Complex and tropical counts via positive characteristic

We study two classical families of enumerative problems: inflection lines of plane curves and theta-hyperplanes of canonical curves. In these problems the complex counts and the tropical counts disagree. Each problem suggests a prime with special behavior. On the one hand, we analyze the reduction modulo these special primes, and we prove that the complex solutions coalesce in uniform clusters. On the other hand, we observe that the counts in special characteristic and in tropical geometry match.     

Hyperbolic Polygons and Real Schottky Groups

In a work due to Aigon and Silhol (also Buser and Silhol) a construction of 10 genus two closed Riemann surfaces is done from a given right angled hyperbolic pentagon. In this note we construct real Schottky groups uniformizations of the corresponding constructions. In particular, we are able to write down the algebraic curves obtained in the above work in terms of the parameters of the real Schottky group. We generalize such a construction for any right angled hyperbolic polygon and also consider an example for a nonright angled pentagon in the last section.     

八信道高温超导多路器的实验研究

文中首先分析八信道高温超导多路器设计的方案,以及实现八信道高温超导多路器的技术;给出了用MgO基片为衬底,YBCO超导膜制备的高温超导滤波器设计仿真曲线及实际测试曲线;并对多路器所用制冷器的制冷量进行了计算;最后给出八信道高温超导多路器的实际测试曲线。     

Compactified Jacobians of curves with spine decompositions

A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1 sheaves and Seshadri’s moduli schemes of S-equivalence classes of semistable torsion-free, rank-1 sheaves. Both are constructed with respect to a choice of polarization. The former are fine moduli spaces which were shown to be complete; here we show that they are actually projective. The latter are just coarse moduli spaces. Here we give a sufficient condition for when these two types of moduli spaces are equal. Eduardo Esteves is Supported by CNPq, Processos 301117/04-7 and 470761/06-7, by CNPq/FAPERJ, Processo E-26/171.174/2003, and by the Institut Mittag–Leffler (Djursholm, Sweden).     

Holonomy group scheme of an integral curve

Let Y be a projective variety over a field k (of arbitrary characteristic). Assume that the normalization X of Y is such that is normal, being the algebraic closure of k. We define a notion of strong semistability for vector bundles on Y. We show that a vector bundle on Y is strongly semistable if and only if its pull back to X is strongly semistable and hence it is a tensor category. In case , we show that strongly semistable vector bundles on Y form a neutral Tannakian category. We define the holonomy group scheme of Y to be the Tannakian group scheme for this category. For a strongly semistable principal G‐bundle , we construct a holonomy group scheme. We show that if Y is an integral complex nodal curve, then the holonomy group of a strongly semistable vector bundle on Y is the Zariski closure of the (topological) fundamental group of Y.     

Self-similar Solutions of Nonlinear Elasticity and Poroelasticity Equations

Recent advances in nonlinear wave propagation in elastic and porous elastic (poro-elastic) material have presented new nonlinear evolutionary equations. The derivation of these equations in three-dimensional space is based on the semilinear Biot theory. The nonlinear elastodynamic equations are derived form the more general model of poro-elastodynamic using consistency arguments. For simplicity, we discuss and carry out the analysis for the nonlinear elastic model. It is found in this article that the methods of symmetry groups and self-similar solutions can furnish solutions to the nonlinear elastodynamic wave equation. It is also found that these models lead to shock wave development in finite time. Necessary conditions for the existence of the solution are given and well-posedness of the Cauchy problem is discussed.     

Metric Sample Spaces of Continuous Geometric Curves and Estimation of Their Centroids

The metric sample space of Fréechet curves (Fréechet , 1934,1951,1961) is based on a generalization of regular curves that covers continuous curves in full generality. This makes it possible to deal with both smooth and non-smooth, even non-rectifiable geometric curves in statistical analysis. In the present paper this sample space is further extended in two directions that are relevant in practice: to incorporate information on landmark points in the curves and to impose invariance with respect to an arbitrary group of isometric spatial transformations. Properties of the introduced sample spaces of curves are studied, specially those concerning to the generation and representation of random curves by random functions.In order to provide measures of central tendency and dispersion of random curves, centroids and restricted centroids ofrandom curves are defined in a general metric framework, and methods for their consistent estimation are derived.     

On the peirce decompositions for freudenthal—kantor triple systems

It is the object of this paper to investigate the Peirce decomposition for Freudenthal-Kantor triple systems, by making use of the concept of anti-derivation of the triple systems.     

Reflectingness and closed timelike curves in space-time

It is shown by Clarke and Felice (J Phys A Math Gen 15:2415–2417, 1982) that under certain conditions a stationary space-time will produce a closed timelike curve through each point of the space-time. Here a simpler proof and a different version of their theorem are provided.