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Volume 40 (2004)
- Issue 4 Pages 1113-
- Issue 3 Pages 625-
- Issue 2 Pages 311-
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Displaying 1-9 of 9 articles from this issue
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Ludvig Faddeev, Alexander Yu. Volkov2004 Volume 40 Issue 4 Pages 1113-1125
Published: 2004
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSThe shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.View full abstractDownload PDF (148K) -
Kazuo Habiro2004 Volume 40 Issue 4 Pages 1127-1146
Published: 2004
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSFor a subset S⊂\mathbb{N}={1, 2, ...} and a commutative ring R with unit, let R[q]S denote the completion \underleftarrow{lim}f(q)R[q]/(f(q)), where f(q) runs over all the products of the powers of cyclotomic polynomials Φn(q) with n∈S. We will show that under certain conditions the completion R[q]S can be regarded as a “ring of analytic functions” defined on the set of roots of unity of order in S. This means that an element of R[q]S vanishes if it vanishes on a certain type of infinite set of roots of unity, or if its power series expansion at one root of unity vanishes. In particular, the completion \mathbb{Z}[q]\mathbb{N}{=}\underleftarrow{lim}n\mathbb{Z}[q]/((1−q)(1−q2)…(1−qn)) enjoys this property.View full abstractDownload PDF (247K) -
Anatol N. Kirillov2004 Volume 40 Issue 4 Pages 1147-1239
Published: 2004
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe report about some results, interesting examples, problems and conjectures revolving around the parabolic Kostant partition functions, the parabolic Kostka polynomials and “saturation” properties of several generalizations of the Littlewood–Richardson numbers. The Contents contains the titles of main topics we are going to discuss in the present paper.View full abstractDownload PDF (664K) -
Valery Alexeev2004 Volume 40 Issue 4 Pages 1241-1265
Published: 2004
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe compare several constructions of compactified jacobians — using semistable sheaves, semistable projective curves, degenerations of abelian varieties, and combinatorics of cell decompositions — and show that they are equivalent. We give a detailed description of the “canonical compactified jacobian” in degree g−1. Finally, we explain how Kapranov's compactification of configuration spaces can be understood as a toric analog of the extended Torelli map.View full abstractDownload PDF (263K) -
Koji Ohkitani2004 Volume 40 Issue 4 Pages 1267-1290
Published: 2004
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSIn this paper we review some classes of exact solutions of the Navier-Stokes equations under a time-independent external straining flow, centering around the celebrated Burgers vortex. The objectives are (i) to clarify the relationship between them and (ii) to examine them as models of turbulence. Particularly we study the Lundgren spiral model for turbulence in the presence of azimuthal vorticity (that is, with axial velocity). The implication on linear stability of the Burgers vortex is briefly discussed.View full abstractDownload PDF (365K) -
Akio Tamagawa2004 Volume 40 Issue 4 Pages 1291-1336
Published: 2004
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSIn the present paper, we consider the following problem: For a given closed point x of a special fiber of a generically smooth family X→S of stable curves (with dim(S)=1), is there a covering Y→X that is generically étale (i.e., étale over the generic fiber(s) of X→S, not only over the generic point(s) of X), where Y is also a family of stable curves, such that the image in X of the non-smooth locus of Y contains x? Among other things, we prove that this is affirmative (possibly after replacing S by a finite extension) in the case where S is the spectrum of a discrete valuation ring of mixed characteristic whose residue field is algebraic over \mathbb{F}p.View full abstractDownload PDF (435K) -
Kyoji Saito2004 Volume 40 Issue 4 Pages 1337-1384
Published: 2004
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSLet V\mathbb{R} be a real vector space with an irreducible action of a finite reflection group W. We study the semi-algebraic geometry of the W-quotient affine variety V//W with the discriminant divisor DW in it and the τ-quotient affine variety V//W//τ with the bifurcation set BW in it, where τ is the \mathbb{G}a-action on V//W obtained by the integration of the primitive vector field D on V//W and BW is the discriminant divisor of the induced projection : DW→V//W//τ.
Our goal is the construction of a one-parameter family of the semi-algebraic polyhedra KW(λ) in V\mathbb{R} which are dual to the Weyl chamber decomposition of V\mathbb{R}.
As an application, we obtain two geometric descriptions of generators for π1 ((V//W)\mathbb{C}reg), satisfying the Artin braid relations.
The key of the construction of the polyhedra KW(λ) is a theorem on a linearization of the tube domain in (V//W)\mathbb{R} over the simplicial cone EW in TW, \mathbb{R}.View full abstractDownload PDF (516K) -
Catherine Donati-Martin, Yan Doumerc, Hiroyuki Matsumoto, Marc Yor2004 Volume 40 Issue 4 Pages 1385-1412
Published: 2004
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSThe aim of this paper is to discuss for Wishart processes some properties which are analogues of the corresponding well-known ones for Bessel processes. In fact, we mainly concentrate on the local absolute continuity relationship between the laws of Wishart processes with different dimensions, a property which, in the case of Bessel processes, has proven to play a rather important role in a number of applications.View full abstractDownload PDF (285K) -
Masayasu Mimura2004 Volume 40 Issue 4 Pages 1413-1431
Published: 2004
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSDownload PDF (1829K)
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