Enumerating indices of Schubert varieties defined by inclusions

By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231,35142,42513,351624)$\mathrm{Av}(4231,35142,42513,351624)$, a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class.     

Iris segmentation using variational level set method

Continuous efforts have been made to process degraded iris images for enhancement of the iris recognition performance in unconstrained situations. Recently, many researchers have focused on developing the iris segmentation techniques, which can deal with iris images in a non-cooperative environment where the probability of acquiring unideal iris images is very high due to gaze deviation, noise, blurring, and occlusion by eyelashes, eyelids, glasses, and hair. Although there have been many iris segmentation methods, most focus primarily on the accurate detection of iris images captured in a closely controlled environment. The novelty of this research effort is that we propose to apply a variational level set-based curve evolution scheme that uses a significantly larger time step to numerically solve the evolution partial differential equation (PDE) for segmentation of an unideal iris image accurately, and thereby, speeding up the curve evolution process drastically. The iris boundary represented by the variational level set may break and merge naturally during evolution, and thus, the topological changes are handled automatically. The proposed variational model is also robust against poor localization and weak iris/sclera boundaries. In order to solve the size irregularities occurring due to arbitrary shapes of the extracted iris/pupil regions, a simple method is applied based on connection of adjacent contour points. Furthermore, to reduce the noise effect, we apply a pixel-wise adaptive 2D Wiener filter. The verification and identification performance of the proposed scheme is validated on three challenging iris image datasets, namely, the ICE 2005, the WVU Unideal, and the UBIRIS Version 1.     

Higher K-Theory of Toric Varieties

A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both Quillen's fundamental result on K-homotopy invariance of regular rings and the stable version of the triviality of vector bundles on affine toric varieties. Moreover, it yields a similar behavior of not necessarily affine toric varieties and, further, of their equivariant closed subsets. The conjecture is equivalent to the claim that the relevant admissible morphisms of the category of vector bundles on an affine toric variety can be supported by monomials not in a nondegenerate corner subcone of the underlying polyhedral cone. We prove that one can in fact eliminate all lattice points in such a subcone, except maybe one point. The elimination of the last point is also possible in 0 characteristic if the action of the big Witt vectors satisfies a very natural condition. A partial result of this in the arithmetic case provides first nonsimplicial examples, actually an explicit infinite series of combinatorially different affine toric varieties, simultaneously verifying the conjecture for all higher groups.Supported by the Deutsche Forschungsgemeinschaft, INTAS grant 99-00817 and TMR grant ERB FMRX CT-97-0107     

Epimorphism sequences between hyperbolic 3-manifold groups

We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.

     

Varieties of two-dimensional cylindric algebras.¶Part I: Diagonal-free case

We investigate the lattice of all subvarieties of the variety Df ₂ of two-dimensional diagonal-free cylindric algebras. We prove that a Df ₂-algebra is finitely representable if it is finitely approximable, characterize finite projective Df ₂-algebras, and show that there are no non-trivial injectives and absolute retracts in Df ₂. We prove that every proper subvariety of Df ₂ is locally finite, and hence Df ₂ is hereditarily finitely approximable. We describe all six critical varieties in , which leads to a characterization of finitely generated subvarieties of Df ₂. Finally, we describe all square representable and rectangularly representable subvarieties of Df ₂. Received May 25, 2000; accepted in final form November 2, 2001.     

Semirings which are unions of rings

Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.``     

Two new C-glycosylflavones from the leaves of Iris lactea var.chinensis

Two new acylated C-glycosylflavones were isolated from the leaves of Iris lactea var. chinensis, and their structures were elucidated on the basis of extensive NMR experiments and mass spectrometry methods and were assigned as 5-hydroxy-4＇- methoxyflavone-7-O-（β-D-2＇＇＇＇4＇＇＇＇-diacetylrhamnopyranosyl）-6-C-[ O-（α-L-6＇＇＇-acetyl-glucpyranosyl）-1→2-β-D-glucopyrano- side] （irislactin A） and 5-hydroxy-4＇,7-dimethoxyflavone-6-C-[O-（α-L-2＇＇＇,3＇＇＇-diacetylrhanmo-pyranosyl）-1→ 2-β-D-glucopyranoside] （irislactin B）.     

Microlocal analysis on wonderful varieties. Regularized traces and global characters

Let be a connected reductive complex algebraic group with split real form . Consider a strict wonderful ‐variety X equipped with its σ‐equivariant real structure, and let X be the corresponding real locus. Further, let E be a real differentiable G‐vector bundle over X . In this paper, we introduce a distribution character for the regular representation of G on the space of smooth sections of E given in terms of the spherical roots of , and show that on a certain open subset of G of transversal elements it is locally integrable and given by a sum over fixed points.