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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.     

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.     

Laws of Large Numbers for Cesàro alpha-integrable Random Variables under Dependence Condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI( α)) and strongly residual Cesàro alpha-integrability (SRCI(α)) are two special kinds of extensions to uniform integrability, and both asymp-totically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(α) property as well as the SRCI(α) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α) property yields strong laws of large numbers, which is the continuation of the corresponding literature.     

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.     

Non‐vacuum field desorption ion source implemented under super‐atmospheric pressure

Standard field desorption (FD) ionization is implemented under high vacuum condition. In this paper, non‐vacuum FD is performed under a super‐atmospheric pressure environment using untreated tungsten wires as FD emitter, and the ion source was coupled to a commercial linear ion trap mass spectrometer. The operating pressure of the ion source was 6 bars which was high enough to provide sufficient dielectric strength to the working gas so that the high voltage that was required for FD could be applied to the emitter without occurrence of electrical discharge. Non‐volatile sample deposited on the bare tungsten wire FD emitter was heated by flowing direct current through the emitter. Similar to vacuum FD, the formation of conical protrusion of the liquefied sample layer under the strong electric field was also observed. Using the present ion source, high pressure field‐desorption of polar neutral compounds, organic salts and ionic liquids is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Normal Coordinate Analysis of Pyridine-N-Oxide

We have been interested for some time in the study of the hydrogen bonded complexes in the far-infrared region with special attention to the adducts between phenol and pyridine-N-oxides (1). In such systems the intermolecular mode vσ was identified and some intramolecular vibrations related to the N-O group were observed to be remarkably shifted consequent on hydrogen bonding. In this context we wished to obtain a force field for the complex which could fit the observational results. Unfortunately for one of the constituents i. e. pyridine-N-oxide a force field, suitable for our purposes, was not available and therefore preliminarily we determined it. We report here the results of such analysis.     

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.     

Erosion of Thin Foils by Sputtering in Hollow Cathodes

A thin copper foil placed diagonally in a cylindrical copper hollow cathode undergoes fast erosion caused by cathode sputtering. Changes in the foil shape are related to current distribution along the hollow cathode axis. The experimental results aid in understanding the increase in spectral lines intensities emitted from conical bottom hollow cathode lamps.     

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.