Spectral Properties and Identities for the Polar Operator with Nonsmooth Periodic Density

Spectral properties of the polar operator depending on the smoothness of the periodic coefficient are studied. The width of the far gaps in the Bloch spectrum is shown to grow for piecewise continuous coefficients, to be asymptotically constant if the coefficient derivative is piecewise continuous, and to decrease in the more smooth cases. The high energy asymptotics of the Lyapunov function, of the quasimomentum and of effective masses are obtained. The spectral identities for the corresponding classical string equation are derived.     

The nonexistence of expansive homeomorphisms of a class of continua which contains all decomposable circle-like continua

A homeomorphism of a compactum with metric is expansive if there is such that if and , then there is an integer such that . It is well-known that -adic solenoids () admit expansive homeomorphisms, each is an indecomposable continuum, and cannot be embedded into the plane. In case of plane continua, the following interesting problem remains open: For each , does there exist a plane continuum so that admits an expansive homeomorphism and separates the plane into components? For the case , the typical plane continua are circle-like continua, and every decomposable circle-like continuum can be embedded into the plane. Naturally, one may ask the following question: Does there exist a decomposable circle-like continuum admitting expansive homeomorphisms? In this paper, we prove that a class of continua, which contains all chainable continua, some continuous curves of pseudo-arcs constructed by W. Lewis and all decomposable circle-like continua, admits no expansive homeomorphisms. In particular, any decomposable circle-like continuum admits no expansive homeomorphism. Also, we show that if is an expansive homeomorphism of a circle-like continuum , then is itself weakly chaotic in the sense of Devaney.

     

Histons: New Quasi-particles and Time-Resolved Fluorescence Shift of Polar Disordered Media

With statistical thermodynamics methods, it is shown that the evolution of a polar luminescence probe + polar disordered medium system after pulse excitation is described by an equation for damped vibrations. From this it follows that in the solvation shell of the excited solute probe, not only synchronous librations but also cooperative jump reorientations of solvent molecules take place, and their damping motion is caused by localized dielectric friction. This collective molecular dynamics is examined as the motion of a quasi-particle called a histon. The histon moment of inertia and mass are determined. The concept of l- and j-histons are also introduced. In terms of this model the full correlation functions for nonequilibrium solvent dynamics are derived. The behavior of steady-state and time-resolved spectra is examined and it is found that the limiting short-wavelength position of the steady-state spectrum at a low temperature and that for time-dependent fluorescence at t 0 are not identical. The histon model has been used for interpretation of the emission band collapse that is observed in long-time evolution experiments. Some other problems of spectral broadening are also discussed. As predicted, sharp expansion of the fluorescence band takes place on an ultrafast time scale due to dephasing of l-histons.     

A method for quantifying the unstable and highly polar drug nafamostat mesilate in human plasma with optimized solid-phase extraction and ESI-MS detection: more accurate evaluation for pharmacokinetic study

An advanced quantification method was developed with solid-phase extraction (SPE) and mass spectrometry (MS) determination for nafamostat, an unstable and highly polar drug, in human plasma. For unstable drugs with an ester group, the main analytical challenge is how to avoid the ester hydrolysis, and strong acid or alkaline conditions should be excluded during sample preparation. Considering that, we developed a relatively mild method with SPE for sample preparation without strong acid and alkaline treatment, which was optimized with different pHs and salt concentrations in phosphate-buffered saline treatment. The results indicated that pH 5 gave the most efficient extraction and 0.1 M salt concentration enhanced the extraction the most, with a minor effect on MS monitoring. The extraction method effectively avoided drug hydrolysis and achieved good drug enrichment over 82.2%. The linear range of quantification was 1.25–160 ng mL⁻¹. The stability of the drug in sample treatment was fully validated according to the sample processing procedure, including the stability in fresh blood, mobile phase, plasma and acidic methanol, and the results indicated that the drug remained stable during the whole sample preparation. Compared with a previous isotope-labeling method, more accurate and specific quantification of plasma concentration was achieved with liquid chromatography–electrospray ionization MS determination. With use of our method, nafamostat mesilate pharmacokinetics in 30 Chinese healthy volunteers was investigated with three doses via intravenous-drip infusion. The pharmacokinetic parameters were also estimated and compared with those of Japanese volunteers (slightly lower plasma concentration and longer terminal elimination half-life for Chinese volunteers). The difference in the pharmacokinetics may be ascribed to the quantification method, because previous isotope labeling may have overestimated the parent drug.     

Conditional limiting distribution of beta-independent random vectors

The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W² is a beta distributed random variable with parameters m/2,(d−m)/2 and (U₁,…,U_m),(U_m+1,…,U_d) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.     

The effect of electron correlation on the conformational space of melatonin

The pineal gland hormone melatonin regulates several physiological processes including circadian rhythm and also alleviates oxidative stress‐induced degenerative diseases. In spite of its important biological roles, no high level ab initio conformational study has been conducted to reveal its structural features. In this work, the conformational flexibility of melatonin was investigated using correlated ab initio calculations. Conformers, obtained previously at the Hartree‐Fock level (HF/6‐31G*), were fully optimized using second order Møller‐Plesset perturbation theory applying the frozen core approximation (MP2(FC)/6‐31G*). Furthermore, single‐point MP4(SDQ,FC)/6‐31G*//MP2(FC)/6‐31G* computations were performed to investigate the effect of higher order perturbation terms. The HF and MP2 conformational spaces are considerably different: the initial 128 structures converged into 102 different local minima as confirmed by frequency calculations; 28 new minima appeared and 26 previous HF local minima disappeared; no “all‐trans” C3 side chain conformations are seen at the MP2(FC) level. The MP2 global minimum conformation is stabilized by an aromatic‐side chain interaction. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

The combinatorial properties of the hyperplanes of DW(5, q) arising from embedding

In De Bruyn Discrete math(to appear), one of the authors proved that there are six isomorphism classes of hyperplanes in the dual polar space DW(5, q), q even, which arise from its Grassmann-embedding. In the present paper, we determine the combinatorial properties of these hyperplanes. Specifically, for each such hyperplane H we calculate the number of quads Q for which is a certain configuration of points in Q and the number of points for which is a certain configuration of points in . By purely combinatorial techniques, we are also able to show that the set of hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding can be divided into six subclasses if one takes only into account the above-mentioned combinatorial properties. A complete classification of all hyperplanes of DW(5, q), q odd, which arise from its Grassmann-embedding, i.e. the division of the above-mentioned six classes into isomorphism classes, will unlike in De Bruyn (to appear) most likely need a group-theoretical approach. Postdoctoral Fellow of the Research Foundation—Flanders (Belgium).     

Tautomerism of monochalcogenosilanoic acids CH3Si(O)XH (X = S,Se, Te) in the gas phase and in the polar and aprotic solution: An ab initio computational investigation

Computational investigations by an ab initio molecular orbital method (HF and MP2) with the 6‐311+G(d,p) and 6‐311++G(2df, 2pd) basis sets on the tautomerism of three monochalcogenosilanoic acids CH₃Si(?O)XH (X = S, Se, and Te) in the gas phase and a polar and aprotic solution tetrahydrofuran (THF) was undertaken. Calculated results show that the silanol forms CH₃Si(?X)OH are much more stable than the silanone forms CH₃Si(?O)XH in the gas‐phase, which is different from the monochalcogenocarboxylic acids, where the keto forms CH₃C(?O)XH are dominant. This situation may be attributed to the fact that the Si? O and O? H single bonds in the silanol forms are stronger than the Si? X and X? H single bonds in the silanone forms, respectively, even though the Si?X (X = S, Se, and Te) double bonds are much weaker than the Si?O double bond. These results indicate that the stability of the monochalcogenosilanoic acid tautomers is not determined by the double bond energies, contrary to the earlier explanation based on the incorrect assumption that the Si?S double bond is stronger than the S?O double bond for the tautomeric equilibrium of RSi(?O)SH (R?H, F, Cl, CH₃, OH, NH₂) to shift towards the thione forms [RSi(?S)OH]. The binding with CH₃OCH₃ enhances the preference of the silanol form in the tautomeric equilibrium, and meanwhile significantly lowers the tautomeric barriers by more than 34 kJ/mol in THF solution. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

氟环唑外消旋体在纤维素-三(3,5-二甲基苯基氨基甲酸酯)手性固定相上的高效液相色谱法拆分

在纤维素-三(3,5-二甲基苯基氨基甲酸酯)（CDMPC）手性固定相上,分别采用正相、反相及极性有机相色谱模式对氟环唑外消旋体进行了拆分,并考察了流动相组成在手性识别中对手性分离的影响。氟环唑在Chiralcel OD-H手性色谱柱（填充CDMPC手性固定相）上采用反相色谱模式,以甲醇-水(体积比为80∶20)为流动相,获得了最佳的拆分,其两对对映异构体的分离度Rs分别为1.64和6.50。     

Molecular field theory for polar,biaxial bent-core nematics

We have studied a polar, biaxial nematic liquid crystal formed from bent-core molecules using molecular field theory. The model includes a simple Heisenberg-form dipolar intermolecular interaction in addition to the usual quadrupolar nematic interaction, and mimics a system consisting of nematogenic bent-core molecules with a large transverse dipole along the bisector of the two molecular arms. Such systems are regarded as good candidates for biaxial nematic liquid crystals. In principle, the molecular dipoles can align, thus stabilising the ordering of the minor axes. Our calculations predict that, for suitable values of the bent-core interarm angle, the biaxial nematic phase can be stabilised at higher temperatures than in the absence of the transverse dipole. In general, the transverse macroscopic polar order stabilises the biaxial nematic phase. In particular, for a large enough dipolar interaction, the Landau point in the pure biaxial nematic develops into a line of first-order polar biaxial nematic-to-isotropic phase transitions.