Ample vector bundles and Bordiga surfaces

Let X be a smooth complex projective variety and let Z ? X be a smooth surface, which is the zero locus of a section of an ample vector bundle ? of rank dimX – 2 ≥ 2 on X. Let H be an ample line bundle on X, whose restriction H _Z to Z is a very ample line bundle and assume that (Z, H _Z ) is a Bordiga surface, i.e., a rational surface having (?², ?? (4)) as its minimal adjunction theoretic reduction. Triplets (X, ?, H) as above are discussed and classified. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Quantum Cohomology Ring of Flag Varieties

We describe the small quantum cohomology ring of complete flag varieties by algebro-geometric methods, as presented in our previous work Quantum cohomology of flag varieties (Internat. Math. Res. Notices, no. 6 (1995), 263-277). We also give a geometric proof of the quantum Monk formula.

     

Balanced superprojective varieties

We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the geometry of superprojective spaces, we extend Donaldson’s definition of balanced manifolds to supermanifolds and we derive the new conditions of a balanced supermanifold. We apply the construction to superpoints viewed as submanifolds of superprojective spaces. We conclude with a list of open issues and interesting problems that can be addressed in the present context.     

导数FTIR结合统计学法应用于中药延胡索质量控制的研究

提出了用单次反射傅里叶变换红外光谱法直接测定延胡索及其伪品的新方法。采用OMNI采样器直接测定法测定了样品的红外光谱,并经过二阶导数光谱转换后进行峰位一致率检验。结果发现延胡索表皮以内部分和外表皮的二阶导数红外光谱峰位基本无差别,而且不同产地的道地药材具有较好的相关性。表皮以内部分于2050～650cm^-1区域在4cm^-1波长区域单位范围内进行统计学处理,结果延胡索与其伪品的差异性极其显。可以采用二阶导数FTIR结合统计学法直接、快速、准确地对延胡索与其伪品的表皮以内部分进行区别鉴定。     

利用傅里叶变换红外光谱法鉴定小麦品种

利用傅里叶变换红外(FTIR)光谱法分析了8个不同小麦品种根部的红外光谱图,对红外光谱图的吸收峰进行了归属分析,通过对各谱图的比对发现,在相同波数范围内,不同的小麦品种其红外谱图的形状、波数及吸收峰的多少有所不同。结果表明不同小麦品种的红外光谱图有明显的差异,其一在2800～2980cm-1波数范围内,此区反映的主要是甲基、亚甲基的伸缩振动,化合物分子链的长短、分子量的大小在此区有显现;其二差别较大的区域在1510～1730cm-1范围内,它反映的主要是酰胺的氮原子及α碳原子取代基的性质,可能是源于基因的差异,此区域内谱图差异较大。因此FTIR光谱法可用于不同小麦品种的鉴别。     

Shades of orthodoxy in Rees-Sushkevich varieties

It is shown that, within the class of Rees-Sushkevich varieties that are generated by completely (0-) simple semigroups over groups of exponent dividing n, there is a hierarchy of varieties determined by the lengths of the products of idempotents that will, if they fall into a group ℋ-class, be idempotent. Moreover, the lattice of varieties generated by completely (0-) simple semigroups over groups of exponent dividing n, with the property that all products of idempotents that fall into group ℋ-classes are idempotent, is shown to be isomorphic to the direct product of the lattice of varieties of groups with exponent dividing n and the lattice of exact subvarieties of a variety generated by a certain five element completely 0-simple semigroup.     

Commuting polarities and maximal partial ovoids of H(4,q2)

In PG(4,q²), q odd, let Q(4,q²) be a non‐singular quadric commuting with a non‐singular Hermitian variety H(4,q²). Then these varieties intersect in the set of points covered by the extended generators of a non‐singular quadric Q₀ in a Baer subgeometry Σ₀ of PG(4,q²). It is proved that any maximal partial ovoid of H(4,q²) intersecting Q₀ in an ovoid has size at least 2(q²+1). Further, given an ovoid O of Q₀, we construct maximal partial ovoids of H(4,q²) of size q³+1 whose set of points lies on the hyperbolic lines 〈P,X〉 where P is a fixed point of O and X varies in O\{P}. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 307–313, 2009     

不同高光谱特征参数区分马铃薯品种的优劣势分析

对马铃薯关键生育期的高光谱遥感图像进行特征提取和分析,提出了一种快速区分不同马铃薯品种的方法。以两个早熟和中熟马铃薯品种为研究对象,采集其块茎形成期、块茎膨大期和淀粉积累期的冠层反射光谱曲线,对实测反射光谱曲线进行Savitzky-Golay滤波平滑和一阶微分处理,以高光谱位置参数、振幅参数、面积参数、宽度参数和反射率参数为研究指标,根据21个高光谱特征参数的贡献率大小,评价了其区分不同马铃薯品种的优劣。结果表明：(1)同一类高光谱特征参数在不同生育期区分马铃薯品种的能力不同: 高光谱位置参数、宽度参数和反射率参数在块茎膨大期区分不同马铃薯品种的能力最强,淀粉积累期次之;高光谱振幅参数和面积参数在淀粉积累期的区分能力最强,块茎膨大期次之,五类高光谱特征参数在块茎形成期的区分能力均最差。(2)同一生育期5类高光谱特征参数区分马铃薯品种的能力也存在差异。在块茎形成期,五类高光谱特征参数的区分能力从强到弱依次为：反射率参数>振幅参数>面积参数>宽度参数>位置参数;在块茎膨大期和淀粉积累期,从强到弱依次为：面积参数>振幅参数>反射率参数>宽度参数>位置参数。综合能力从强到弱依次为：面积参数>振幅参数>反射率参数>宽度参数>位置参数。     

State operators on generalizations of fuzzy structures

We enlarge the language of R?-monoids, which are a non-commutative generalizations of both MV algebras and BL algebras, by adding a unary operation that describes algebraic properties of a state (= an analog of probability measures). The resulting algebras are called stateR?-monoids and state-morphismR?-monoids. We present basic properties of such algebras. We describe subdirectly irreducible algebras, some generators of the varieties of state-morphism R?-monoids, and an interplay between states and state operators.