Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Let {(ξni, ηni), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as(S_1, ρ_n S_1 +(1-ρ_n~2S_2)~(1/2)), ρn∈(0, 1), where(S1, S2) is a bivariate spherical random vector. For the distribution function of radius (S_1~2+ S_2~2)~(1/2) belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of ρn to 1 is given. In this paper,under the refinement of the rate of convergence of ρn to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.     

L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

Nanosecond-time-resolved infrared spectroscopic study of fast relaxation kinetics of protein folding by means of laser-induced temperature-jump

Elucidating the initial kinetics of folding pathways is critical to the understanding of the protein folding mechanism. Transient infrared spectroscopy has proved a powerful tool to probe the folding kinetics. Herein we report the construction of a nanosecond laser-induced temperature-jump （T-jump） technique coupled to a nanosecond timeresolved transient mid-infrared （mid-IR） spectrometer system capable of investigating the protein folding kinetics with a temporal resolution of 50 ns after deconvolution of the instrumental response function. The mid-IR source is a liquid N2 cooled CO laser covering a spectral range of 5.0μm （2000 cm^-1）-6.5μm （1540 cm^-1）. The heating pulse was generated by a high pressure H2 Raman shifter at wavelength of 1.9μm. The maximum temperature-jump could reach as high as 26±1℃. The fast folding/unfolding dynamics of cytochrome C was investigated by the constructed system, providing an example.     

Multivariate risk models under heavy‐tailed risks

In this paper, we consider four common types of ruin probabilities for a discrete‐time multivariate risk model, where the insurer is assumed to be exposed to a vector of net losses resulting from a number of business lines over each period. By assuming a large initial capital for the risk model and regularly varying distributions for the net losses, we establish some interesting asymptotic estimates for ruin probabilities in terms of the upper tail dependence function of the net loss vector. Our results insightfully characterize how the dependence structure among the individual net losses affect the ruin probabilities in an asymptotic sense, and more importantly, from our main results, explicit asymptotic estimates for those ruin probabilities can be obtained via specifying a copula for the net loss vectors. Copyright © 2013 John Wiley & Sons, Ltd.     

Enhanced Photocatalytic Activity of Titanium Dioxide Supported on Hexagonal Mesoporous Silica at Lower Coverage

The photocatalytic activities of titanium dioxide (TiO₂) supported on hexagonal mesoporous silica (HMS), zeolite Y (NaY) were investigated by using the photodegradation of 2,4,6-trichlorophenol (TCP) as test reactions. It was found that the photocatalytic activity of TiO₂ on HMS was much higher than that of TiO₂ powders, and that of TiO₂ on NaY. It was also found that TiO₂/HMS had maximal photocatalytic activity at a lower Ti content. The larger the pore size of HMS used as the support of TiO₂, the better the photocatalytic activity of TiO₂ for degradating of organic pollutant. These observations suggested that the supported structure was a main factor responsible for enhancement of the photocatalytic activity of TiO₂. Characterization of the samples by TEM, XRD, BET, and UV-vis diffuse reflectance spectra indicated that the structures of HMS and TiO₂ were confirmed and TiO₂ did not enter into the HMS framework and was formed as nanoparticles on all supports.     

The alkoxide sol–gel process in the calcium phosphate system and its applications†

A single calcium glycolate was synthesized. The alkoxide was stable under ambient atmosphere. The calcium glycolate, phosphoric acid and P(OH) _x (OEt)_{3− x} were used as the precursors. Acetic acid was used as a reagent to modify the calcium glycolate and to change the acidity of the mixtures of the precursors. Mixtures of the calcium glycolate and phosphoric acid in a Ca/P ratio of 1.67 showed unusual sol–gel behavior. A transparent gel could be formed depending on the content of acetic acid and the extent of stirring. The behavior is attributed to a high viscosity and a large molecular size of the ethylene glycol solvent, leading to a strong dependence of the reactions in the mixtures on the diffusion process, greatly affected by stirring. When the mixtures of the calcium glycolate and PO(OH) _x (OEt) _{3− x} contained acetic acid at an acetic acid/Ca ratio of 3, stable alkoxide solutions with Ca/P ratios of 1.0, 1.5 and 1.67 could be formed. Different calcium phosphate compounds and hydroxyapatite coatings on alumina substrates could easily be formed from the alkoxide solutions. The chemical homogeneity provided by the alkoxide route leads to easy formation of the required products. Copyright © 1999 John Wiley & Sons, Ltd.     

Increasing structure dimensionality of copper(I) complexes by varying the flexible thioether ligand geometry and counteranions

This work focuses on the systematic investigation of the influences of pyrimidine-based thioether ligand geometries and counteranions on the overall molecular architectures. A N-containing heterocyclic dithioether ligand 2,6-bis(2-pyrimidinesulfanylmethyl)pyridine (L1) and three structurally related isomeric bis(2-pyrimidinesulfanylmethyl)benzene (L2-L4) ligands have been prepared. On the basis of the self-assembly of CuX (X = I, Br, Cl, SCN, or CN) and the four structurally related flexible dithioether ligands, we have synthesized and characterized 10 new metal-organic entities, Cu4(L1)2I4 1, Cu4(L1)2Br4 2, [Cu2(L2)2I2.CH3CN]n 3, [Cu(L3)I]n 4, [Cu(L3)Br]n 5, [Cu(L3)CN]n 6, [Cu(L4)CN]n 7, [Cu2(L4)I2]n 8, [Cu2(L4)(SCN)2]n 9, and [[Cu6I5(L4)3](BF4).H2O]n 10, by elemental analyses, IR spectroscopy, and X-ray crystallography. Single-crystal X-ray analyses show that the 10 Cu(I) complexes possess an increasing dimensionality from 0D (1 and 2) to 1D (3-5) to 2D (6-9) to 3D (10), which indicates that the ligand geometry takes an essential role in the framework formation of the Cu(I) complexes. The influence of counteranions and pi-pi weak interactions on the formation and dimensionality of these coordination polymers has also been explored. In addition, the photoluminescence properties of Cu(I) coordination polymers 4-10 in the solid state have been studied.     

Synthesis and biological evaluation of novel piperidin-4-ol derivatives

Abstract  

A series of novel piperidin-4-ol derivatives were designed, synthesized, and evaluated for potential treatment of HIV. The compounds were obtained via an efficient synthetic route in excellent yields and have been characterized by ¹H NMR, ¹³C NMR, MS, and elemental analysis. The CCR5 antagonistic activities of the compounds have also been evaluated.     

Four distinctive 1-D lanthanide carboxylate coordination polymers: Synthesis,crystal structures and spectral properties

Four novel lanthanide coordination polymers [Pr(mal)(OH)(bipy) · 2H₂O]_n (1), {[Dy¹(SBA)₃(H₂O)₂][Dy²(SBA)₃(H₂O)₂] · 4H₂O}_n (2), {[Tb(OHnic)(Onic)(H₂O)₅ · (OHnicH)] · H₂O}_n (3) and {[Sm(OHnic)(Onic)(H₂O)₅ · (OHnicH)] · H₂O}_n (4) (Hmal = maleic acid, HSBA = 4-sulfobenzoic acid, OHnicH = 6-hydroxynicotinic acid and bipy = 2,2′-bipyridine) have been synthesized and determined by single crystal X-ray diffraction. Complex 1 is a 1-D helical chain with seven-coordinated praseodymium centers. Complex 2 forms 1-D chain-like molecular structure containing two crystallographically unique dysprosium centers, the Dy¹ center is seven-coordinated while Dy² is eight-coordinated. The isomorphous complexes 3 and 4 exhibit an unprecedented 1-D chain-like polymeric structure through hydroxyl oxygen atoms of bridging Onic²⁻ anions linking up the neighboring central ions, and there exist three types of 6-OHnicH ligands in the structural unit which is rare for lanthanide carboxylate complexes. The photophysical properties of these complexes were studied using ultraviolet absorption spectra, fluorescence excitation and emission spectra.