Mesures d'indépendance linéaire de carrés de périodes et quasi-périodes de courbes elliptiques

A linear independence measure over Q is obtained for values of some generalized hypergeometric functions at rational points and for the squares of real periods and quasi-periods of elliptic curves in Legendre form y²=x(x−1)(x−1/q) for almost every q∈Z.     

Fractal Interpolation on a Torus

A very general method of fractal interpolation on T ¹ is proposed in the first place. The approach includes the classical cases using trigonometric functions, periodic splines, etc. but, at the same time, adds a diversity of fractal elements which may be more appropriate to model the complexity of some variables. Upper bounds of the committed error are provided. The arguments avoid the use of derivatives in order to handle a wider framework. The Lebesgue constant of the associated partition plays a key role. The procedure is proved convergent for the interpolation of specific functions with respect to some nodal bases. In a second part, the approximation is then extended to bidimensional tori via tensor product of interpolation spaces. Some sufficient conditions for the convergence of the process in the Fourier case are deduced.      

Surfaces in $${\mathbb{S}^2\times\mathbb{R}}$$ with a canonical principal direction

We show a way to choose nice coordinates on a surface in and use this to study minimal surfaces. We show that only open parts of cylinders over a geodesic in are both minimal and flat. We also show that the condition that the projection of the direction tangent to onto the tangent space of the surface is a principal direction, is equivalent to the condition that the surface is normally flat in . We present classification theorems under the extra assumption of minimality or flatness. J. Fastenakels is a research assistant of the Research Foundation—Flanders (FWO). J. Van der Veken is a postdoctoral researcher supported by the Research Foundation—Flanders (FWO). This work was partially supported by project G.0432.07 of the Research Foundation—Flanders (FWO).     

Classification of quasi-minimal slant surfaces in Lorentzian complex space forms

From J-action point of views, slant surfaces are the simplest and the most natural surfaces of a (Lorentzian) Kähler surface (\(\tilde M,\tilde g\), J). Slant surfaces arise naturally and play some important roles in the studies of surfaces of Kähler surfaces (see, for instance, [13]). In this article, we classify quasi-minimal slant surfaces in the Lorentzian complex plane C ₁ ² . More precisely, we prove that there exist five large families of quasi-minimal proper slant surfaces in C ₁ ² . Conversely, quasi-minimal slant surfaces in C ₁ ² are either Lagrangian or locally obtained from one of the five families. Moreover, we prove that quasi-minimal slant surfaces in a non-flat Lorentzian complex space form are Lagrangian.     

介质导电率成像数值反演的正则化方法

磁共振技术(MREIT)是一种新的医学成像技术,它利用介质内部的部分磁场信息来重建介质内部的导电率.本文对调和Bz反演算法,提出了利用样条插值函数来处理误差输入数据的正则化方法,并给出了正则化方法的误差估计,在此基础上,我们还考虑了调和Bz算法对多个导电率异常的算法实现,检验了该方法对误差输入数据借助于正则化方法可能达到的空间分辨率,本文的工作为调和Bz算法利用实测的误差数据提供了一条可行的途径.     

Direct approach to <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates in homogenization theory

We derive interior L ^p -estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of ε, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L ^p -corrector result for approximate solutions.      

Theoretical study on the [Si, C, N, O] potential energy surface

The structures, energetics, spectroscopies, and stabilities of the doublet [Si, C, N, O] radical are explored at the density functional theory and ab initio levels. Sixteen isomers are located, connected by 29 interconversion transition states. At the CCSD(T)/6-311+G(2df)//QCISD/6-311G(d)+ZPVE level, the lowest lying isomer is a linear SiNCO 1 (0.0 kcal/mol) mainly featuring a cumulene | . Si = N = C = O. The second and third low-lying isomers are bent OSiCN 2 (8.8) and bent OSiNC 3 (11.1), respectively. All the three low-lying isomers 1, 2, 3, and another high-lying species 5 (75.4) with a linear SiCNO structure are shown to have considerable kinetic stability and may be experimentally observable. The predicted results of isomers 1 and 2 are consistent with the previous mass spectrometry experiments. Moreover, the fourth low-lying species SiOCN 4 (23.9) with bent structure is expected to be observable in low-temperature environments. The bonding nature of the five isomers 1, 2, 3, 4, and 5 is analyzed. The calculated results are compared with those of the analogous molecules C(2)NO and Si(2)NO. Implications in interstellar space and N,O-doped SiC vaporization processes are also discussed.     

Complete nonorientable minimal surfaces in a ball of

The existence of complete minimal surfaces in a ball was proved by N. Nadirashvili in 1996. However, the construction of such surfaces with nontrivial topology remained open. In 2002, the authors showed examples of complete orientable minimal surfaces with arbitrary genus and one end. In this paper we construct complete bounded nonorientable minimal surfaces in with arbitrary finite topology. The method we present here can also be used to construct orientable complete minimal surfaces with arbitrary genus and number of ends.

     

On the nondegeneracy of constant mean curvature surfaces

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces are nondegenerate; that is, the Jacobi operator Δ_f + | A_f |² has no L² kernel. In fact, if ∑ has genus zero with k ends, and if f (∑) is embedded (or Alexandrov immersed) in a half-space, then we find an explicit upper bound for the dimension of the L² kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres. R.K. partially supported by NSF grants DMS-0076085 at GANG/UMass and DMS-9810361 at MSRI, and by a FUNCAP grant in Fortaleza, Brazil. J.R. partially supported by an NSF VIGRE grant at Utah. Received: January 2005; Accepted: June 2005     

On the chemical structure of phosphorus compounds in phosphoric acid-activated carbon

Chemical structure of phosphorus species in polymer-based phosphoric acid-activated carbon SP800 was investigated by X-ray photoelectron spectroscopy. It has been shown that most probable structure for phosphorus species is condensed phosphates bound to carbon lattice via COP bonding.