Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Affine Hecke algebras and the Schubert calculus

Using a combinatorial approach that avoids geometry, this paper studies the structure of K_T(G/B), the T-equivariant K-theory of the generalized flag variety G/B. This ring has a natural basis (the double Grothendieck polynomials), where is the structure sheaf of the Schubert variety X_w. For rank two cases we compute the corresponding structure constants of the ring K_T(G/B) and, based on this data, make a positivity conjecture for general G which generalizes the theorems of M. Brion (for K(G/B)) and W. Graham (for H_T^*(G/B)). Let [X^λ]K_T(G/B) be the class of the homogeneous line bundle on G/B corresponding to the character of T indexed by λ. For general G we prove “Pieri–Chevalley formulas” for the products , , , and , where λ is dominant. By using the Chern character and comparing lowest degree terms the products which are computed in this paper also give results for the Grothendieck polynomials, double Schubert polynomials, and ordinary Schubert polynomials in, respectively K(G/B), H_T^*(G/B) and H^*(G/B).     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

适应型住宅设计

对适应型住宅的概念、主要特点和建筑设计要点进行了分析阐述,对适应型住宅的设计作了进一步的探索,提出若干建议。     

流态混凝土高效减水剂CAN与水泥适应性

为了解决流态混凝土试验和应用中存在的问题，从配合比设计及施工工艺的角度研究了流态混凝土工作性能和质量，认为流态混凝土的外加剂与水泥的适应性是影响流态混凝土品质的关键因素。通过高效减水剂CAN与水泥适应性试验，分析石膏形态、水泥凝结与坍落度损失的关系、碱含量对水泥水化的影响、高硅酸二钙水泥与坍落度损失关系的基础上，阐明了水泥不适应性与外加剂的品种、作用机理、原材料的选用和制造工艺、胶凝材料的成份、细度、水泥磨细阶段的差异有关，同时还受环境温度、加料方式和外加剂用量的影响。     

不同小麦品种剑叶的光合速率、影响因素及其与穗重关系的研究

作者选取四川推广的主要小麦品种(系)15个，在灌浆期测定其剑叶的叶绿体含量，并分二次测定其净光合速率、胞间CO2浓度、气孔导度和蒸腾速率．收获期取样测定单穗重、收获指数和生物产量．统计分析表明，单稳重1．6g以下和收获指数46％以下的品种，灌浆前期的净光合速率、胞间CO2浓度、气孔导度和蒸腾速率较高，灌浆后期较低．单穗重1．6g以上和收获指数48％以上的品种，表现正好相反．这表明较高的灌浆速率和较长的灌浆时间有利于提高穗重和改善光合产物的分配．在灌浆初期，剑叶的净光合速率与单穗重和收获指数呈负相关或相关不显著，但灌浆后期却表现极显著正相关．净光合速率与灌浆后期的胞间CO2浓度、与前期和后期的气孔导度均呈显著正相关，但与蒸腾速率无关．这说明，净光合速率的高低与气孔因素的关系大于非气孔因素．     

数学新课程在西南地区适应性调查研究

数学新课程改革与实验顺利展开的关键在于全国统一性与地方多样性的有机协调和互动融合．为此，通过对西南新课改实验区管理者、教师、学生、家长及师范生的调查，初步解析了制约新课程实施过程中多样性和统一性有机协调的相关因素，诊断出数学新课程在西南地区的适应性水平，提出了相应的理论思考和实践建议．     

弱化与强化——对听障学生平面设计专业教育现状的思考

听障学生的平面设计教育长期处于停滞不前的状态,在课程设置方面陷入了尴尬境地。根据以往教学中出现的问题,我们应在教学理念上、教学手段、自信心地培养上进行全方位的调整,有针对性地对教学进行强化与弱化,增强受教育者的信心,使学生在专业学习的同时更加适应社会的发展,为自己谋得一席之地。     

低温锻炼对野生型colombia拟南芥在渗透胁迫下的适应性初探

本文探讨了低温锻炼后野生型colombia拟南芥在渗透胁迫下的适应性，结果表明：低温处理的材料POD酶活性和游离脯氨酸含量明显高于未低温处理材料，并且SOD酶活性维持相对的稳定性，具有相对较强的适应性。     

长绒棉枯萎病分布及品种(品系)抗性评价

2000～2002年我们对新疆长绒棉主要种植区棉花枯萎病分布、危害症状、现有主栽长绒棉品种及部分品种(品系)的抗性进行了调查研究.新疆长绒棉枯萎病病症以黄色网纹型为主,兼有黄化型、紫红型、青枯型,除系统侵染整株造成子叶、真叶、茎杆产生病症外,棉花枯萎病还造成棉花雷、铃的苞叶叶脉黄化,呈现黄色网纹.长绒棉枯萎病发病严重,现有主栽长绒棉品种对棉花枯萎病均不抗病,2001年调查结果表明,供试32个长绒棉品种(品系)抗病性均较差,病情指数为70.15%～99.53%.