Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.

(a) The curves z(s) and z(s, t) were not required to be simple curves. This made the task of approximating them with continuously differentiable curves very easy. (b) The Cauchy integral theorem also holds if the function z(s) describing the curve C is merely piecewise continuously differentiable. For in this case we carry out the integration by parts in (6) over each subinterval on which zs(s)...

Let Xns(11) denote the modular curve associated to the normalizer of a non-split Cartan subgroup of level 11; see [10, Appendix]. This curve has genus 1, is defined over Q and parametrizes elliptic curves with a certain level 11 structure. The interest of Theorem 1.1 lies in the fact that Xns(11) is isomorphic over Q to the curve E and that rational points (x, y) on E for which x/(xy − 11) is i...

Currently, by default, integral curves are repeatedly re-computed in different flow visualization applications, such as FTLE field computation, sourcedestination queries, etc., leading to unnecessary resource cost. We present a compression-based data reuse framework for integral curves, in order to greatly reduce their retrieval cost, especially in a resource-limited environment. In our design,...

We propose a segmentation method for vector fields. Our segmentation is driven by integral curve attributes that are used to classify different behaviors of integral curves. In particular, we assign an attribute value to each spatio-temporal position based on the integral curve that passes through it. With this attribute information, our segmentation first performs a region classification. Then...

Michel LAURENT Abstract. Let F (X,Y ) = ∑m i=0 ∑n j=0 ai,jX iY j be an absolutely irreducible polynomial in Z[X,Y ]. Suppose that m ≥ 1, n ≥ 2 and that the polynomial ∑n j=0 am,jY j is reducible in Q[Y ], has n simple roots and an unique real root. Let L be a totally real number field and let (ξ, ζ) ∈ OL ×L be such that F (ξ, ζ) = 0. We give an upper bound for the absolute height H(ξ) which dep...

Рассматриваются сингулярные интегральные операторы на кусочно гладкой кривой в весовых лебеговых и гёльдеровых пространствах с непрерывными матричными коэффициентами. В отличие от классического случая эти помимо сингулярного оператора Коши содержат также некомпактные специального вида, которые определяются ядром, приближенно однородным степени −1 относительно расстояний до узлов кривой. Подобны...