On perturbations of matrix pencils with real spectra, a revisit

This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.

     

Mbekhta's subspaces and a spectral theory of compact operators

Let be an operator on an infinite-dimensional complex Banach space. By means of Mbekhta's subspaces and , we give a spectral theory of compact operators. The main results are: Let be compact. . The following assertions are all equivalent: (1) 0 is an isolated point in the spectrum of (2) is closed; (3) is of finite dimension; (4) is closed; (5) is of finite dimension; . sufficient conditions for to be an isolated point in ; . sufficient and necessary conditions for to be a pole of the resolvent of .

     

Inner bounds for the spectrum of quasinormal operators

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

     

脉冲电场对木瓜蛋白酶影响的荧光光谱分析

木瓜蛋白酶溶液在电场强度为50 kV·cm-1,频率1 500 Hz,脉冲宽度40 μs的脉冲电场下接受19 800个脉冲处理后,其活性降低了56.5％。文章采用荧光偏光光谱对处理前后的样品进行了分析。 处理后酶样的荧光强度明显大于处理前,在峰值位置其荧光强度增加超过50％,峰位从342 nm移到了346 nm左右,其荧光偏振幅度明显减小。由此推断出木瓜蛋白酶经脉冲电场处理后酶蛋白的α-螺旋结构松散拉伸,分子内部的氨基酸残基暴露于分子表面,并有部分发生离解游离于溶液中,导致活性部位的结构发生变化,最终导致酶失活。     

Study of absorption spectra of gasolines and other hydrocarbon mixtures in the second overtone region of the CH<Subscript>3</Subscript>, CH<Subscript>2</Subscript>, CH groups

We have obtained experimental and model absorption spectra for individual hydrocarbons (toluene, benzene, n-heptane, and iso-octane) and their mixtures in the near IR range (λ = 1080–1220 nm). We model the spectra of nonsynthetic gasolines obtained under the same conditions by combining the spectra of three pure hydrocarbons. We show that the octane number of the studied gasoline is linearly related to the toluene (or benzene) concentrations in the model mixture. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 157–161, March–April, 2007.     

Vibrational spectroscopic study of budesonide

The Raman spectrum of budesonide is reported for the first time, and molecular assignments are proposed on the basis of ab initio BLYP DFT calculations with a 6‐31 G* basis set and vibrational wavenumbers predicted on a quasi‐harmonic approximation. Comparison with previously published infrared data has explained several spectral features, and the relative band intensities in the CO and CC stretching regions are interpreted. The results from this study provide data that can be used for the preparative process monitoring of budesonide, an important steroidal pharmaceutical in various dosage forms, and its interaction with excipients and other components. Copyright © 2007 John Wiley & Sons, Ltd.     

Raman spectroscopy of halogen‐containing carbonates

Raman spectroscopy complemented with infrared spectroscopy has been used to study a series of selected natural halogenated carbonates from different origins, including bastnasite, parisite and northupite. The position of CO₃²⁻ symmetric stretching vibration varies with the mineral composition. An additional band for northupite at 1107 cm⁻¹ is observed. Raman spectra of bastnasite, parisite and northupite show single bands at 1433, 1420 and 1554 cm⁻¹, respectively, assigned to the ν₃ (CO₃)²⁻ asymmetric stretching mode. The observation of additional Raman bands for the ν₃ modes for some halogenated carbonates is significant in that it shows distortion of the CaO₆ octahedron. No ν₂ Raman bending modes are observed for these minerals. The band is observed in the infrared spectra, and multiple ν₂ modes at 844 and 867 cm⁻¹ are observed for parisite. A single intense infrared band is found at 879 cm⁻¹ for northupite. Raman bands are observed forthe carbonate ν₄ in‐phase bending modes at 722 cm⁻¹ for bastnasite, 736 and 684 cm⁻¹ for parisite and 714 cm⁻¹ for northupite. Multiple bands are observed in the OH stretching region for selected bastansites and parisites, indicating the presence of water and OH units in the mineral structure. The presence of such bands brings into question the actual formula of these halogenated carbonate minerals. Copyright © 2007 John Wiley & Sons, Ltd.     

Electro- and photoluminescence of compounds based on doped zinc sulfide in the 500–750-nm range

The influence of atmospheric passivation on the electro- and photoluminescent properties of ZnS powders doped with In and/or CuCl is investigated. The processes proceeding in the material during thermal doping with In and/or CuCl as well as participation of oxygen in forming the electro- and photoluminescent radiation centers are discussed. The possibility of creating electro- and photoluminophors based on ZnS that have a continuous spectrum in the visible range with the same spectral density is shown. An electroluminophor based on ZnS:In,Cu,Cl that emits radiation with practically the same spectral density in the 550–750-nm range has been created as well as a photoluminophor based on ZnS:In that emits similarly within the range 500 < < 700 nm.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 90–93, January–February, 2005.     

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R₃', R₂', and R₁' lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG:Cr³⁺ as well as thermal shifts of GSZFS, R₁ line and R₂ line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R₁ line and R₂ line of ruby, several conclusions have also been obtained.     

Infrared spectra of carbon monoxide-hydrogen sulfide van der Waals complexes in the C-O stretching region

The CO-stretching vibration-rotation spectra of CO-H₂S, CO-D₂S, and CO-HDS complexes have been studied in the 2150 cm⁻¹ region using a supersonic slit-jet expansion and a tunable diode laser spectrometer. The spectra were analyzed with the help of very recent microwave pure rotational studies of the same complexes. Two bands were assigned for each of the symmetric hydrogen sulfide isotopes, corresponding to the two nuclear spin modifications, para and ortho. The band origins were blue shifted, relative to the free CO molecule, by about 3.8 cm⁻¹ for CO-H₂S and 4.3 cm⁻¹ for CO-D₂S. These are considerably smaller shifts than exhibited by the related CO-water complexes, indicating that the intermolecular forces in CO-H₂S are weaker and more isotropic.