Gradient modeling for multivariate quantitative data

We propose a new parametric model for continuous data, a “g-model”, on the basis of gradient maps of convex functions. It is known that any multivariate probability density on the Euclidean space is uniquely transformed to any other density by using the gradient map of a convex function. Therefore the statistical modeling for quantitative data is equivalent to design of the gradient maps. The explicit expression for the gradient map enables us the exact sampling from the corresponding probability distribution. We define the g-model as a convex subset of the space of all gradient maps. It is shown that the g-model has many desirable properties such as the concavity of the log-likelihood function. An application to detect the three-dimensional interaction of data is investigated.     

Photochemical reaction of trimethyl acetate on Pt/TiO2(110)

Nanometer-sized Pt particles were prepared on an atomically flat surface of rutile TiO(2). Trimethyl acetate (TMA) adsorbed on the Pt-modified surface was photochemically decomposed under ultraviolet light irradiation in a vacuum. Residing TMA anions were imaged by a scanning tunneling microscope to deduce the local rate of decomposition. Increasing the number density of Pt particles led to an enhancement of the initial reaction rate. The degree of this enhancement did not depend on the distance from the Pt particles.     

Self-assembly of coordination molecular baskets as inorganic analogues of cyclotriveratrylenes (CTV)

A [3 + 3] modular self-assembly gives rise to the formation of basket-shaped, crown ether-functionalized, nano-sized trimetallo-macrocycles, which function as structural analogues of cyclotriveratrylenes (CTV).     

Second-order terms for the variances and covariances of the number of prime factors—Including the square free case

We obtain second-order terms for the variance and covariance of $\text{Ω(n)}$ and ω(n), the number of prime divisors counted with and without multiplicity, and connect these results to a formula of Renyi. We discuss the heuristic connection with the Landau-Sathe extension of the prime number theorem and develop new expansions for the mean and variance of ω(n) in the square free case.     

TG-MS characterisation of pig bone in an inert atmosphere

A challenge for forensic examiners is the ageing and characterisation of bone fragments or decomposed skeletal remains. Due to the sensitivity of thermal methods to morphological states, thermal analysis has been selected as a technique which could overcome the difficulties. In this preliminary study, TG-MS was applied to the characterisation of bone fragments derived from the compact bone of pig rib specimens. TG-MS curves were collected by heating bone samples to 1000°C in an argon atmosphere. Under these conditions, both the organic and inorganic phases decomposed, producing a variety of organic fragments and carbon dioxide. Pyrolysis of the organic phase, which is composed predominantly of collagen, occurred resulting in the observation of ion fragments up to 110 amu. Selected fragments were monitored and their observation is discussed in terms of the decomposition of both the collagen phase and the inorganic carbonated hydroxyapatite phase.     

Asymmetric synthesis of a xanthine dehydrogenase inhibitor (S)-(−)-BOF-4272: Utility of chiral alkoxysulfonium salts

A practical synthetic method for a xanthine dehydrogenase inhibitor, (S)-(−)-BOF-4272, was established utilizing an asymmetric oxidation of diaryl sulfide BOF-4269. The oxidation of the sulfide with 1-chlorobenzotriazole carried out in the presence of 4-cyanopyridine and chiral 2-phenylcyclohexanol gave a high enantiomeric excess (73%ee). The sulfoxides in each enantiomerically pure form could be obtained by treating with alkaline hydrolysis or thermolysis of one the diastereomeric intermediate sulfonium salts (>99%de). Thus the transformation into the sulfoxides occur with virtually perfect inversion (alkaline hydrolysis) or retention (thermolysis). It is therefore possible to obtain the target sulfoxide, (S)-(−)-BOF-4272, from both the two diastereomeric sulfonium intermediates.     

Pyrazolato-bridged polynuclear palladium and platinum complexes. Synthesis,structure, and reactivity

Cyclic trinuclear complexes [Pd(3)(mu-pz)(6)] (1) and [Pd(3)(mu-4-Mepz)(6)] (2) and dinuclear complex [Pd(2)(mu-3-t-Bupz)(2)(3-t-Bupz)(2)(3-t-BupzH)(2)] (3) have been prepared by the reactions of [PdCl(2)(CH(3)CN)(2)] with pyrazole (pzH), 4-methylpyrazole (4-MepzH), and 3-tert-butylpyrazole (3-t-BupzH), respectively, in CH(3)CN in the presence of Et(3)N. In the absence of the base, treatment of [PdCl(2)(CH(3)CN)(2)] with pzH gave the mononuclear complex, [Pd(pzH)(4)]Cl(2) (6). The reaction of [PtCl(2)(C(2)H(5)CN)(2)] with pzH in the presence of Et(3)N under refluxing in C(2)H(5)CN afforded the known dimeric Pt(II) complex, [Pt(pz)(2)(pzH)(2)](2) (7). The protons participating in the hydrogen bonding in 3 and 7 are easily replaced by silver ions to give the heterotetranuclear complex [Pd(2)Ag(2)(mu-3-t-Bupz)(6)] (4) and the heterohexanuclear complex [Pt(2)Ag(4)(mu-pz)(8)] (5). The complexes 1-6 are structurally characterized.     

Synthesis and properties of bisdehydro[4n+2]annulenediones

Bisdehydro[14]- and [18]annulenediones have been synthesized by cyclic dimerization of corresponding -ethynyl acid chlorides in the presence of palladium-copper catalyst in triethylamine-benzene and fully characterized by analyses and their ¹H-NMR, mass, electronic and IR spectroscopic evidences.     

Effect of solution extrusion rate on morphology and performance of polyvinylidene fluoride hollow fiber membranes using polyvinyl pyrrolidone as an additive

<正>Polyvinylidene fluoride(PVDF) hollow fiber membranes prepared from spinning solutions with different polyvinyl pyrrolidone(PVP) contents(1%and 5%) at different extrusion rates were obtained by wet/dry phase process keeping all other spinning parameters constant.In spinning these PVDF hollow fibers,dimethylacetamide(DMAc) and PVP were used as a solvent and an additive,respectively.Water was used as the inner coagulant.Dimethylformamide(DMF) and water(30/70) were used as the external coagulant.The performances of membranes were characterized in terms of water flux,solute rejection for the wet membranes.The structure and morphology of PVDF hollow fiber were examined by BET adsorption,dry/wet weight method and scanning electron microscopy(SEM).It is found that the increase in PVP content and extrusion rate of spinning solution can result in the increase of water flux and decrease of solute rejection.The improvements of interconnected porous structure and pore size are induced by shear-thinning behavior of spinning solution at high extrusion rates,which could result in the increase of water flux of hollow fiber membranes.The increase of extrusion rate also leads to the increase of membrane thickness due to the recovery effect of elastic property of polymer chains.     

Electrochemical Elucidation of the Facilitated Ion Transport Across a Bilayer Lipid Membrane in the Presence of Neutral Carrier Compounds

The ion transport facilitated by neutral carrier compounds (valinomycin, nonactin) has been investigated by cyclic voltammetry in the several electrolyte solutions (KF, KCl, KBr, KNO₃, KSCN, KClO₄), and we demonstrated the effect of the counter anions on the facilitated transport of K⁺ from the viewpoint of electroneutrality. Voltammograms for the ion transport were generated at steady state and the current density between W1 and W2, j_W1–W2, increased with the absolute value of the applied membrane potential, E_W1–W2. Then, the magnitude of j_W1–W2 at a certain E_W1–W2 increased with the hydrophobicity of the counter anion. It was proved that the logarithm of |j_W1–W2|at a certain E_W1–W2 is almost proportional to the hydration energy of the counter anion. This indicates that not only K⁺ but also the counter anion distributes into the BLM. Therefore, the magnitude of j_W1–W2 at a certain E_W1–W2 increased with an increase of pH, because the hydroxide ion was served as a counter anion. Based on the variation of the zero‐current potential in case of various asymmetrical ionic compositions, it is found that the amount of cation transport is much larger than that of anion transport.