Differential equations uniquely determined by algebras of point symmetries

We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some relevant algebras of vector fields on ℝ^k (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted by the considered Lie algebras. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 486–494, June, 2007.     

Approximation of signals from local averages

This work is concerned with approximation of a signal from local averages. It improves a result of Butzer and Lei [P.L. Butzer, J. Lei, Approximation of signals using measured sampled values and error analysis, Commun. Appl. Anal. 4 (2000) 245–255].     

Weighted Kolmogrov–Smirnov type tests for grouped Rayleigh data

We consider goodness of fit tests for the Rayleigh distribution with grouped data. New Kolmogrov–Smirnov type tests are suggested and compared with the traditional chi-square and likelihood ratio tests. The results show that some of the suggested tests have a good power performance as compared with the traditional ones.     

一类多元Gauss-Weierstrass 算子线性组合的加权Lp-逼近

本文研究一类多元Gauss-Weierstrass算子的线性组合加Jacobi型权逼近的性质,利用加权矩量不等式及加权K-泛函、光滑模等工具,建立了这类算子在Lp(1≤p≤∞)空间的正、逆定理和逼近阶的特征刻划.     

Co@SiO2核壳式纳米磁性粒子的合成、性质表征及在细胞分离和细胞芯片上的应用

合成了Co@SiO2核壳式纳米粒子,并采用透射电镜(TEM)、X射线衍射(XRD)、扫描电镜(SEM)和振动样品磁强计(VSM)对其形状、尺寸、荧光及磁特性进行了表征,探讨了其在细胞分离和细胞芯片上的应用和原理.     

Identification of a dissipation coefficient by a variational method

A generalized inverse problem for the identification of the absorption coefficient for a hyperbolic system is considered. The well-posedness of the problem is examined. It is proved that the regular part of the solution is an L ₂ function, which reduces the inverse problem to minimizing the error functional. The gradient of the functional is determined in explicit form from the adjoint problem, and approximate formulas for its calculation are derived. A regularization algorithm for the solution of the inverse problem is considered. Numerical results obtained for various excitation sources are displayed.     

Linearisation and potential symmetries of certain systems of diffusion equations

We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by expressing the equations in a partially and wholly conserved form, and then by performing a potential symmetry analysis on those systems that can be linearised. We give several examples of such systems, and in a specific case we show how linearising and hodograph-type mappings can lead to new solutions of the diffusion system.     

压差式矢量水听器方位估计中的干扰抵消

矢量水听器由于能获取声场中标量（声压）和矢量（振速）信息，因此单个的矢量水听器就可实现目标方位估计。单个矢量水听器是利用信号的声压和质点振速之间相关性进行信号方位估计，但是当存在干扰，并且干扰和信号之间相关时，如果对运用能量流进行方位估计的方法不加改进，则会出现很大的误差，甚至出现错误的估计。本文提出一种存在已知噪声干扰情况下的干扰抵消方法，并针对该方法进行了仿真试验，最后运用湖试数据进行了验证。结果表明，该方法能有效地减弱相千千柑对信号的影响，实现对信号的方位估计。     

中国西部城镇化发展的“三分”构想

在经济全球一体化和经济区域化已成为当今世界经济发展大势的背景下，西部区域经济之所以发展不利，根本原因是区域经济理论陈旧落后，缺乏创新的区域发展思维。这些深层次的问题得不到解决，西部的城镇化水平和区域经济难以得到快速发展。因此，“三分构想”的提出是十分必要和迫切的。     

介观耗散互感耦合电路的库仑阻塞效应

给出了介观耗散互感耦合电路的量子化方法,并在介观电路中电荷量子化的基础上给出了介观耗散互感耦合电路的库仑阻塞条件.