Some families of Mordell curves associated to cubic fields

We introduce some Mordell curves of two different natures both of which are associated to cubic fields. One set of them consists of those elliptic curves whose rational points over the rational number field are described by or closely related to cubic fields. The other is a one-parameter family of Mordell curves which gives all (cyclic) cubic twists and all quadratic twists of the Fermat curve X³+Y³+Z³=0.     

On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

粘塑性介质中球形孔洞的动态增长

 提出了一个新的粘塑性介质中球形孔洞在高加载率作用下的演化方程。方程中考虑了应变率、局部惯性和介质的硬化效应，并对这些影响进行了数值分析和讨论。数值分析结果表明：孔洞的增长对外加载率和应变率十分敏感，在高加载率条件下局部惯性效应对孔洞增长有着重要影响，随着加载率的增加，这种影响增大。另外，得到了使孔洞增长的临界应力值的表达式。     

Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp（0〈p〈1）Spaces

We consider the solutions of refinement equations written in the form

非线性应变波耦合组的吸引子的正则性

本文研究了非线性应变波方程与Schr(?)dinger方程耦合系统Cauchy问题吸引 子的正则性.获得了该系统在空间Eo中存在整体吸引子Ao,并且Ao与E1中的强吸 引子A1相等.     

Differentiable conjugacy of the Poincaré type vector fields on

We prove that on , except for those germs of vector fields whose linear parts are conjugated to , any two Poincaré type vector fields are at least conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.

     

Analysis of Two-Dimensional Optical Fields Using an Additional Shift

A solution to the phase problem in optics is considered within the context of registration and analysis of two-dimensional stationary optical fields transformed by the object under study or fields forming an image. To obtain information on amplitude and phase distributions of the light field analyzed, a method of registration of two intensity distributions is used. The first distribution corresponds directly to the amplitude distribution. The other is formed for the sum of the initial field and the field shifted along a certain direction. The intensity distributions obtained allow one to calculate the two-dimensional structure of the field under study. It is noteworthy that the method requires no iteration procedures in solving the problem. This leads to speeding up of the processing and analysis of the information. Two variants of optical schemes for the analysis of light fields are considered. The first one corresponds to registration of the image of the analyzed plane and the second to registration of the spectrum of the spatial frequencies.     

Optically detected nuclear magnetic resonance at the sub-micron scale

Nuclear magnetic resonance is arguably one of the most powerful techniques available today to characterize diverse systems. However, the low sensitivity of the standard detection method constrains the applicability of this technique to samples having effective dimensions not less than a few microns. Here, we propose a novel scheme and device for the indirect detection of the nuclear spin signal at a submicroscopic scale. This approach--for which the name Dipolar Field Microscopy is suggested--is based on the manipulation of the long-range nuclear dipolar interaction created between the sample and a semiconductor tip located close to its surface. After a preparation interval, the local magnetization of the sample is used to modulate the nuclear magnetization in the semiconductor tip, which, in turn is determined by an optical inspection. Based on results previously reported, it is shown that, in principle, images and/or localized high-resolution spectra of the sample can be retrieved with spatial resolution proportional to the size of the tip.     

动态塑性试验技术

对动态塑性试验技术作了扼要综述。简单介绍了各种试验方法的基本原理及其应用范围,并评述了各自所具有的特点和不足之处。      

幂硬化介质中平面应力动态裂纹的尖端弹塑性场

本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。