有限温度QED中的轫致辐射修正

用有限温度场论方法,通过计算费曼图分析了在QED中由于温度效应导致的新红外发散.结果表明零温场论中的红外发散和由温度效应引起的红外发散可以用描写虚过程的费曼图同时消除.计算了轫致辐射中光子的辐射几率,在Eikonal近似下所得到的结果和半经典近似给出的结果一致.     

Grazing-angle scattering of electromagnetic waves in periodic Bragg arrays

A new powerful approximate approach for the theoretical analysis of Bragg scattering in oblique strip-like periodic arrays with the scattered wave propagating almost parallel to the array boundaries – grazing-angle scattering (GAS) – is introduced and justified. This approach is based on allowance for the diffractional divergence of the scattered wave by means of the parabolic equation of diffraction and Fourier analysis. The divergence is demonstrated to be an intrinsic physical cause of GAS. Detailed theoretical analysis of steady-state GAS is carried out for bulk and guided optical modes. It is demonstrated that the most interesting feature of GAS in arrays of width that is greater than a critical width is a unique combination of two strong simultaneous resonances with respect to frequency and angle of scattering. In such wide arrays, GAS is demonstrated to be not only unusually sensitive to angle of scattering, but also to small variations of array width and grating amplitude. Entire concentration of the resonantly strong scattered wave inside the array is shown to be possible. A relationship between GAS, conventional Bragg scattering, and extremely asymmetrical scattering (i.e. where the scattered wave propagates parallel to the array boundaries) is analysed. Applicability conditions for the used approximations and obtained results are derived and discussed.     

Double-resonant extremely asymmetrical scattering of electromagnetic waves in periodic arrays separated by a gap

Two strong simultaneous resonances of scattering – double-resonant extremely asymmetrical scattering (DEAS) – are predicted in two parallel, oblique, periodic Bragg arrays separated by a gap, when the scattered wave propagates parallel to the arrays. One of these resonances is with respect to frequency (which is common to all types of Bragg scattering), and another is with respect to phase variation between the arrays. The diffractional divergence of the scattered wave is shown to be the main physical reason for DEAS in the considered structure. Although the arrays are separated, they are shown to interact by means of the diffractional divergence of the scattered wave across the gap from one array into the other. It is also shown that increasing separation between the two arrays results in a broader and weaker resonance with respect to phase shift. The analysis is based on a recently developed new approach allowing for the diffractional divergence of the scattered wave inside and outside the arrays. Physical interpretations of the predicted features of DEAS in separated arrays are also presented. Applicability conditions for the developed theory are derived.     

Allowance for angular divergence in the generation of the second harmonic in crystals with a regular domain structure

We obtained basic analytical expressions for the efficiency of the second harmonic in nonlinear crystals with a regular domain structure; in these expressions we took into account the angular divergence of the laser beam. The calculation was done in the geometric-optics approximation of the given field of laser radiation. We show that the expressions obtained are similar to the corresponding expressions for homogeneous nonlinear crystals. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 134–138, January–February, 2000.     

二次系统奇点的分支问题

本水文研究了(Ⅱ)和(Ⅲ)类的二次系统奇点的分支,并回答了[1]中提出的问题.     

An algorithm with randomly varying truncation for adaptive Beam-Formers

A recursive algorithm with randomly varying truncation for adaptive Bram-Formers is proposed. Simple conditions are obtained to guarantee for this algorithm the global convergence almost everywhere.     

有界凸区域上的Dirichlet问题的正则性

本文主要讨论在有界凸区域上具Lipschitz连续系数的散度型椭圆算子的解的二阶导数的可积性问题．并且得到了相应的结论．     

A Method for Avoiding the Divergence Difficulties of Quant urn Mechanics

Abstract High-ordered correction of wavefunction for Schrodinger equation with one dimensional potential V(x) and interaction Hamiltonian H′(x) has been found by introducing a new particular solution φ_Ek⁽⁰⁾ for H′(z) = 0. Convergence conditions of the rvavefunction lead to the formulas of energy corrections and scattering amplitudes. It is shown that the result can avoid some divergence difficulties of quantum mechanics.     

高温下夸克场真空图中的红外发散

用热传播子的实时形式对高温条件下夸克(忽略质量)场三圈真空图进行了详细地计算,找出了其中和费米–狄拉克统计因子有关的红外发散积分的类型,并对这种发散积分进行了正规化,进一步把真空图中的红外发散全部孤立出来了.     

Segmentation of Heteropolymer Sequences Specifying Subsequences with Different Composition and Statistical Properties

We have studied the segmentation of two‐letter AB heterosequences composed of subsequences with different composition and distribution of A and B monomer units along the chain. Our approach is based on the segmentation function S(k) introduced in the present work and on the Jensen–Shannon divergence measure determined with respect to the probabilities of the lengths of uniform blocks of A and B monomer units. It is shown that the function S(k) is extremely sensitive to the sequence statistics. Even visual analysis of S(k) allows judgment on some features of sequence statistics. In particular, function S(k) is constant for random copolymers, it is an oscillating function for random block copolymers and shows monotonic growth up to some constant value for proteinlike copolymers. However, due to significant fluctuations observed for short sequences, the function S(k) can be effectively used only for segmentation of a heterosequence composed of very long subsequences. On the other hand, we find that the Jensen–Shannon divergence measure does not allow one to judge the type of statistics, but is extremely efficient for segmentation of a heterosequence. Therefore, the two introduced functions, being mutually complementary, provide an effective approach for recognizing and segmentation of heterosequences. As an example, the methods developed are applied for concatenating sequences of different proteins.

Segmentation function S(k, l, x) as a function of parameter k and starting number x of “window” for a sequence composed of elastin and ribonuclease sequences.