION Analysis) Harmonic Analysis, Complex Variables Vassilis Klonias Associate Professor DIVISION Applied Math - Statistics) Statistics Mihalis Kolountzakis Associate Professor DIVISION Analysis) Harmonic Analysis, Combinatorial Number Theory Georgios Kossioris Assistant Professor DIVISION Applied Math - Statistics) Nonlinear PDE and applications Christos Kourouniotis Assistant Professor DIVISION Algebra - Geometry) Geometry Alexandros Kouvidakis Assistant Professor DIVISION Algebra - Geometry) Algebraic Geometry Doukissa Kritikou Lecturer DIVISION Applied Math - Statistics) Statistics Michael Lambrou Associate Professor DIVISION Analysis) Functional Analysis Haralambos Makridakis Assistant Professor (until July 26, 2001)

38. HallMathematics.com :: Handbook Of Convex Geometry : Volume A You are here Mathematics Geometry Topology Handbook of convex geometry Volume A. Search (books). Handbook of convex geometry Volume A. http://hallmathematics.com/index.php/Mode/product/AsinSearch/0444895965/name/Han

HallMathematics.com the most comprehensive Mathematics portal. Find Mathematics databases from our Mathematics metasearch Browse our Mathematics directory about the topic you want Read Reviews, Compare and Buy the item you want from the most trusted shop in the world You are here: Mathematics Handbook of Convex Geometry : Volume A Search ... (books) Handbook of Convex Geometry : Volume A Catalog: Book Manufacturer: North-Holland Authors: P.M. Gruber, J.M. Wills Release Date: 01 August, 1993 Availability: Special Order List Price: Our Price: Used Price: More Details from Amazon.com Amazon international Enlarge image HallMathematics.com

39. Glossary A convex body is, technically, a closed and bounded convex set with nonzero volume.convex geometry The study of convex shapes, usually in Euclidean space. http://www.math.ucdavis.edu/profiles/glossary.html

Glossary by Greg Kuperberg Index: A B C D ... Z A algebraic geometry Traditionally, the geometry of solutions in the complex numbers to polynomial equations. Modern algebraic geometry is also concerned with algebraic varieties, which are a generalization of such solution sets, as well as solutions in fields other than complex numbers, for example finite fields. algebraic topology The branch of topology concerned with homology and other algebraic models of topological spaces algebraic variety A space which is locally the solution locus to a set of polynomial equations. Algebraic varieties are for algebraic geometry topological spaces are for topology manifolds . However, algebraic varieties may also have complicated singular sets and may be parametrized with rings other than the complex numbers. (For the technical reason that the real numbers are not algebraically closed, one does not consider algebraic varieties over the real numbers in the straightforward sense.) alternating-sign matrix A matrix of 0's, 1's, and -1's such that, if the zeroes are deleted from any row or column, the remaining entries alternate in sign and begin and end with 1. almost complex manifold A manifold with the property that each tangent space has the structure of a complex vector space, but the complex structures are not necessarily compatible with true complex coordinates as they are for a complex manifold.

40. Spring School 2001 - List Of The Talks 2). April 18, Wednesday, Petra Smolikova HighDimensional ConvexGeometry (1), Karl Koehler High-Dimensional convex geometry (3). 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

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