Symmetries and conservation laws of partial differential equations: Basic notions and results

The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed.     

基于成像机理的小波包变换多聚焦图像融合

由于可见光成像系统的聚焦范围有限,因而在成像过程中,除聚焦良好的物体能生成清晰的图像外,该物体前后一定距离外的所有物体都将呈现不同程度的模糊.为了获得场景内所有物体均清晰的图像,在分析了多聚焦图像成像机理的基础上,提出了一种基于小波包变换的融合方法.它是将成像系统先聚焦在一部分对象上,得到其清晰的图像;然后再将其聚焦在另一部分对象上,得到另一清晰的图像;最后把这两幅实验图像加以融合,从而获得场景内所有物体均清晰的图像.实验结果表明,基于小波包变换的融合方法能够将信号的频带进行多层次划分,对高频成分也能进一步地分解,可有效综合多聚焦图像.     

Physicochemical and Acoustic Properties of Water-Based Magnetic Colloid

A velocity and absorption coefficient of sound for magnetic fluid (MF) based on water are studied in the frequency range of 12–132 MHz as a function of the concentration of dispersed phase, the uniform magnetic field, the storage time, and the temperature. The MF dispersed phase consist of magnetite Fe₃O₄ particles stabilized with sodium oleate. The parameters of sound propagation are measured within temperature interval 0–80°C. Densities of MF and sodium oleate are also measured as a function of temperature. Volume concentrations of magnetic fluid components (water, magnetite, and sodium oleate adsorbed on the surface of magnetic particles) are determined. Densities, heat capacities, coefficients of heat conductivity and thermal expansion of aggregates are estimated. Aggregate size distribution in the studied magnetic fluid is described by the log-normal function. Parameters characterizing the aggregate size distribution are determined and their interpretation is given.     

Points Beneath a Hyperbola and the Circle Problem. A Spectral Approach

This is the first introductory part of a paper in which a spectral idea is presented for the solution of the circle problem and the problem on the points beneath a hyperbola. In the second and third parts, technical details of such a solution will be given. Bibliography: 4 titles.     

A generalized square of the zeta function. The spectral decomposition. II

An estimate of the remainder in the spectral decomposition of the generalized ζ function is given, which is more precise than the known ones. This paper is a continuation of a previous paper published in one of the preceding issues. Bibliography: 1 title. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 77–92.     

城市垃圾与煤在CFBC试验台上的混烧试验

城市垃圾的焚烧处理一直是人们关注的研究领域。本文详细报告了一种城市垃圾与劣质煤在0.15兆瓦CFBC试验台上的混烧试验。试验结果表明,城市垃圾与劣质煤在循环流化床中的混烧可以很好地满足稳定和高温燃烧的要求,通过添加石灰石等含钙物料可以有效地在燃烧过程巾控制SO2、HCl和二(?)英类污染物的生成。     

Nonhomogeneous Rankin convolutions

The properties of the Rankin convolutions of two eigenfunctions of different parities from the discrete part of the spectrum of the Laplace operator are studied. Analytical continuability of these convolutions into the left half-plane is proved and a functional equation of Riemann type is obtained. Applications to arithmetical convolutions are given. In particular the asymptotics of such convolutions is obtained by using the nonhomogeneous Rankin convolutions. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 37–51.     

A generalized square of the zeta function. Spectral decompositions

The spectral decomposition for the square of the classical Riemann zeta function ζ²(s) is generalized to the case of the product of two such functions ζ(s₁) · ζ(s₂) of different arguments. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 17–44.