Application of algebraic method to the high overtones of C6H6 and C6D6

Both the spectra and infrared transition strengths of C₆H₆ and C₆D₆ for the C? H stretching overtones up to as high as v = 10 are described in high precision with few parameters (six for the spectra and four for the transition strengths) by the Iachello–Oss algebraic model. The Hamiltonian model is solved in the symmetry adapted bases, which are constructed by the symmetrized boson representation (SBR) technique. The results show that the combination of the algebraic method and SBR technique is a powerful method for describing vibrations of large molecules and high overtones. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

关于两两NQD列的若干极限性质

本文讨论了两两ＮＱＤ列的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型弱大数律及Ｊａｍｉｓｏｎ型加权和的强稳定性，指出了两两ＮＱＤ列与独立列的一个本质性区别，从而提出了解决两两ＮＱＤ旬几乎处处收敛和完全收敛的一种方式。     

Student enrichment in mathematics: a case study with first year university students

ABSTRACT

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an enrichment programme. Following the intervention, students completed a questionnaire and a few were interviewed to establish their experiences of the enrichment programme. We discuss the successes and pitfalls of the intervention and report on the impact it had on the participants.     

A relaxation times coupling method to construct acoustic relaxation calibration for two-frequency measuring gas compositions

In our previous work (Hu et al., 2014), a method has been proposed to detect gas compositions by locating the acoustic spectral peaks, which can be detected only by two-frequency acoustic measurements in practice. However, as a ‘Detection Calibration’, the effective relaxation area (ERA) constructed by existing theoretical model cannot match the two-frequency measurements when there are more than one strong relaxational components in gas mixtures. This paper proposes a method to construct the ERA by coupling the decoupled single relaxation times together to a whole relaxation time. For gas mixtures with only one single relaxation process, the predicted ERA results match with the experimental data better than those predicted by the existing model. Moreover, for gas mixtures in which more than one relaxation process are significant, the ERA results predicted by the proposed method also match with the detection results of two-frequency measurements better than the existing model. This relaxation time coupling based ERA constructing method is validated by the application in low-quality natural gas detection.     

On weak–strong uniqueness for the compressible Navier–Stokes system with non-monotone pressure law

We show the weak–strong uniqueness property for the compressible Navier–Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.     

Vibrational relaxation of a molecule in strong interaction with a reservoir: Nonmonotonic temperature dependence

This theoretical study of the vibrational relaxation of a molecule in interaction with a reservoir uncovers a noteworthy temperature (T) dependence of the time evolution of the relaxation. Its rate increases with T in one interval but decreases in another. The feature arises not for a weak molecule-reservoir interaction but only for coupling strong enough to require polaronic dressing transformations. Our treatment, based on a recent generalization of the well-known Montroll–Shuler equation for relaxation and an explicit calculation of bath correlations from the microscopically specified Hamiltonian, could provide an alternative explanation of an “inverted” T-dependence of relaxation in an experimental report by Fayer and collaborators on W(CO)₆ dissolved in CHCl₃.     

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary ρ-mixing random variables with finite and infinite second moments under weaker mixing rates.Some earlier results are improved.As applications,some results of the law of the iterated logarithm with finite and infinite variance are obtained,also a conjecture raised by Shao in 1993 is solved.     

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In this paper, we mainly studied the limit properties for the countable nonhomogeneous Markov chains. We established some limit properties for the functions of the countable nonhomogeneous Markov chains with variables under the convergence in the sense, which extended the similar conclusions for the functions with two variables. At last, as a corollary, we given the similar result in the homogeneous Markov stock market.     

1,1,3,3‐Tetratriflylpropene (TTP): A Strong,Allylic C–H Acid for Brønsted and Lewis Acid Catalysis

Tetratrifylpropene (TTP) has been developed as a highly acidic, allylic C–H acid for Brønsted and Lewis acid catalysis. It can readily be obtained in two steps and consistently shows exceptional catalytic activities for Mukaiyama aldol, Hosomi–Sakurai, and Friedel–Crafts acylation reactions. X‐ray analyses of TTP and its salts confirm its designed, allylic structure, in which the negative charge is delocalized over four triflyl groups. NMR experiments, acidity measurements, and theoretical investigations provide further insights to rationalize the remarkable reactivity of TTP.