Non-special, non-canal isothermic tori with spherical lines of curvature

This article examines isothermic surfaces smoothly immersed in Möbius space. It finds explicit examples of non-special, non-canal isothermic tori with spherical lines of curvature in two systems by analyzing Darboux transforms of Dupin tori. In addition, it characterizes the property of spherical lines of curvature in terms of differential equations on the Calapso potential of the isothermic immersion, and investigates the effect of classical transformations on this property.

     

Some aspects of the Hodge conjecture

I will discuss positive and negative results on the Hodge conjecture. The negative aspects come on one side from the study of the Hodge conjecture for integral Hodge classes, and on the other side from the study of possible extensions of the conjecture to the general K?hler setting. The positive aspects come from algebraic geometry. They concern the structure of the so-called locus of Hodge classes, and of the Hodge loci. This article is based on the 1st Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 25 and 26, 2006.     

创造一种体现地域场所精神的居住空间形态

通过对地域个性的本质、影响个性的相关因子及个性创作的原则的分析,提出了创造居住空间个性的关键是打破固有化的设计思维模式、保护本土特征、考虑人文因素、寻求方案的突破点以及体现时代精神等几个方面,并结合实例作了进一步的阐释.     

On Generic Well-posedness of Restricted Chebyshev Center Problems in Banach Spaces

Let B （resp. K, BC,KC） denote the set of all nonempty bounded （resp. compact, bounded convex, compact convex） closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem （F, G） is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC ／ G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B ／B° （resp. K ／ B°, BC ／B°, KC ／ B°） is a-porous in B （resp. K,BC, KC）. Moreover, we prove that for most （in the sense of the Baire category） closed bounded subsets G of X, the set K ／ B° is dense and uncountable in K.     

Five peculiar theorems on simultaneous representation of primes by quadratic forms

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It is a theorem of Kaplansky that a prime is representable by both or none of x²+32y² and x²+64y², whereas a prime is representable by exactly one of these binary quadratic forms. In this paper five similar theorems are proved. As an example, one theorem states that a prime is representable by both or none of x²+20y² and x²+100y², whereas a prime is representable by exactly one of these forms. A heuristic argument is given why there are no other results of the same kind. This argument relies on the (plausible) conjecture that there are exactly 485 negative discriminants Δ such that the class group C(Δ) has exponent 4.

Video

For a video summary of this paper, please visit http://www.youtube.com/watch?v=l_yRq0oqKx4.     

基于组LASSO的重组近亲杂交合作小鼠基因位点定位研究

重组近亲杂交合作小鼠品系(CC-RIX)具有很多优点,特别是在复杂疾病的数量性状位点定位方面,具有较高功效.本文在现有研究基础上,考虑了仅含主基因效应的混合线性定位模型,并通过组LASSO惩罚函数法对问题进行转换,然后采用迭代加权最小二乘法对转换后的问题进行求解.从而克服了设计矩阵容易奇异,计算速度慢等计算上的难题.模...     

Higher dimensional Shimura varieties in the Prym loci of ramified double covers

In this paper, we construct Shimura subvarieties of dimension bigger than one of the moduli space ${\mathsf{A}}_p^{\delta }$ of δ-polarized abelian varieties of dimension p, which are generically contained in the Prym loci of (ramified) double covers. The idea is to adapt the techniques already used to construct Shimura curves in the Prym loci to the higher dimensional case, namely, to use families of Galois covers of ${\mathbb{P}}^1$. The case of abelian covers is treated in detail, since in this case, it is possible to make explicit computations that allow to verify a sufficient condition for such a family to yield a Shimura subvariety of ${\mathsf{A}}_p^{\delta }$.