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11.
We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. Applying this method to complexes arising from graphs, we give topological meaning to classical graph invariants. As a consequence, we answer some questions raised in (Ehrenborg and Hetyei in Eur. J. Comb. 27(6):906–923, 2006) on the independence complex and the dominance complex of a forest and obtain improved algorithms to compute their homotopy types.  相似文献   
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We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of \mathbbP2{\mathbb{P}^2} at distinct points lying on a (possibly reducible) cubic.  相似文献   
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Background  

Cystic fibrosis (CF) airway pathology is a fatal, autosomal, recessive genetic disease characterized by extensive lung inflammation. After induction by TNF-α, elevated concentrations of several pro-inflammatory cytokines (i.e. IL-6, IL-1β) and chemokines (i.e. IL-8) are released from airway epithelial cells. In order to reduce the excessive inflammatory response in the airways of CF patients, new therapies have been developed and in this respect, medicinal plant extracts have been studied. In this article we have investigated the possible use of bergamot extracts (Citrus bergamia Risso) and their identified components to alter the expression of IL-8 associated with the cystic fibrosis airway pathology.  相似文献   
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We introduce two new linear differential operators which are invariant with respect to the unitary group SU(n). They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials.  相似文献   
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We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a combination of the “determinant method” with an m-descent on the curve.  相似文献   
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In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree d ≥ 3 from its inflection lines? We answer the posed question positively for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve.  相似文献   
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