Singularly Perturbed Linear and Semilinear Hyperbolic Systems: Kinetic Theory Approach to Some Folk’s Theorems

The fact that a solution of a wave equation with strong damping can be approximated by a solution of an appropriate diffusion equation has been common knowledge to physicists and mathematicians for a few decades. In numerous branches of science one can find attempts to prove this results by various ad hoc methods. However, it seems to be difficult to trace a rigorous and exhaustive treatment of the subject. By using a recently developed asymptotic procedure, first applied in kinetic theory, we present a systematic approach to a wide spectrum of singularly perturbed hyperbolic problems and we also hope that our method will provide new insight into the field.     

后腔镜对掺Yb3+双包层光纤激光器性能影响的研究

采用自行研制的内包层为矩形的掺Yb^3 双包层石英光纤，以透射率不同的一组二向色镜为后腔镜构成了双包层光纤激光器。实验证明：后腔镜具有较高透射率为佳；后腔镜可以实现对激光波长的控制；激光斜率效率与后腔镜透射率之间的关系符合指数变化规律，在本实验的条件下，斜率效率的最大值约60％。     

Intermediate regime of light diffraction by surface ultrasonic waves in planar gyrotropic optical waveguides

The intermediate regime of optoacoustic interaction, similar to the Bragg one, with Rayleigh surface ultrasonic waves in gyrotropic planar waveguides is studied. A system of equations of bound waves is presented that describes planar optoacoustic interaction in the intermediate, Raman-Natoh, and Bragg regimes of light diffraction by surface ultrasonic waves. It is shown that the optical activity of a wavequide film favors the incident light energy pumping to diffracted light for a TE-polarization wave and decelerates this process for an incident TM-polarization wave. Mozyr' State Pedagogical Institute, 28, Studencheskaya St., Mozyr', 247760, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 3, pp. 412–416, May–June, 1997.     

Development of an X-ray detector using surface plasmon resonance

A new X-ray detector using surface plasmon resonance (SPR) is proposed. The detector consists of a prism coated with a thin metal film and semiconductor film. Optical laser pulse induces SPR condition on the metal surface, and synchronized X-ray pulse which is absorbed into the semiconductor film can be detected by measuring the change of the resonance condition of the surface plasmon. The expected time and spatial resolution of this detector is better than that of conventional X-ray detectors by combining this SPR measurement with ultra-short laser pulse as the probe beam. Our preliminary investigation using Au and ZnSe coated prism implies this scheme works well as the detector for the ultra-short X-ray pulse.     

Optimal decay rates and the selfadjoint property in overdamped systems

We deal with abstract linear strongly damped wave equations. In the so-called overdamped regime we show the occurrence of two interesting phenomena. The first is the existence of an explicit special inner product which makes the problem selfadjoint. The second is an improvement of the decay rate for more regular solutions that will be of an exponential-polynomial type. Furthermore, we prove the optimality of this decay rate.     

Absorption spectroscopy using a coherent transition radiation millimeter wave light source

The characteristics and applicability of the absorption spectroscopy system using the coherent transition radiation light source have been investigated. The configurations of the system are relatively simple. The operational conditions of an electron linear accelerator have been evaluated. The stability of the light intensity has been within ±2–3% in a wavenumber range of 4–13 cm⁻¹. The light intensity has been found to be more than six orders of magnitude higher than that for the lowest limit for detection.     

晶体中三阶有效非线性系数的计算方法

经过对ｘ（３）ｉｊｋｌ的脚标进行简化压缩处理，首次得出了全部晶体点群共１１种不同的Ｘ（３）ｉｍ矩阵表达形式及Ｋｌｅｉｎｍａｎ对称条件成立下的简化形式，给出了各类晶体中四波相互作用过程中Ｘ（３）＾ｅｆｆ的计算方法。     

Momentum space distribution of electrons in an atom using hydrogenic wave functions

A formulation is developed to derive exact analytic expressions for electron-electron correlation and density of electrons in momentum space using hydrogenic wave functions. It is shown that for large atoms the expression for density of electrons has a simple form.     

山背波:对飞机的潜在威胁

山背波对飞机的潜在威胁现已毋庸置疑。为了提高在这方面作出更确切判断的能力并能进一步找出实践中可行的相应措施，首要的问题就是必须对山背波本身有足够的认识，而这正是当前国内文献中极为薄弱的环节。有鉴于此，本文系统地、较全面地介绍了山背波这种独特的次声波，对其发生机理和基本特征、以及作为其直接衍生物的相关云相和晴空湍流－－后者正是对飞机的主要潜在威胁所在－－作出简明扼要的评述。