Shining metal cups : A luminescent tube of triangular cross‐section and stoppered by a silver ion (see picture: Re yellow, N blue, O red) is formed in two steps from commercial materials. The silver ion can be removed to give a tube, and both species are potential hosts for small ions and molecules; a change in luminescence is triggered by the encapsulation of silver.
We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry
in order to prove that, given a Cr function , we have
where . This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse–Sard theorem, is not necessary: the conclusion of the Morse
decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse–Sard
theorem (with sharp differentiability assumptions). 相似文献
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain regions of the phase space, which correspond to neighbourhoods of the maximal set \(\mathcal M\), i.e.,the set of points where the observable is maximised. The main novelty here is the fact that we consider that the set \(\mathcal M\) may have a countable number of points, which are associated by belonging to the orbit of a certain point, and may have accumulation points. In order to prove the existence of distributional limits and study the intensity of clustering, given by the Extremal Index, we generalise the conditions previously introduced in Freitas (Adv Math 231(5): 2626–2665, 2012, Stoch Process Appl 125(4): 1653–1687, 2015). 相似文献
The host-guest assembly of CB7 with a series of alkyl(trimethyl)ammonium (C(n)TA(+)) surfactants of different chain lengths (n=6-18) has been studied. The complexation behaviour was investigated by NMR spectroscopy, isothermal titration calorimetry and kinetics measurements. The combined results of these techniques provided evidence for the formation of 1:1 inclusion and 2:1 external complexes in the cases of C(n)TA(+) with n=12-18. The binding constants for the 1:1 complexes are independent of the alkyl chain length of the surfactant, whereas a relationship between K(2:1) and the chain length of the surfactant was found for the 2:1 complexes. 相似文献
The dative N-B bond was used to simply assemble heterocycles with a skeleton akin to the 5-oxofuro[2,3-b]furan motif. Twenty-five new N-B heterocycles were prepared via a highly efficient one-pot four-component reaction in yields and diastereoselectivities up to 95% and >97%, respectively. Several reaction intermediates were discovered using electrospray ionization mass spectroscopy which set the basis for the mechanism elucidation using DFT calculations. 相似文献
The development of analytical techniques that enable the use of hair as an alternative matrix for the analysis of drugs of abuse is useful for confirming the exposure in a larger time window (weeks to months, depending on the length of the hair shaft). In the present study a methodology aimed at the simultaneous quantification of cocaine and morphine in human hair was developed and validated. After decontamination, hair samples (20?mg) were incubated with a mixture of methanol/hydrochloric acid (2:1) at 65?°C overnight (~16?h) in order to extract the drugs of the matrix. Purification was performed by solid-phase extraction using mixed-mode extraction cartridges. After derivatization with N-methyl-N-(trimethylsilyl) trifluoroacetamide, blank, standards and samples were analyzed by gas chromatography/electron impact-mass spectrometry (GC-EI/MS). The method proved to be selective, as there were no interferences of endogenous compounds with the same retention time as cocaine, morphine and ethylmorphine (internal standard). The regression analysis for both analytes showed linearity in the range 0.25-10.00?ng/mg with correlation coefficients ranging from 0.9989 to 0.9991. The coefficients of variation oscillated between 0.83 and 14.60%. The limits of detection were 0.01 and 0.02?ng/mg, and the limits of quantification were 0.03 and 0.06?ng/mg for cocaine and morphine, respectively. The proposed GC-EI/MS method provided an accurate and simple assay with adequate precision and recovery for the quantification of cocaine and morphine in hair samples. The proof of applicability was performed in hair samples obtained from drug addicts enrolled in a Regional Detoxification Treatment Center. The importance of hair samples is highlighted, since positives results were obtained when urine immunoassay analyses were negative. Copyright ? 2012 John Wiley & Sons, Ltd. 相似文献