傅里叶自解卷积-红外光谱分析法应用于中药天麻的鉴别研究

采用水平衰减全反射-傅里叶变换红外光谱法(HATR-FTIR)对不同产地的野生及种植天麻与伪品芭蕉芋、芋及马铃薯进行了测定,并通过傅里叶自解卷积(FSD)进行了转换。在各种带宽因子及增强因子下对真伪品傅里叶自解卷积红外光谱的差异程度进行了分析研究,结果发现带宽因子在75.0～76.0,增强因子为3.2时,天麻与伪品的FSD-IR的差异程度最为明显。结果表明,尽管从FTIR中很难发现野生及种植天麻、无性繁殖及有性繁殖天麻之间的差异,但从FSD-IR中可以看出他们之间的差异。而天麻正品与伪品之间的FSD-IR差别也较大。因此该法可简便、快速、准确地识别不同的天麻及其伪品。     

Chern Classes of Gauss–Manin Bundles of Weight 1 Vanish

We show that the Chern character of a variation of polarized Hodge structures of weight one with nilpotent residues at dies up to torsion in the Chow ring, except in codimension 0.     

A Duality Theorem for Étale p-Torsion Sheaves on Complete Varieties over a Finite Field

Let X be an arbitrary variety over a finite field k and p=char k,n N. We will construct a complex of étale sheaves on X together with trace isomorphism from the highest étale cohomology group of this complex onto Z/pⁿZ such that for every constructible Z/pⁿZ-sheaf on X the Yoneda pairing is a nondegenerate pairing of finite groups. If X is smooth, this complex is the Gersten resolution of the logarithmic de Rham–Witt sheaf introduced by Gros and Suwa. The proof is based on the special case proven by Milne when the sheaf is constant and X is smooth, as well as on a purity theorem which in turn follows from a theorem about the cohomological dimension of C_i-fields due to Kato and Kuzumaki. If the existence of the Lichtenbaum complex is proven, the theorem will be the p-part of a general duality theorem for varieties over finite fields.     

On the Infinitesimal Rigidity of Homogeneous Varieties

Let XP be a variety (respectively an open subset of an analytic submanifold) and let xX be a point where all integer valued differential invariants are locally constant. We show that if the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Segre P× P, n,m2, a Grassmaniann G(2,n+2), n4, or the Cayley plane OP², then X is the corresponding homogeneous variety (resp. an open subset of the corresponding homogeneous variety). The case of the Segre P²×P² had been conjectured by Griffiths and Harris in [GH]. If the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Veronese v₂(P) and the Fubini cubic form of X at x is zero, then X=v₂ (P) (resp. an open subset of v₂(P)). All these results are valid in the real or complex analytic categories and locally in the C category if one assumes the hypotheses hold in a neighborhood of any point x. As a byproduct, we show that the systems of quadrics I₂(P P) S²C, I₂(P¹× P) S²C and I₂(S₅) S²C¹⁶ are stable in the sense that if A S^* is an analytic family such that for t0,AA, then A₀A. We also make some observations related to the Fulton–:Hansen connectedness theorem.     

Complex multiplication of exactly solvable Calabi–Yau varieties

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi–Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi–Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the varieties by the complex multiplication symmetry. The geometric structure that provides a conceptual interpretation of the relation between geometry and conformal field theory is discrete, and turns out to be given by the torsion points on the abelian varieties.     

污染气体红外光谱鉴别器的优化设计

针对污染气体红外光谱特征分布的复杂性，结合几种线性分类器的特点，通过对每个环节的深入分析，设计出一种混合多叉树状光谱鉴别器。实验结果表明：此光谱鉴别器不仅结构简洁，设计合理，具有很高的分类能力和判别准确率，而且具有较好的灵活性和稳定性，完全满足快速识别的需要，是一种高效的光谱鉴别器。     

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.