非齐次对称特征值问题

引言 用SR~(n×n)表示所有。n×n实对称矩阵的集合。R~n表示n维线性空间。||·||_2表示向量的Euclid范数或矩阵的谱范数。 本文研究如下问题: 问题ISEP 给定矩阵A∈SR~n×n和向量b∈R~n,求实数λ和向量X∈R~n使得 AX=λX+b, (1) ||X||_2=1. (2) 若b=0,则问题ISEP就是通常的实对称矩阵特征值问题,若b≠0,则问题ISEP称为非齐次对称特征值问题,使(1)和(2)式成立的数λ和向量X分别称为非齐次特征值和相应的非齐     

The use of nuclear track detectors as an environmental solar ultraviolet radiation dosimeter

Investigation of using CR-39 nuclear track detectors as solar ultraviolet radiation (SUVR) dosimeter was studied. The nuclear track detectors were irradiated with Cf-252 (alpha and fission fragments) before exposure to sun light. The exposure of nuclear track detectors to SUVR were carried out under two different conditions (i) the detector was mounted on a solar tracker mechanism which always rotate towards the sun, and (ii) fixed on a horizontal surface. The measurements were performed for different periods extended from one to eight weeks continuously at Dhahran - Saudi Arabia. The period extended from the middle of July to middle of September: the hottest months in Saudi Arabia. The weekly integrated SUVR measured by Eppley sensor was ranged from 2400 W. h. m⁻² for one week up to 21000 W.h.m⁻² for eight weeks. The results indicate linear correlation between both the track diameters of alphas and fission fragments and the total exposure to SUVR. The results clearly demonstrate that it is possible to use the nuclear track detectors as an environmental and personal SUVR dosimeters.     

Induced and back scattering in a ruby laser

From the condition of generation (of the reproducibility of opposite waves for a pass around a resonator) it follows that in addition to amplitude-phase changes an active medium must also compensate for backscatter in the resonator. The most probable mechanism involved in this compensation is nonlinear backscatter. In the process of generation, nonlinear scattering compensates for resonator scattering as a result of self-regulation. Amplitude-frequency characteristics are determined by the types of vibrations of a resonator, whereas nonlinear effects specify these characteristics. Higher College of Communication, 8/2 Staroborisovskii Trakt, 220114, Minsk, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 881–887, November–December, 1998.     

Computations of eigenpair subsets with the MRRR algorithm

The main advantage of inverse iteration over the QR algorithm and Divide & Conquer for the symmetric tridiagonal eigenproblem is that subsets of eigenpairs can be computed at reduced cost. The MRRR algorithm (MRRR=multiple relatively robust representations) is a clever variant of inverse iteration without the need for reorthogonalization. STEGR, the current version of MRRR in LAPACK 3.0, does not allow for subset computations. The next release of STEGR is designed to compute a (sub‐)set of k eigenpairs with ??(kn) operations. Because of the special way in which eigenvectors are computed, MRRR subset computations are more complicated than when using inverse iteration. Unlike the latter, MRRR sometimes cannot ignore the unwanted part of the spectrum. We describe the problems with what we call ‘false singletons’. These are eigenvalues that appear to be isolated with respect to the wanted eigenvalues but in fact belong to a tight cluster of unwanted eigenvalues. This paper analyses these complications and ways to deal with them. Published in 2006 by John Wiley & Sons, Ltd.     

Silica surface controversies,strong adsorption sites,their blockage and removal. Part I

Summary The review describes many different controversies concerning the surface chemistry of silica. The first part concerns the variable nature of alkyl bonded phases for HPLC, the physical requirements for silica and the role of silanols as adsorption centres. The existence of a small population of strong adsorption sites is pointed out and the reasons for the strong and undesirable adsorption discussed; the part played by trace metals in the silica matrix is emphasised.     

Preparation of alumina by sol-gel process,its structures and properties

Alumina monolithic gel has been prepared by ammonia method from anhydrous aluminium chloride and n-butanol using formamide as the solvent. The gel has been made by hydrochloric acid catalysis and using large quantity of water for hydrolysis (molar ratio of water to aluminium-n-butoxide, R>99). Transparent alumina xerogel of size 37.5×20×5 mm approximately has been prepared. The alumina gel has been dried and sintered at 400°C, 1000°C and 1200°C respectively and the powders formed thereby have been examined by XRD, FTIR spectroscopy, SEM and particle size analysis. These studies have confirmed the formation of -alumina at 1200°C having particle size as low as 0.2 m or less along with agglomerates. The density of the powder has increased gradually, where as its particle size has decreased, with the increase of the sintering temperature.     

Liquid phase hydrogenolysis of dibenzyl ether over metals of the VIIIth group

It has been shown that depending on the catalyst and the solvent used, during the conversion of dibenzyl ether to toluene hydrogenolysis of C-O ether bonds, dehydrogenation and hydrogenolysis of benzyl alcohol formed, hydrogenation and decarbonylation of benzaldehyde, and the recombination of benzyl radicals and the benzylation of toluene can take place. The activity of catalysts in hydrogenolysis reactions of dibenzyl ether and benzyl alcohol to produce toluene decreases as follows: Pd/C>Pd>Raney Ni>Rh, whereas the selectivity drops down in the order: Raney Ni>Pd>Pd/C>Rh. The reaction rates depend on the solvent and diminish in the order: ethanol>2-propanol>benzene.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1257–1261, July, 1993.     

Thin-layer chromatography with high-boiling mobile phases.1. Investigation of the flow of the high-boiling mobile phases

This paper considers some aspects of a new TLC technique using a molten mobile phase which is solid under ambient conditions. The flow of high-boiling mobile phase at elevated temperature in thin-layer chromatography has been investigated and it is shown that the equation Z_f² = kt is not applicable to migration of the high boiling mobile phase front. The flow stability of the high-boiling mobile phase is noted. It is suggested on the basis of studies of concentration profiles of the solidified mobile phases by scanning photometers that the shape of the mobile phase concentration profile be taken into account in calculation of R_f Values.