熔石英相位共轭镜无损工作状态分析

基于非线性光学耦合波方程组建立了聚焦泵浦条件下熔石英玻璃材料中SBS过程的物理模型并编制了相应的数值求解程序,研究了SBS介质内激光场的时空发展特征,从而试图揭示SBS介质的内在破坏机制并寻求相应的加固措施.通过数值模拟程序研究了焦点处激光功率密度以及SBS反射率与激光能量的依赖关系,发现SBS对介质内的激光场具有"限幅"作用,即在注入能量大幅度提升的情况下,内部的激光场强度只有较小的增加,这种机制使大能量的固体介质PCM成为可能.分析激光脉宽以及耦合透镜焦距等参数对SBS过程的影响发现,精细选择系统参数,在熔石英玻璃材料中有可能无损伤地实现高效的SBS过程.     

The Lattice of Interpretability Types of Cantor Varieties

For integers 1 m < n, a Cantor variety with m basic n-ary operations _i and n basic m-ary operations _k is a variety of algebras defined by identities _k(₁( ), ... , _m( )) = _k and i(₁( ), ... ,_n( )) = y _i, where = (x ₁., ... , x _n) and = (y ₁, ... , y _m). We prove that interpretability types of Cantor varieties form a distributive lattice, , which is dual to the direct product ₁ × ₂ of a lattice, ₁, of positive integers respecting the natural linear ordering and a lattice, ₂, of positive integers with divisibility. The lattice is an upper subsemilattice of the lattice of all interpretability types of varieties of algebras.     

Support Varieties for Selfinjective Algebras

Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70.     

Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces

We prove that the varieties of complete pairs of zero-dimensional subschemes of lengths d ₁ 2, d ₂ 4 on a smooth irreducible projective algebraic surface are singular.     

Intersection Cohomology on Nonrational Polytopes⋆

We consider a fan as a ringed space (with finitely many points). We develop the corresponding sheaf theory and functors, such as direct image R_* ( is a subdivision of a fan), Verdier duality, etc. The distinguished sheaf , called the minimal sheaf plays the role of an equivariant intersection cohomology complex on the corresponding toric variety (which exists if is rational). Using we define the intersection cohomology space IH(). It is conjectured that a strictly convex piecewise linear function on acts as a Lefschetz operator on IH(). We show that this conjecture implies Stanley's conjecture on the unimodality of the generalized h-vector of a convex polytope.     

The de Rham Bundle on a Compactification of Moduli Space of Abelian Varieties

In this paper, we show that the Chern classes c _k of the de Rham bundle defined on any good toroidal compactification of the moduli space of Abelian varieties of dimension g are zero in the rational Chow ring of , for g=4, 5 and k>0.     

Kazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations

In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials P _x , _w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic on all subexpressions of any fixed reduced expression for w. As a consequence of our results on Kazhdan-Lusztig polynomials, we show that the Poincaré polynomial of the intersection cohomology of the Schubert variety corresponding to w is (1+q) ^l(w) if and only if w is 321-hexagon-avoiding. We also give a sufficient condition for the Schubert variety X _w to have a small resolution. We conclude with a simple method for completely determining the singular locus of X _w when w is 321-hexagon-avoiding. The results extend easily to those Weyl groups whose Coxeter graphs have no branch points (B C _n , F ₄, G ₂).     

The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

Infrared chemical imaging: Spatial resolution evaluation and super-resolution concept

Chemical imaging systems help to solve many challenges in various scientific fields. Able to deliver rapid spatial and chemical information, modern infrared spectrometers using Focal Plane Array detectors (FPA) are of great interest. Considering conventional infrared spectrometers with a single element detector, we can consider that the diffraction-limited spatial resolution is more or less equal to the wavelength of the light (i.e. 2.5-25 μm). Unfortunately, the spatial resolution of FPA spectroscopic setup is even lower due to the detector pixel size. This becomes a real constraint when micron-sized samples are analysed. New chemometrics methods are thus of great interest to overcome such resolution drawback, while keeping our far-field infrared imaging spectrometers. The aim of the present work is to evaluate the super-resolution concept in order to increase the spatial resolution of infrared imaging spectrometers using FPA detectors. The main idea of super-resolution is the fusion of several low-resolution images of the same sample to obtain a higher-resolution image. Applying the super-resolution concept on a relatively low number of FPA acquisitions, it was possible to observe a 30% decrease in spatial resolution.