跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.     

Toeplitz Operators with Semi-Almost-Periodic Matrix Symbols on Hardy Spaces

We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H ^p (1<p<). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p=2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.     

Interrelationship of the Torsional and Rotational States of Asymmetric Nonrigid Molecules

The incorrectness of solution of a torsional-rotational equation for asymmetric nonrigid molecules in the system of internal axes is shown; this incorrectness is caused by the broken interrelationship between the torsional quantum number and the parity of the rotational quantum number K.     

Formation of Metallophthalocyanine Trimers in Liquid Solutions

For solutions of the complexes of phthalocyanine (PhC) with magnesium (Mg-PhC) and of tetrachloromethyl-PhC with zinc (Zn-PhCCh) in mixtures of glycerin with dimethyl formamide (DMF) and for Zn-PhCCh in toluene and DMF it has been found that the electron absorption spectra substantially depend on the substance concentration. It is shown that these changes are attributable to the association of the molecules of pigments. The number of molecules in the associates and the equilibrium constants for this association are determined. The formation of the trimers of Mg-PhC in binary solutions and the dimers of Zn-PhCCh in toluene, DNF, and binary solutions has been established. It has been found that on association the Q absorption bands of the pigments shift to shorter wavelengths as compared to the bands of the monomers. For the Mg-PhC trimers, the shift is = 1410 cm^–1, while for the Zn-PhCCh dimers it is 990 cm^–1 in toluene, 930 cm^–1 in DMF, and 925 cm^–1 in the mixture of DMF with glycerin. It is concluded that the structure of the trimers and dimers is of the type of a stack in which molecules are arranged in parallel one above the other at a distance of 3.5 to 4.0 Å between the planes of the molecules. In association, the fluorescence intensity of the pigments decreases substantially (the decrease corresponds to the decrease in the concentration of the monomer molecules of phthalocyanines), with the fluorescence spectra remaining unchanged. Consequently, the associates of the pigments do not display pronounced fluorescence.     

Effect of Deuteration on Quasiline Electronic‐Vibrational Spectra of Phthalocyanine

Quasiline electronicvibrational spectra of fluorescence and absorption (excitation of fluorescence in selective recording) of the molecules of phthalocyanine deuterated around the periphery of benzene rings (H₂Phcd ₁₆) and the center of the macrocycle (D₂Phc) are obtained. The vibrational frequencies of the ground state are almost insensitive to this deuteration (except for vibrations with the participation of angular deformations). In excitation spectra, changes in deuteration are more pronounced due to the effects of nonadiabatic vibronic interaction of the vibrational sublevels of the S ₁ state and of the purely electronic level S ₂.     

Optical Reflection Spectrum of the Human Tympanic Membrane

The results of an investigation of the reflection spectrum of the human tympanic membrane in the visible and near IR ranges ( = 400–900 nm) are reported.     

Elements with generalized bounded conjugation orbits

For a pair of linear bounded operators and on a complex Banach space , if commutes with then the orbits of under are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams.     

用ABCD矩阵法计算四通式单光栅展宽器的展宽量

以激光束的ABCD传输矩阵理论及Collins积分公式为基础,计算简单实用的四通式单光栅展宽器的色散量,并求出相应展宽量。     

Infrared spectral study of molecular vibrations in amorphous, nanocrystalline and AlO(OH) · αH2O bulk crystals

Amorphous, nanocrystalline, and bulk AlO(OH) · xH₂O crystals have six fundamental modes (FM) of vibration in a nonlinear AlO(OH) molecular structure. Most of them appear in groups of four IR and Raman bands. Their positions and relative intensities differ significantly in three specimens. The nanocrystals (monoclinic structure with z=8 molecules per unit cell) have four OH stretching bands at values enhanced by up to 360 cm⁻¹ at 3120, 3450, 3560 cm⁻¹ in comparison to those in bulk crystals or amorphous specimens. The first two bands are broad, bandwidth Δν_1/2200 to 350 cm⁻¹, while the other two are sharp, Δν_1/290 cm⁻¹. The sharp bands shift to 3525 and 3595 cm⁻¹ after heating the sample at 100°C. They no longer appear after heating at 300 or 500°C for 2 h (the specimen decomposes to Al₂O₃), leaving behind only two bands at 3100 and 3400 cm⁻¹. A Δν_1/2 value of 500 cm⁻¹ appears in the 3400 cm⁻¹ in a delocalized distribution of H atoms. Two bands also occur at 3098 and 3300 cm⁻¹ in bulk crystals (orthorhombic structure with z=4) or at 2990 and 3515 cm⁻¹ in an amorphous sample. More than one bands appear in a FM vibration in occurrence of sample in more than one conformers. The amorphous sample has approximately the same conformer structure as the bulk crystals. An amorphous surface structure exists in nanocrystals with a group of three bands at 1420, 1510 and 1635 cm⁻¹ in an interconnected network structure. It encapsulates the nanocrystals in an amorphous shell. Its volume fraction, 33% estimated from the integrated intensity in three bands, determines 2.2 nm thickness in the shell in spherical shape of nanocrystals in 35 nm diameter.