关于《一类奇异边值问题的正解》的注记

文[4]通过构造反例断言文[1]中定理的必要性证明有误,本文首先指出文[4] 的这个断言不正确,然后对文[4]中定理2.1作了本质性的改进.     

锂锰尖晶石红外光谱的研究

本文对锂锰尖晶石的红外光谱进行了研究。由于锂锰尖晶石的晶体结构属于Fd3m空间群,锂离子占据四面体空隙(8a位置),锰离子占据八面体空隙(16d位置)。根据群论的知识,对锂锰尖晶石晶体中离子的振动方式与红外活性之间的内在关系进行了讨论。并列出了锂锰尖晶石的红外光谱实验数据。通过理论分析,我们推断:位于618.6和501.5cm~(-1)的红外吸收带分别来源于Mn(Ⅳ)-O和Mn(Ⅲ)-O键在晶体中的不对称伸缩振动(单元为Mn(Ⅳ)O_6和Mn(Ⅲ)O_6八面体),位于1124cm~(-1)的弱红外吸收带来源于Li-O键的不对称伸缩(单元为LiO_4四面体)。还有一些低于400cm~(-1)的可能吸收带在400～4000cm~(-1)范围内未能检测到。这一结论的可靠性通过锂锰尖晶石和掺杂的锂锰尖晶石的红外光谱实验数据得到证实。     

Design of thin-walled viscoelastic shells with allowance for damage

Azerbaidzhan Institute of Construction Engineering, Baku. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 55–64, January, 1991.     

Geometrical study of paraxial light beam transmission in free space

By introducing an imaginary space transform curvature ρ_s, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory of straight line while propagating. Moreover, this curvature couples with that of the wave front of the paraxial beam ρ_w, and therefore a complex curvature ρ_c is constructed, which can be employed to investigate the behavior of the light transmission and to generalize the ABCD law. Project supported by the National Hi-Tech Inertial Confinement Fusion Committee, the Guangdong Natural Science Foundation the Postdoctoral Foundation of Guangdong and National Postdoctoral Foundation of China.     

Intramolecular heterocyclization with accompanying exoiminization in the reaction of ammonia with 2-chloroperfluoro-1-cyclohexene-1-thiocyanate

The reaction of ammonia with 2-chloroperfluoro-1-cyclohexene-1-thiocyanate leads to 2-amino-7-iminoperfluoro-4,5,6-trihydrobenzo-1,3-thiazole (II) due to intramolecular heterocyclization in the Thorpe reaction with the concurrent exoiminization. Analysis of the IR spectra of (II) in CCl₄ and in the solid phase indicated that molecules of (II) in the crystal form hydrogen-bonded centrosymmetric dimers (D), which are in equilibrium with free molecules of (II) in solution.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2366–2370, October, 1991.The authors express their gratitude to D. I. Zagorevskii for taking the mass spectrum of (II) and to L. S. German for a useful discussion of this work.     

Integral manifolds and the reduction principle in stability theory. III

It is shown how, with the help of approximate integral manifolds, to solve the reduction problem in stability theory in the nonsingular critical case. A generalization of the first fundamental Lyapunov-Malkin theorem in critical cases is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1324–1329, October, 1991.     

Coulomb blockade electrometer with a high-T c island

We report on a successful attempt to fabricate a Coulomb blockade electrometer consisting of an ultrasmall YBa₂Cu₃O_7−δ (YBCO) island coupled to two gold electrodes through a high-resistance native surface tunnel barrier. A third electrode placed near the island was used as an electrostatic gate. Spectra typical for tunneling into the YBCO superconductor were reproducibly measured. At temperatures below 0.5 K the low-bias conductance was suppressed by the Coulomb blockade. The blockade could be periodically varied by the gate potential. An external magnetic field of up to 5 T strongly influenced the transport via the island but without any change in the period of the Coulomb oscillations. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 112–117 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

高精度CCD尺寸自动检测系统的光学系统设计

介绍测量精度为±０．００３ｍｍ的ＣＣＤ尺寸检测系统的光学系统设计特点及远心物镜设计原理，并给出了测试结果。     

Fredholm property of elliptic boundary value problems for partial differential and differential- operator equations

In this paper we find conditions on boundary value problems for elliptic differential-operator equations of the 4-th order in an interval to be fredholm. Apparently, this is the first publication for elliptic differential-operator equations of the 4-th order, when the principal part of the equation has the form u′?n(t) + Au″(t) + Bu(t), where AB^-1/2 is a bounded operator and is not compact. As an application we find some algebraic conditions on boundary value problems for elliptic partial equations of the 4-th order in cylindrical domains to be fredholm. Note that a new method has actually been suggested here for investigation of boundary value problems for elliptic partial equations of the 4-th order.