Congratulations to Professor K. Itô

In this paper we describe a story how a Moscow mathematician solved an important problem in ergodic theory using It? multiple stochastic integrals.     

Local Perturbations of Quantum Waveguides

We give necessary and sufficient conditions for the occurrence of eigenvalues of the Schrodinger operator in strips and cylinders under small localized perturbations. We construct asymptotic approximations for the eigenvalues. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 358–371, December, 2005.     

Using Fractal Function Auto-correlative Method to Confirm Fractal Dimension of Function Graph

The effects of light wave propagating in atmospheric turbulence are investigated experimentally, it is essential to measure the physical variable with time. In order to analyze appropriately these data, it is utilized the fractal function auto-correlative method to describe the fractal dimension of function graph of image-space. The fractal dimension Dg=1.47 of function graph is derived from the power spectral analysis of measuring data. It shows that the Kolmogorov' turbulent model is not completely in accord with actual atmospheric turbulence.     

CO2激光自差信号的功率谱研究

利用10MHz高速数据采集和处理系统分析了激光自差信号的功率谱.其功率谱分布在低频区;当多普勒频移增大时,自差信号的带宽增加,功率谱对频率的积分收敛于信号的功率.实验结果还表明,利用高速数据采集和处理的分析方法,比频谱分析仪有更多的优点.     

Effect of neutron irradiation on optical spectra of α-Al2O3 and α-SiO2 single crystals

Using two crystal dielectrics (α-Al₂O₃ and α-SiO₂) as examples, the author studied the effect of large neutron-radiation doses on their optical spectra. The variation in IR spectra in the region of α-SiO₂ stretching and deformation vibrations is investigated; its relation to changes in the structure of the irradiated crystal is discussed. Institute of Nuclear Physics, Academy of Sciences of the Republic of Uzbekistan, Ulugbek Settlement, Tashkent, 702132. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 135–138, January–February, 1999.     

Absorption spectra of the products of resorcin transformation in concentrated perchloric acid

Results of an investigation of the electronic absorption spectra of polymeric compounds spontaneously formed as a result of resorcin dissolution in 70% perchloric acid are reported. It is shown that acetone is the most convenient solvent for analytic purposes, since it allows specific detection of poly-m-phenylene oxide in a wide wavelength range. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 247–250, March–April, 1999.     

咔唑、蒽和苝的同时恒能量同步荧光法分析

建立了咔唑、蒽和苝的同时恒能量同步荧光分析法。对方法的优越性进行了比较说明。实验是在自制带恒能量扫描多功能荧光分光计上进行的。咔唑、蒽和苝的检测限分别为1ng/ml、0.8ng/ml和0.5ng/ml,相对标准偏差不大于4.4％。     

镧系离子与L—组氨酸配合物^13CNMR波谱及其结构的研究

本文以XL-200型超导NMR谱仪对镧系离子与L-组氨酸配合物进行了一系列的研究,测得微酸性条件下的顺磁诱导位移,对这些诱导位移进行分析计算,得到了各磁性核的配合物生成位移、接触位移和准接触位移,同时以准接触位移为依据,对配合物结构进行模拟,获得了有关的结构参数.并对镧系离子在磁学性质上的特征进行了讨论.     

The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential

We study the effect of an eigenvalue appearing from the boundary of the essential spectrum of the Schrödinger operator perturbed by a rapidly oscillating compactly supported potential. We prove sufficient conditions for the existence and absence of such an eigenvalue and obtain the first few terms of its asymptotic expansion for the case where this eigenvalue exists.     

Fast-electron optical spectrum of a two-dimensional electron gas in the presence of the Rashba effect

We examine how the Rashba spin-orbit interaction (SOI) affects the fast-electron optical spectrum of a two-dimensional electron gas (2DEG). It is found that for a spin-split 2DEG, the spectrum of optical absorption is mainly induced by plasmon excitation via inter-SO electronic transition. From the width and position of the spectrum, the Rashba spin-splitting can be identified optically and, therefore, important spintronic properties can be measured though optical experiments.