近红外光谱技术对闽南乌龙茶品种的识别研究

采用近红外光谱技术建立了一种快速无损的乌龙茶品种识别方法。收集闽南地区不同茶场中铁观音、黄金桂、本山、毛蟹与梅占等5个品种共210份具有代表性的乌龙茶样品,采集近红外光谱数据,选用1 100~1 300nm,1 640~2 498nm作为检测波长范围,利用主成分分析法(principal component analysis,PCA)建立模型,并在实验过程中比较多元散射校正(multiplicative scatter correction,MSC)与标准正态变量校正(standard normal variate,SNV)两种数据预处理方法对模型的影响。实验结果表明,多元散射校正对模型的影响优于标准正态变量校正,对校正集的识别准确率达到了96%,对预测集中样品的识别准确率达到了90%。实验结果证明了采用近红外光谱技术可以快速无损识别闽南地区乌龙茶,具有较强的实用价值和推广价值。     

Varieties without minimal generators

While many familiar varieties have a minimal varietal generator, i.e., a regular projective finitely presentable regular generator such that none of its retracts is a regular generator, and even a unique one, we present (a) a variety having no minimal varietal generator at all and (b) a variety having two non-isomorphic minimal varietal generators. Moreover we demonstrate that the same effects can happen with respect to a weaker notion of minimality and are common even in module categories. Received April 7, 1999; accepted in final form July 10, 2000.     

Periods of ordinary abelian varieties in characteristic p

For ordinary abelian varieties in characteristicp>0, we define an analogue of the period lattice and of the parametrization by ^g and give some applications.     

Families of varieties of general type over compact bases

Let be a smooth family of canonically polarized complex varieties over a smooth base. Generalizing the classical Shafarevich hyperbolicity conjecture, Viehweg conjectured that Y is necessarily of log general type if the family has maximal variation. A somewhat stronger and more precise version of Viehweg's conjecture was shown by the authors in [S. Kebekus, S.J. Kovács, Families of canonically polarized varieties over surfaces, preprint math.AG/0511378; Invent. Math. (2008), doi: 10.1007/s00222-008-0128-8; S. Kebekus, S.J. Kovács, The structure of surfaces mapping to the moduli stack of canonically polarized varieties, arXiv: 0707.2054v1 [math.AG], 2007] in the case where Y is a quasi-projective surface. Assuming that the minimal model program holds, this very short paper proves the same result for projective base manifolds Y of arbitrary dimension.     

Homology of planar polygon spaces

In this paper, we study topology of the variety of closed planar n-gons with given side lengths . The moduli space where , encodes the shapes of all such n-gons. We describe the Betti numbers of the moduli spaces as functions of the length vector . We also find sharp upper bounds on the sum of Betti numbers of depending only on the number of links n. Our method is based on an observation of a remarkable interaction between Morse functions and involutions under the condition that the fixed points of the involution coincide with the critical points of the Morse function.      

On Identity Bases of Exclusion Varieties for Monoids

An exclusion variety is a variety that is maximal with respect to not containing some semigroup. It is shown that if the bases of all exclusion varieties for some periodic semigroup S are known, then the bases of exclusion varieties for the monoid S ¹ can be computed.     

Automorphisms of Relatively Free Nilpotent Lie Algebras

Let L be a relatively free nilpotent Lie algebra over ? of rank n and class c, with n ≥ 2; freely generated by a set 𝒵. Give L the structure of a group, denoted by R, by means of the Baker–Campbell–Hausdorff formula. Let G be the subgroup of R generated by the set 𝒵 and N _Aut(L)(G) the normalizer in Aut(L) of the set G. We prove that the automorphism group of L is generated by GL _n (?) and N _Aut(L)(G). Let H be a subgroup of finite index in Aut(G) generated by the tame automorphisms and a finite subset X of IA-automorphisms with cardinal s. We construct a set Y consisting of s + 1 IA-automorphisms of L such that Aut(L) is generated by GL _n (?) and Y. We apply this particular method to construct generating sets for the automorphism groups of certain relatively free nilpotent Lie algebras.     

Boundedness for Some Rationally Connected Threefolds in ℙ6

We prove boundedness of rationally-connected threefolds in ?⁶ under some extra-assumptions.     

高光谱技术的羊肉品种多波段识别研究

利用可见/近红外(400～1 000 nm)及近红外(900～1 700 nm)高光谱成像技术对宁夏地区滩寒杂交、盐池滩羊、小尾寒羊三个品种羊肉进行识别研究。针对不同波段光谱特点,分别优选出Baseline及SG卷积平滑光谱预处理方法,并运用连续投影算法(SPA)提取特征波长,结合线性判别分析(LDA)及径向基核函数支持向量机(RBFSVM)模型进行全波段及特征波长识别分析。结果表明不同波段高光谱对羊肉品种识别均获得较好效果,其中400～1 000 nm波段采用Baseline-Fullwave-RBFSVM及12个特征波长下准确率为100%与98.75%,900～1 700 nm波段采用Baseline-Fullwave-RBFSVM及7个特征波长下准确率为96.25%与87.80%;RBFSVM非线性分类准确率高于LDA线性判别结果,400～1 000 nm波段识别准确率优于900～1 700 nm波段,说明三种羊肉在色泽纹理上差异比成分含量显著,利用高光谱成像技术结合RBFSVM方法能够获得较优的羊肉品种识别效果。     

The group SK1 for simple algebras

We prove that the reduced Whitehead group SK ₁(A) is generically nontrival for any central simple algebra A of index divisible by 4. This work has been supported by the NSF grant DMS #0355166.