Search results for "BERT"

Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

On the graded identities and cocharacters of the algebra of 3×3 matrices

2004

Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the grade…

Regularity and h-polynomials of toric ideals of graphs

2020

For all integers 4 ≤ r ≤ d 4 \leq r \leq d , we show that there exists a finite simple graph G = G r , d G= G_{r,d} with toric ideal I G ⊂ R I_G \subset R such that R / I G R/I_G has (Castelnuovo–Mumford) regularity r r and h h -polynomial of degree d d . To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O’Keefe that compares the depth and dimension of toric ideals of graphs.

Tensor-product states and local indistinguishability: an optical linear implementation

2000

In this paper we investigate the properties of distinguishability of an orthogonal set of product states of two three level particle system by a simple class of joint measures. Here we confine ourselves to a system of analysis built up of linear elements, such as beam splitters and phase shifters, delay lines, electronically switched linear devices and auxiliary photons. We present here the impossibility of realization of a perfect never falling analyzer with this tools.

Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space

2002

AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.

MR2374457 (2009j:28033) Kakihara, Yûichirô Integration with respect to Hilbert-Schmidt class operator valued measures. Applied functional analysis, 2…

2009

Integration with respect to Hilbert-Schmidt class operator valued measures

Studio Morfoanatomico di Himantoglossum robertianum ed H.hircinum (Orchideaceae) della Sicilia

2009

The diagnosis of polycystic ovary syndrome in adolescents

2010

In women, the definition of polycystic ovary syndrome (PCOS) has become broad and includes several possible phenotypes. Because several features of PCOS may be in evolution in adolescents, we suggest that only firm criteria should be used to make a diagnosis of PCOS during adolescence. Hyperandrogenism, oligomenorrhea, and ovarian morphology change during adolescence and are discussed individually. Adolescents with incomplete criteria for a firm diagnosis of PCOS should be followed up carefully and may be diagnosed at a later time.

Paul Bert et l'instruction publique

2001

Paul Bert (1833-1886) a été professeur de physiologie à la Sorbonne, membre de l'Académie des sciences, député républicain, ministre de l'Instruction publique et des Cultes du gouvernement Gambetta, et résident général au Tonkin et en Annam. Il a participé à tous les degrés de la réforme de l'enseignement, et a surtout été avec Jules Ferry, le fondateur de l'école gratuite, laïque et obligatoire. Partisan de la laïcité, il a lutté, au nom de la liberté de conscience, pour la suppression de l'enseignement religieux et l'introduction de l'instruction civique et morale. Ce combat de la laïcisation a été en même temps celui mené contre le cléricalisme. Il a également voulu fonder l'école de la …

La libre-pensée de Paul Bert

2003

Ce texte est une retranscription de l'émission de France Culture du 9 février 2003; National audience