November 2011
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1 Read
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November 2011
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1 Read
November 2011
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1 Read
January 2010
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20 Reads
Notices of the American Mathematical Society
January 2006
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7 Reads
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1 Citation
Mitteilungen der Deutschen Mathematiker-Vereinigung
January 2005
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9 Reads
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12 Citations
Pure and Applied Mathematics Quarterly
December 2004
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6 Reads
Asian Journal of Mathematics
May 2004
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407 Reads
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1 Citation
Memorial article with Knapp as editor and with the other nine people as authors
January 2004
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25 Reads
Notices of the American Mathematical Society
January 2002
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6 Reads
Mitteilungen der Deutschen Mathematiker-Vereinigung
January 2001
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62 Reads
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3 Citations
An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
... The integer g is called the genus of the family. The first embedded surface is a K3 surface of genus 9, embedded in CP 9 by the pillow (2,2)- pillow degeneration (see [6] for details). The resulting embedding can be degenerated into a union of 16 planes, such that the whole degenerated object would " resemble a pillow " (see figure 1 for clarification). ...
January 2001
... In particular, we will use that rotations can be parametrized by unit quaternions (which can be identified with the unit 3-sphere S 3 ), as well as the following formulae (see, e.g. [11,22]): ...
January 1991
... The combinatorial and group theory properties of the number 6 are described in considerable detail in Shaw (1994), along with a tie-up with the properties of the Klein quadric in the space IPB 6 , B 6 = 2 V 4 . Other references include Janusz & Rotman (1982), Cameron & Van Lint (1991) and Tits (1991). ...
January 1991
... where c i .E/ denotes the i -th Chern class of E. In fact, by [15,Section 1.8], all genera are of the form ...
January 1992
... Whether we are in the even case or the odd case depends in general on the situation. For the 6-sphere, the base of the light cone in Minkowski space R(7, 1), we are in the odd case, but for signatures (5,3) or dually (3,5), the 6-sphere is replaced by the complex projective 3-space P , or its dual P * , the real ACS is integrable and we are in the even case. This is just linear algebra and easily checked. ...
Reference:
The Non-Existent Complex 6-Sphere
January 1959
Bulletin de la Société mathématique de France
... A class of complex hyperbolic lattices in PU (2, 1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch (see Hirzebruch, in: Arithmetic and geometry, vol II, volume 36 of Progress in Mathematics, Birkhäuser, Boston, pp 113-140, 1983;Barthel et al., in: Aspects of mathematics, D4. Friedrich Vieweg & Sohn, Braunschweig, 1987 and Tretkoff, in: Complex ball quotients and line arrangements in the projective plane, volume 51 of mathematical notes, Princeton University Press, Princeton, 2016) in terms of line arrangements. ...
January 1987
... The proof of (2) is a direct application of Theorem 2.1 and Proposition 3.5, and the fact that the functor * V ⊗ B −⊗ B U * is also exact. Namely, by [31,Theorem V.4.1], the bimodules * V and U * are projective as B-modules. ...
January 1979
... Solutions to hyperbolic conservation laws often stay in an admissible state set G, also called the invariant domain. For instance, the solutions to initial value problems of scalar conservation laws satisfy a strict maximum principle (MP) [14]. Physically, both the density and pressure in the solutions to the compressible Euler equations should stay positive. ...
January 2000
... Each vertex x ∈ V n represents an individual at site x within a population of size n. From the perspective of an interacting particle system (IPS) (see Kipnis and Landim (1999); Liggett (1985)), we say that a configuration σ ∈ Ω n has a particle at site x ∈ V n if σ x = 1. If σ x = 0, we say that the site x is empty. ...
January 1999
... The contact process (sometimes also referred to as the SIS epidemic model) is a Markovian interacting particle system, which was first introduced to the mathematical literature by Harris [17] and has been studied extensively on hypercubic lattices throughout the 1970s, 1980s and early 1990s. An introduction to this classical theory as well as an overview of its main results is provided in the monographs [27,28]. In the 2000s renewed interest in the contact process emerged in the context of complex networks, and in particular researchers began to investigate the behaviour of the process on large but finite random graphs as a toy model for the spread of disease or information in a variety of mesoscopic systems, see, for example, [12] for an account of rigorous results in this area. ...
January 1999