Simulation of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

Summary Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates. Received 11 March 1997; accepted for publication 18 March 1998     

若干新的p进制Hardy-Littlewood-Pólya型不等式

本文建立了若干新的具最佳常数因子的p进制Hardy-Littlewood-Pólya型不等式，同时也给出了它们的等价形式以及一些特殊结果.     

The near-field effect in a system of two-level dipole particles

We have solved a self-consistent problem on interaction of two dipole atoms located at an arbitrary distance from each other with the field of a quasiresonance light wave, whose intensity is sufficient for the system to manifest nonlinear properties. The atoms are considered as two-level systems described by means of Bloch optical equations, while the field inside of the system includes both Coulomb and retarded parts. We consider a situation where atoms are identical and the distance between them is much smaller than the length of an outer light wave. The distribution of an electric field both inside of a small object and outside of it is found numerically. It is shown that the amplitude of the electric field in a wave zone depends substantially on the frequency of the external field and interatomic distance, while the field distribution differs from the field pattern of an electric dipole. At definite values of the external field intensity an optical multistability is a feature of the system under investigation. We have elucidated the conditions under which the multistability is manifested in the present system. The results obtained are considered as the near-field effect in the optics of small objects, which makes it possible to investigate the structure of small objects by means of optical radiation. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 3, pp. 375–378, May–June, 2000. The present work was supported by the Russian Foundation for Fundamental Research (grant 98-02-16035) and by a grant from the Federal Purpose-Oriented Program “Integration.”     

Maximum principles for a fourth order equation from thin plate theory

This paper focuses on a nonlinear equation from thin plate theory of the form Δ(D(x)Δw)−(1−ν)[D,w]+c(x)f(w)=0. We obtain maximum principles for certain functions defined on the solution of this equation using P-functions or auxiliary functions of the types used by Payne [L.E. Payne, Some remarks on maximum principles, J. Anal. Math. 30 (1976) 421-433] and Schaefer [P.W. Schaefer, Solution, gradient, and laplacian bounds in some nonlinear fourth order elliptic equations, SIAM J. Math. Anal. 18 (1987) 430-434].     

纤维悬浮流场动力学研究综述

阐述了纤维悬浮流研究的学术价值及其在实际中的应用，回顾了近10年来该领域的主要研究结果，提出了尚未解决而又非常重要的几个问题，指出了该领域的发展前景。     

Improved Faddeev-Jackiw quantization of the electromagnetic field and Lagrange multiplier fields

We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given. We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method. Moreover, it is simpler than the usual one if one needs to obtain new secondary constraints. Therefore, the improved Faddeev-Jackiw method is essential. Meanwhile, we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.     

平面电磁波性质的推导与讨论

简洁推导平面电磁波的基本关系式并由此讨论平面电磁波的性质．     

Totally skew embeddings of manifolds

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension.     

Spin precession of a charged particle in a uniform magnetic field on a static space-time

We investigate the ratio of spin precession frequency to orbital frequency for a spinning charged particle confined to circular orbit in the equatorial plane of a compact object, with a uniform magnetic field, as described by the Wald and the Ernst potentials. In order to see the difference in behaviours for particles with differentg values we consider the cases of electron and proton separately.     

广义Bianchi恒等式的某些应用

本文给出由非不变性拉氏量导致的广义Bianchi恒等式的若干应用。导出强守恒律,用于某些场论,得到相应的弱守恒律,讨论了非不变拉氏量系统的Dirac约束。