41. [math/9804023] Another Low-technology Estimate In Convex Geometry Another lowtechnology estimate in convex geometry. Authors Greg Kuperberg (UCDavis) Comments 11 pages Subj-class Metric Geometry Journal-ref Math. http://arxiv.org/abs/math.MG/9804023

Mathematics, abstract math.MG/9804023 From: Greg Kuperberg [ view email ] Date: Mon, 6 Apr 1998 06:55:13 GMT (5kb) Another low-technology estimate in convex geometry Authors: Greg Kuperberg (UC Davis) Comments: 11 pages Subj-class: Metric Geometry Journal-ref: Math. Sci. Res. Inst. Publ. 34 (1999), 117-121 Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

42. [math/0312268] Convex Geometry Of Orbits convex geometry of Orbits. Authors Alexander Barvinok, Grigoriy Blekherman Subjclass Metric Geometry; Algebraic Geometry; Combinatorics http://arxiv.org/abs/math.MG/0312268

Mathematics, abstract math.MG/0312268 From: Alexander Barvinok [ view email ] Date: Fri, 12 Dec 2003 21:35:59 GMT (19kb) Convex Geometry of Orbits Authors: Alexander Barvinok Grigoriy Blekherman Comments: 26 pages Subj-class: Metric Geometry; Algebraic Geometry; Combinatorics MSC-class: Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

43. GMU Math Department Convex and Discrete Geometry, mainly general and combinatorial properties of Sorin Revenko (convex geometry, 2002), Ion Ciobanu (Graph Theory, 1995), http://math.gmu.edu/www/people/Soltan.htm

Faculty Colloquium Research Recent Research ... Degree Programs Valeriu Soltan Professor Phone: (703) 993-1474 Fax: (703) 993-1491 E-mail: vsoltan@gmu.edu Degree Dr., 1985, Institute of Cybernetics, Academy of Sciences of Ukraine, Generalized Convexity. Research Convex and Discrete Geometry, mainly general and combinatorial properties of convex sets in n dimensions (see selected publications Teaching Favorite courses: Convex and Discrete Geometry, Convex Analysis, Computational Geometry. This semester courses Recent Research Articles Pairs of convex bodies with centrally symmetric intersections of translates, Discrete Comput. Geom. 33 (2005), 605-616. Antipodality properties of finite sets in Euclidean space, Discrete Math. 290 (2005), 221-228 (with H. Martini). The characteristic intersection property of line-free Choquet simplices in E d , Discrete Comput. Geom. 29 (2003), 561-573. A theorem on affine diameters of convex polytopes, Acta Sci. Math. Szeged 69 (2003), 431-440 (with H. Martini). Helly-type theorems on definite supporting lines for k -disjoint families of convex bodies in the plane, pp. 387-396, in: Discrete Geometry, M. Dekker, New York, 2003 (with S. Revenko).

44. Citebase - Convex Geometry Of Orbits G/A, B97 K. Ball, An elementary introduction to modern convex geometry, Flavorsof Geometry, Math. Sci. Res. Inst. Publ., vol. 31, Cambridge Univ. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:math/0312268

45. Citebase - A Low-technology Estimate In Convex Geometry A lowtechnology estimate in convex geometry. Authors Kuperberg, Greg G/A,2 Gilles Pisier, The volume of convex bodies and Banach space geometry, http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:math/9211216

46. CMIS Research - Image Analysis - Applications/Work Overview - Hyperspectral Imag Most of the methods are based on a convex geometry model, which says that If the convex geometry model is true, and if there are M materials in a scene, http://www.cmis.csiro.au/iap/RecentProjects/hyspec_eg.htm

About CSIRO Doing Business Education Publications ... Image Analysis Application Areas Biotechnology Health Asset Monitoring Exploration ... Other Areas Skills Segmentation Feature Extraction Statistical Analysis Stereo Vision ... Staff Image Analysis Activities 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.

47. Small Sets In Convex Geometry And Formal Independence Over ZFC, Menachem Kojman Small sets in convex geometry and formal independence over ZFC. Source Abstr.Appl. Anal. 2005, no. 5 (2005), 469–488 Abstract http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.aaa/1122298480

Current Issue Past Issues Search this Journal Editorial Board ... Viewing Abstracts with MathML Menachem Kojman Small sets in convex geometry and formal independence over ZFC Source: Abstr. Appl. Anal. Abstract: reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations. Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Alternatively, the document is available for a cost of $20. Select the "buy article" button below to purchase this document from a secured VeriSign, Inc. site.

48. Alexander Koldobsky: Fourier Analysis In Convex Geometry Fourier Analysis in convex geometry Alexander Koldobsky Publication Year 2005ISBN 08218-3787-7 Mathematical Surveys and Monographs, vol. 116 http://www.ams.org/bookpages/surv-116/

Additional Material for the Book Book Web Pages AMS Bookstore Fourier Analysis in Convex Geometry Alexander Koldobsky Publication Year: 2005 ISBN Mathematical Surveys and Monographs, vol. 116 This page is maintained by the author. Contact information: Alexander Koldobsky Department of Mathematics University of Missouri Columbia, MO, 65211 koldobsk@math.missouri.edu This page will be used for updates and additional material. Comments: webmaster@ams.org Privacy Statement Search the AMS

49. Proceedings Of The American Mathematical Society B KM Ball, An Elementary Introduction to Modern convex geometry, K G.Kuperberg, Another lowtechnology estimate in convex geometry. http://www.ams.org/proc/2004-132-09/S0002-9939-04-07484-2/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6826 (e) ISSN 0002-9939 (p) Previous issue Table of contents Next issue Articles in press ... All issues A geometric inequality and a low -estimate Author(s): Bo'az Klartag Journal: Proc. Amer. Math. Soc. MSC (2000): Primary 46B20, 52A20, 52A40 Posted: April 21, 2004 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: We present an integral inequality connecting volumes and diameters of sections of a convex body. We apply this inequality to obtain some new inequalities concerning diameters of sections of convex bodies, among which is our ``low -estimate''. Also, we give novel, alternative proofs to some known results, such as the fact that a finite volume ratio body has proportional sections that are isomorphic to a Euclidean ball. References: [B] K. M. Ball, An Elementary Introduction to Modern Convex Geometry , appeared in Flavors of Geometry, Ed. S. Levy, Mathematical Sciences Research Institute Publications, vol. 31, Cambridge University Press, Cambridge, 1997.

50. Teaching geometry IIII, Analytic convexity I-II, Combinatorial convexity I-II, bodies and lattices I-II, Mathematical programming and convex geometry I-II. http://teo.elte.hu/fs/mat2teach.html

Academic Ranks Hungarian Names INSTITUTE OF MATHEMATICS II Teaching The professors and researchers with science degree take part in the Mathematics Doctoral School offered in various branches of mathematics. The Doctoral School includes two programs, named as Theoretical Mathematics, Applied Mathematics. The graduate students, having completed the 6-semester curriculum, receive a Ph.D. degree. Department of Applied Analysis B. Sc. And M. Sc. Training (for students of mathematics, applied mathematics, mathematics and physics, chemistry and mathematics, physics, geology, geophysics, meteorology, biology, engineering-physics, chartography) Undergraguate level Science training courses for students of mathematics: Analysis I (L P), Analysis II (L+P), Analysis III (L+P), Analysis IV (L+P), Ordinary differential equations (L+P), Partial differential equations (L+P), Orthogonal series (L), Functional Analysis (L+P), Functional Analysis II (L+P) for students of applied mathematics: Analysis I (L+P), Analysis II (L+P), Analysis III (L+P), Ordinary differential equations (L+P), Partial differential equations (L+P), Functional Analysis (L+P)

51. Beiträge Zur Algebra Und Geometrie / Contributions To Algebra And Geometry, Vol A Methodologically Pure Proof of a convex geometry Problem. Victor Pambuccian.Department of Integrative Studies, Arizona State University West, http://www.emis.de/journals/BAG/vol.42/no.2/9.html

A Methodologically Pure Proof of a Convex Geometry Problem Victor Pambuccian Department of Integrative Studies, Arizona State University West, P. O. Box 37100, Phoenix AZ 85069-7100, USA, e-mail: pamb@math.west.asu.edu Abstract: We prove, using the minimalist axiom system for convex geometry proposed by W. A. Coppel, that, given $n$ red and $n$ blue points, such that no three are collinear, one can pair each of the red points with a blue point such that the $n$ segments which have these paired points as endpoints are disjoint. Classification (MSC2000): Full text of the article: DVI file (31 kilobytes) PostScript file (173 kilobytes) PDF file (152 kilobytes) Previous Article Next Article Contents of this Number ELibM for the EMIS Electronic Edition

52. Events - AG 7 Discrete convex geometry. 2. 4. February 2003 Paris, France, convex geometryand Knots . 4.45 - 5.15 pm, Martin Henk http://www.mathematik.tu-darmstadt.de/ags/ag7/Veranstaltungen/DiscConvGeom_en.ht

About us Secretary's Office Members Research ... How to find us AG 7: Discrete Optimization Discrete Convex Geometry 2. - 4. February 2003 Sunday, February, 2 Venue: Department of Mathematics, Schlossgartenstr. 7, 1 st floor, room 134 2.00 - 3.00 p.m. Bernd Sturmfels Berkeley, USA "The Geometry of Nash Equilibria" 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" 5.00 - 5.30 p.m. Simon King Darmstadt "On a Topological Representation Theorem for Oriented Matroids" 5.30 - 6.00 p.m. Phillippe Cara Brussels, Belgium, (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. Berlin "Some New Construction Techniques For 4-Dimensional Polytopes" 10.30 - 11.00 a.m. Szeged, Hungary "On the Construction of Classes of Perfect 4-Polytopes" 11.00 - 11.30 a.m. Amos Altshuler Beer Sheva,Israel "On Low-Dimensional Pseudodomanifolds" 11.30 - 12.00 a.m.

53. Abstract And Applied Analysis SMALL SETS IN convex geometry AND FORMAL INDEPENDENCE OVER ZFC. MENACHEM KOJMAN.Received 28 June 2004. To each closed subset S of a finitedimensional http://www.hindawi.com/journals/aaa/volume-2005/S1085337505503051.html

Home About this Journal Forthcoming Articles Author Index ... Contents AAA 2005:5 (2005) 469-488. DOI: 10.1155/AAA.2005.469 SMALL SETS IN CONVEX GEOMETRY AND FORMAL INDEPENDENCE OVER ZFC MENACHEM KOJMAN Received 28 June 2004 To each closed subset S of a finite-dimensional Euclidean space corresponds a -ideal of sets S which is -generated over S by the convex subsets of S . The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations. The following files are available for this article: Full-Text PDF for institutional subscribers REFERENCES [1] S. Agronsky, A. M. Bruckner, M. Laczkovich, and D. Preiss

54. International Mathematics Research Notices IMRN 19929 (1992) 181183. DOI 10.1155/S1073792892000205. A LOW-TECHNOLOGYESTIMATE IN convex geometry. GREG KUPERBERG. Received 23 July 1992. http://www.hindawi.com/journals/imrn/volume-1992/S1073792892000205.html

Home About this Journal Forthcoming Articles Author Index ... Contents IMRN 1992:9 (1992) 181-183. DOI: 10.1155/S1073792892000205 A LOW-TECHNOLOGY ESTIMATE IN CONVEX GEOMETRY GREG KUPERBERG Received 23 July 1992. The following files are available for this article: Full-Text PDF for institutional subscribers Mathematical Reviews review for MathSciNet subscribers Hindawi Publishing Corporation

55. PolyurethaneWeb: Polyurethane Foams, Coatings, Adhesives, Elastomers And Equipme convex geometry adhesive film system for laser capture microdissection. AbstractA tissue sample is conventionally visualized in a microscope. http://www.polyurethaneweb.com/patents.php?aktion=2&no=237251

56. Recent Publications, Gideon Schechtman convex geometry and Local Theory of Normed Spaces. An ``isomorphic version ofDvoretzky s theorem (with VD Milman), CR Acad. Sci. Paris t. 321 S\ erie I, http://www.wisdom.weizmann.ac.il/mathusers/gideon/pubsTopics/recentPubsByTopicLo

Convex Geometry and Local Theory of Normed Spaces An ``isomorphic" version of Dvoretzky's theorem (with V.D. Milman Global vs. local asymptotic theories of finite dimensional normed spaces (with V.D. Milman ), Duke Math. J. 90 (1997), 7393. An ``isomorphic" version of Dvoretzky's theorem II (with V.D. Milman ), Convex geometric analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, (1999). Averages of norms and behavior of families of projective caps on the sphere (with A.E. Litvak and V.D. Milman Averages of norms and quasi-norms (with A.E. Litvak and V.D. Milman ), Math. Annalen 312 (1998), 95124. (with A. Zvavitch ), Math. Nachr. 227 (2001), 133142. Concentration, results and applications , in preparation for handbook, preliminary version available. Finite dimensional subspaces of $L_p$ (with W.B. Johnson ), Handbook of the Geometry of Banach Spaces, Vol 1, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam (2001), 837870. (with J. Zinn

57. Artem Zvavitch Conference on Gaussian Measure and Geometric Convexity, Snowbird, Utah, July, 2004.AMS Special Session on Analytic convex geometry, Lawrenceville, NJ, http://www.math.kent.edu/~zvavitch/resume.html

Personal resume Artem Zvavitch Department of Mathematical Sciences 327 Mathematics and Computer Sciences Bldg Kent State University Kent, OH, 44242 USA Phone: (330)-672-3316 e-mail: zvavitch@math.kent.edu URL: http://www.math.kent.edu/~zvavitch Citizenship Israel. Born 06.09.1974, Moscow, Russia Marital Status married + 2. Wife: Tatiana Zvavitch Children: daughters Polina (born 22.06.1994) and Maya (born 05.08.1999). Fields of interest: Convex Geometry Geometric Functional Analysis Probability Harmonic Analysis Education: Ph.D. student of Gideon Schechtman , Weizmann Institute of Science, Department of Mathematics,(Rehovot, Israel). M.Sc. student of Oded Schramm , Weizmann Institute of Science, Department of Mathematics,(Rehovot, Israel). B.Sc. student, Moscow State University, Mechanics and Mathematics Department. Graduated Moscow School # 67 (Moscow, USSR). Appointments 2004-present: Assistant Professor, Department of Mathematical Sciences, Kent State University. Post Doctoral Fellow, Mathematics Department, University of Missouri-Columbia. Awards/Research Grants National Science Foundation Grant in Classical Analysis, Grant Number DMS-0504049, Amount $79,626

58. Polytechnic University Department Of Mathematics: Research Faculty convex geometry, geometric and analytic inequalities Phone (718) 2603366 Emailelutwak@poly.edu Office RH 305G. Harvansh Manocha http://www.math.poly.edu/people/research_faculty.phtml

Research Faculty Instructional Team Research Faculty Administrative Team Juan Carlos Alvarez (on leave) Ph.D., Rutgers University Symplectic and contact geometry, integral geometry, Finsler manifolds, geometry of normed spaces Phone: Email: jalvarez@poly.edu Office: Keith Ball (on leave) Ph.D., Cambridge University Functional analysis, combinatorics, convexity David Chudnovsky Ph.D., Ukrainian Academy of Sciences Number theory, mathematical physics, large scale numerical computation Gregory Chudnovsky Ph.D., Ukrainian Academy of Sciences Number theory, mathematical physics, large scale numerical computation Jonathan Cornick Ph.D., Northern Illinois University Chomology of infinite groups, CW-complexes and homological algebra Phone: Email: jcornick@poly.edu Office: Jerome S. Epstein Ph.D., New York University Differential geometry and mathematical physics Phone: Email: jepstein@poly.edu Office: Zsuzsanna Gonye Ph.D., SUNY at Stony Brook Kleinian and Fuchsian groups, complex analysis Phone: Email: zgonye@poly.edu Office: Kathryn Kuiken Ph.D., Polytechnic Institute of New York

59. Publications Of Károly Böröczky, Jr. In Combinatorial convex geometry and Toric Varieties, (G. Ewald, congruent convex domains, Discrete and Computational Geometry, 30 (2003), 185193. http://www.ceu.hu/math/People/Faculty/Boroczky/Publications of Károly Böröczk

PUBLICATIONS of KÁROLY BÖRÖCZKY, Jr. K. Böröczky, Jr., I.Z. Ruzsa: Note on an inequality of Wegner, submitted. K. Böröczky, Jr.: Extremal mean width when covering the one-skeleton, submitted. K. Böröczky, Jr.: Finite coverings in the hyperbolic plane, Discrete and Computational Geometry, accepted. K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality, Adv. Math., accepted. U. Betke, K. Böröczky, Jr.: Finite lattice packings and the Wulff-shape , Mathematika, accepted. K. Böröczky, Jr.: Toric varieties and continued fractions, In: Combinatorial Convex Geometry and Toric Varieties, (G. Ewald, B. Teissier eds.), Birkhäuser, accepted. K. Böröczky, Jr.: Valuations and the combinatorial Riemann-Roch theorem, In: Combinatorial Convex Geometry and Toric Varieties, (G. Ewald, B. Teissier eds.), Birkhäuser, accepted. K. Böröczky, Jr., M. Reitzner: Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes, Annals of Applied Prob., 14 (2004), 239-273. T. Bisztriczky, K. Böröczky, Jr., D.S. Gunderson: Cyclic polytopes, hyperplanes, and codes,

60. MaPhySto And StocLab Summer School On Stereology And Geometric Tomography Geometric tomography has connections with convex geometry, geometric probing inrobotics, computerized tomography, and other areas. http://www.maphysto.dk/oldpages/events/S-and-GT2000/

MaPhySto and StocLab Summer School on Stereology and Geometric Tomography Sandbjerg Manor, 20-25 May, 2000 The aim of the summer school was to give an overview of modern stereology and its relation to geometric tomography, including both the mathematical and statistical theory and the practical applications. Content Stereology is the area of stochastics dealing with statistical inference about spatial structures from geometric samples of the structure such as two-dimensional sections and one-dimensional probes. The development of stereological methods involve the use of advanced mathematical tools, especially from geometric measure theory and integral geometry. Stereology is now in world-wide use in many areas of biology and medicine, most importantly in neuroscience and cancer grading. Other areas of application are geology, metallography and mineralogy. A disector consists of a reference plane and a look-up plane, a distance h apart. Illustration of the sampling relevant for estimation of length in R , based on projections on a vertical plane.

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