The Gram Matrix of a PT-Symmetric Quantum System

The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy unconventional completeness and orthonormality relations. These relations reflect the properties of a pair of bi-orthonormal bases associated with non-hermitean diagonalizable operators. In a similar vein, such a dual pair of bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a particular structure: its inverse is obtained by simply swapping the signs of some its matrix elements.     

Temperature coefficient of NH chemical shifts of thioamides and amides in relation to structure

NH chemical shift temperature coefficients have been measured in a large series of N-substituted-3-piperidinethiopropionamides in which the NN distances are short but of varied length, as well as in a couple of the corresponding amides and in some simpler amides and thioamides. Geometries are calculated by means of ab initio DFT methods. The N-substituted-3-piperidinethiopropionamides show in most cases strong intramolecular N–HN hydrogen bonds according to IR spectra and ab initio calculations. For compounds with rather short NN distances the S=C–N–H moiety is non-planar. Dihedral angles as small as 160° are found. The NH chemical shift coefficients measured in non-polar solvents in all the N-substituted-3-piperidinethiopropionamides are more negative (−8 to −17 ppb/K) than in non-hydrogen bonded thioamides. For the latter in non-polar solvents like CDCl₃ and toluene the temperature coefficients are as small as −1 to −4 ppb/K. The large negative effects can be related not only to the non-planarity of the thioamide group in a way that the more pronounced the non-planarity the more negative the temperature coefficients, but also to strong hydrogen bonding and the fact that the acceptor is a nitrogen. For similar amides with non-planar amide groups and nitrogen acceptor large negative temperature coefficients are likewise seen. In polar solvents like DMF the effects in simple thioamides are uniform and close to −6 ppb/K, whereas in the more complex compound like 4p(t) the temperature coefficient is close to 0. An essential feature of measuring temperature coefficients of compounds without strong intramolecular hydrogen bonds in non-polar solvents and at low temperatures is to keep the concentration low enough to avoid dimerisation.     

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).     

Study on the covalence of Cu and chemical bonding in an inorganic fullerene-like molecule, [CuCl]20[Cp*FeP5]12 [Cu-(CH3CN)+2Cl-]5, by a density functional approach

The electronic structure and chemical bonding in a recently synthesized inorganic fullerene-like molecule, [CuCl]₂₀[Cp*FeP₅]₁₂[Cu-(CH₃CN) ⁺ ₂Cl⁻]₅ has been studied by a density functional approach. Geometrical optimization of the three basic structural units of the molecule is performed with Amsterdam Density Functional Program. The results are in agreement with the experiment. Localized MO’s obtained by Boys-Foster method give a clear picture of the chemical bonding in this molecule. The reason why CuCl can react with Cp*FeP₅ in solvent CH₃CN to form the fullerene-like molecule is explained in terms of the soft-hard Lewis acid base theory and a new concept of covalence.     

Study on the covalence of Cu and chemical bonding in an inorganic fullerene-like molecule, [CuCl]_(20)[Cp~*FeP_5]_(12)[Cu-(CH_3CN)_2~+Cl~-]_5, by a density functional approach

The titled inorganic fullerene-like molecule (hereafter abbreviated as IFM) was recently synthe-sized by Bai et al.[1], which attracts a lot of interests from inorganic and organometallic chemists, and questions are raised for this smart molecule: (ⅰ) Why CuCl can react with Cp*FeP5 in solvent CH3CN to form IFM? (ⅱ) What is the nature of chemical bond-ing? (ⅲ) What is the covalence of Cu in this mole-cule? In this paper we intend to answer these questions in terms of the soft-hard …     

多小波子空间上的单小波表示

本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.     

Monoesterification of styrene–maleic anhydride copolymers with alcohols in ethyl benzene: Catalysis and kinetics

A kinetic investigation on the monoesterification reaction of the maleic anhydride residue (MA) in styrene-maleic anhydride copolymers with aliphatic alcohols was carried out in ethyl benzene solution. By comparison to classic catalysts such as tributylamine (TBA) and pyridine, 4-dimethylaminopyridine (4DMAP) is by far the most effective catalyst for this reaction. While both general base and nucleophilic mechanisms contribute to the reaction catalyzed by TBA or pyridine, a nucleophilic mechanism prevails with 4DMAP. This reaction is reversible, and its chemical equilibrium constant decreases significantly with increasing temperature. Both kinetic and thermodynamic results showed that in the presence of 4DMAP, the forward and reverse reactions are second and first order, respectively. The existence of side reactions, reactivity of two styrene-maleic anhydride copolymers of different MA contents as well as two aliphatic alcohols of different lengths are also addressed. © 1993 John Wiley & Sons, Inc.     

Banach空间上的框架与Riesz基

本文讨论Banach空间上框架、无冗框架与Riesz基之间的关系及它们的稳定性．     

Chemical synthesis and electric properties of the conducting copolymer of aniline and o‐aminophenol

A copolymer, poly(aniline‐co‐o‐aminophenol), was prepared chemically by using ammonium peroxydisulfate as an oxidant. The monomer concentration ratio of o‐aminophenol to aniline strongly influences the copolymerization rate and properties of the copolymer. The optimum composition of a mixture for the chemical copolymerization consisted of 0.3 M aniline, 0.021 M o‐aminophenol, 0.42 M ammonium peroxydisulfate, and 2 M H₂SO₄. The result of cyclic voltammograms in a potential region of ?0.20 to 0.80 V (vs.SCE) indicates that the electrochemical activity of the copolymer prepared under the optimum condition is similar to that of polyaniline in more acid solutions. However, the copolymer still holds the good electrochemical activity until pH 11.0. Therefore, the pH dependence of the electrochemical property of the copolymer is improved, compared with poly(aniline‐co‐o‐aminophenol) prepared electrochemically, and is much better than that of polyaniline. The spectra of IR and ¹H NMR confirm that o‐aminophenol units are included in the copolymer chain, which play a key role in extending the usable pH region of the copolymer. The visible spectra of the copolymers show that a high concentration ratio of o‐aminophenol to aniline in a mixture inhibits the chain growth. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5573–5582, 2007