Chow’s Theorem for Semi-abelian Varieties and Bounds for Splitting Fields of Algebraic Tori

A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori.     

改进的QGA-ELM算法水稻叶面积指数反演模型

为了通过植被指数（VI）准确、可靠的获取不同施肥梯度、不同品种的水稻叶面积指数（LAI）,提出了一种基于改进的QGA-ELM算法应用于水稻LAI反演。首先通过8折交叉验证确定极限学习机(ELM)最佳的隐含层神经元个数与隐含层激活函数类型,再通过引入组合动态旋转角策略、单点混沌交叉操作、混沌变异操作、确定性选择策略、量子灾变操作对量子遗传算法（QGA）进行改进,最后使用改进后的QGA算法优化ELM神经网络输入层到隐含层的连接权值和隐含层的阈值。为了验证该模型普适性和有效性,依次建立多元线性回归、BP、ELM、QGA-ELM、改进的QGA-ELM算法5种模型,并在不同数据集上进行反演效果比较,结果表明：（1）对比QGA-ELM算法和改进的QGA-ELM算法进化过程,改进的算法能有效提升模型寻优能力,避免算法早熟,且能寻得更优结果。（2）对比五种算法在不同数据集上的反演效果,验证了NDVI,RVI与LAI之间主要为非线性关系,且ELM神经网络模型反演效果要优于BP神经网络模型和多元线性回归模型。（3）对比五种算法在不同数据集上的反演效果,改进的QGA-ELM算法绝大部分情况下拥有最高的反演精度和最低的误差,改进后的算法反演精度得到了明显提升,泛化性能也得到了增强。（4）改进的QGA-ELM算法在各种施肥梯度上均具有最高反演精度和最低误差,且精度较高,能为不同生长状况水稻LAI反演提供依据。（5）五种模型对庆和香LAI反演精度均要高于龙稻18,而改进的QGA-ELM算法在不同水稻品种上依然具有较高的反演精度,且在不同水稻品种上反演精度相差极小,远低于其他四种模型,能很好适应不同水稻品种LAI反演要求,极大提升模型的稳定性性,为不同水稻品种反演提供参考意义。     

Functors of the category of abelian sheaves on regular affine scheme

In this short paper, we prove that ifR is a regular local ring of unequal characteristic, then there exists an additive covariant functorG from the category of abelian sheaves on SpecR to the category of abelian groups such that id _R (G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.     

Regular Cayley maps for finite abelian groups

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical form for A. The case when A is normal in G involves the relationship between the rank of A and the exponent of the automorphism group of A, and the general case uses Ito's theorem to analyze the factorization G = AY, where Y is the (cyclic) stabilizer of a vertex. Supported in part by the N.Z. Marsden Fund (grant no. UOA0124).     

Rook Poset Equivalence of Ferrers Boards

A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of when two Ding Schubert varieties have identical Schubert cell structures. This also produces a complete classification of isomorphism types of lower intervals of 312-avoiding permutations in the Bruhat order.     

不可数求和型Hahn-Schur定理

The classical countable summation type Hahn-Schur theorem is a famous result in summation theory and measure theory. An interesting problem is whether the theorem can be generalized to non-countable summation case? In this paper, we show that the answer is true.     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

A vanishing theorem for modular symbols on locally symmetric spaces

A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV. Received: December 8, 1996     

A class of congruences in partial Abelian semigroups

In this paper, by basing on the special morphism of Habil, we introduce and study a class of congruences in partial Abelian semigroups and obtain some interesting properties. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Modular quintics in ℙ4

We will examine the arithmetic of some of the members of a pencil of symmetric quintics in projective 4‐space. We will give evidence for the modularity of some of the exceptional members (even the non‐rigid ones) and give a proof in one rigid case. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)