Subtractive Categories

We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1_X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.Mathematics Subject Classifications (2000) 18C99, 18E05, 08B05.     

On Constantive Simple and Order-Primal Algebras

A finite algebra is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order ≤ on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; ≤). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras.* Research supported by the Hungarian research grant No. TO34137 and by the János Bolyai grant.** Research supported by the Thailand Research Fund.     

Soluble Groups and Varieties of <Emphasis Type="Italic">l</Emphasis>-Groups

A sufficient condition is given under which factors of a system of normal convex subgroups of a linearly ordered (l.o.) group are Abelian. Also, a sufficient condition is specified subject to which factors of a system of normal convex subgroups of an l.o. group are contained in a group variety . In particular, for every soluble l.o. group G of solubility index n, n ⩾ 2, factors of a system of normal convex subgroups are soluble l.o. groups of solubility index at most n − 1. It is proved that the variety of all lattice-ordered groups, approximable by linearly ordered groups, does not coincide with a variety generated by all soluble l.o. groups. It is shown that if is any o-approximable variety of l-groups, and if every identity in the group signature is not identically true in , then contains free l.o. groups.Supported by FP “Universities of Russia” grant UR. 04. 01. 001.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 355–367, May–June, 2005.     

Varieties with small discriminant variety

Let be a smooth complex projective variety, let be an ample and spanned line bundle on , defining a morphism and let be its discriminant locus, the variety parameterizing the singular elements of . We present two bounds on the dimension of and its main component relying on the geometry of . Classification results for triplets reaching the bounds as well as significant examples are provided.

     

中街山海域渔业动物群落结构的季节变化

针对2011年中街山海域4个航次调查数据,利用相似性指数和多样性指数,对该海域的渔业动物群落结构的季节性变化进行了分析。结果表明：除秋季甲壳类占优势外,各个季节鱼类均为优势类群;从资源密度值变化情况来看,中街山海域夏季CPUE最高,为51．5kg,h;从各个季节生物优势种类组成来看,优势种种类数达17种,其中绝大部分为鱼类,龙头鱼和棘头梅童鱼为3个季节均出现的优势种,优势度最高的季节为秋季,单物种最高生物量比重为26．5％;冬夏两季生物量优势度略低于秋季,单物种最高生物量比例为26．2％和20．2％;春季生物量优势度最低,最高单种生物量比重仅为16．5％。     

Real double flag varieties for the symplectic group

In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group G and the symmetric subgroup L, the Levi part of the Siegel parabolic $P_S$. We give a detailed treatment of the case of the maximal parabolic subgroups Q of L corresponding to Grassmannians and the product variety of $G/P_S$ and $L/Q$; in particular we classify the L-orbits here, and find natural explicit integral transforms between degenerate principal series of L and G.     

Folding procedure for Newton-Okounkov polytopes of Schubert varieties

The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and gives a systematic method of constructing toric degenerations of projective varieties. In the case of Schubert varieties, their Newton-Okounkov polytopes are deeply connected with representation theory. Indeed, Littelmann’s string polytopes and Nakashima-Zelevinsky’s polyhedral realizations are obtained as Newton-Okounkov polytopes of Schubert varieties. In this paper, we apply the folding procedure to a Newton-Okounkov polytope of a Schubert variety, which relates Newton-Okounkov polytopes of Schubert varieties of different types. As an application, we obtain a new interpretation of Kashiwara’s similarity of crystal bases.     

Higher Gauss maps of Veronese varieties—A generalization of Boole’s formula and degree bounds for higher Gauss map images

The image of the higher Gauss map for a projective variety is discussed. The notion of higher Gauss maps here was introduced by Fyodor L. Zak as a generalization of both ordinary Gauss maps and conormal maps. The main result is a closed formula for the degree of those images of Veronese varieties. This yields a generalization of a classical formula by George Boole on the degree of the dual varieties of Veronese varieties in 1844. As an application of our formula, degree bounds for higher Gauss map images of Veronese varieties are given.     

区域集群下板材订单配置模型及算法研究

针对集群企业板材资源滞留、无法共享、加工旺季材料短缺等问题,依据区域板材特性和区域企业集群地理相关优势,建立以减少需求方板材订单采购费用最小化为目标的板材订单分配模型,采用以粒子群、免疫算法相结合的混合调度算法。计算过程中,将订单分配对应企业编号作为免疫系统的抗体基因,通过比较适应度函数解与订单预算成本的关系,将抗体群区分为支配解与非支配解,提高算法对抗原的免疫能力和最优解的选择概率。最后以板材订单分配实例进行试验仿真,分别采用PSO算法与IA-PSO算法进行试验对比,对平台上6家订单发布企业寻找合适地理位置相近和价格相对低廉的供应商。试验结果表明,IA-PSO算法能够有效地解决区域集群内板材订单的匹配问题,并且在寻找价格更低和位置更合适的供应商上更有优势。     

Spherical Tropical Geometry: a Survey of Recent Developments

This is a survey of some recent results on spherical tropical geometry.