Shuffles of copulas

We show that every copula that is a shuffle of Min is a special push-forward of the doubly stochastic measure induced by the copula M. This fact allows to generalize the notion of shuffle by replacing the measure induced by M with an arbitrary doubly stochastic measure, and, hence, the copula M by any copula C.     

Modeling junctions of plates and beams by means of self-adjoint extensions

On the basis of an asymptotic analysis of elliptic problems on thin domains and their junctions, a model of a mixed boundary value problem for a second-order scalar differential equation on the union of 3D thin beams and a plate is constructed. One end of each beam is attached to the plate, and on the other end, the Dirichlet conditions are imposed; on the remaining part of the joint boundary, the Neumann boundary conditions are set. An asymptotic expansion of the solution to such a problem has certain distinguishing features; namely, the expansion coefficients turn out to be rational functions of the large parameter |lnh| (where h ∈ (0, 1] is a small geometric parameter), and the solution to the limit problem in the longitudinal section of the plate has logarithmic singularities at the junction points with the beams. Thus, the classical settings of boundary value problems are inadequate to describe the asymptotics, and the technique of self-adjoint extensions and function spaces with separated asymptotics must be used.     

A Critical Review on the Analysis of Metal Soaps in Oil Paintings

Up to 70 % of the oil paintings conserved in collections present metal soaps, which result from the chemical reaction between metal ions present in the painted layers and free fatty acids from the lipidic binders. In recent decades, conservators and conservation scientists have been systematically identifying various and frequent conservation problems that can be linked to the formation of metal soaps. It is also increasingly recognized that metal soap formation may not compromise the integrity of paint so there is a need for careful assessment of the implications of metal soaps for conservation. This review aims to critically assess scientific literature related to commonly adopted analytical techniques for the analysis of metal soaps in oil paintings. A comparison of different analytical methods is provided, highlighting advantages associated with each, as well as limitations identified through the analysis of reference materials and applications to the analysis of samples from historical paintings.     

Ethanolic extract of Rubia peregrina L. (Rubiaceae) inhibits haloperidol-induced catalepsy and reserpine-induced orofacial dyskinesia

In the traditional Sardinian system of medicine, Rubia peregrina L. (Rubiaceae) is reported as an aphrodisiac herb. Since the aphrodisiacs may also have antioxidant and dopaminergic activities, the aim of this study was to study the effect of ethanolic extract of aerial parts of R. peregrina for the scavenging of free DPPH radicals and the inhibition of haloperidol-induced catalepsy in mice and reserpine-induced orofacial dyskinesia in rats. The extract exhibited significant antioxidant activity in a free radical DPPH assay with IC(50)?=?55.6?μg?mL(-1), which was very close to IC(50) of ascorbic acid. The extract of R. peregrina (100 and 200?mg?kg(-1) intraperitoneally, i.p.) significantly inhibited haloperidol (1?mg?kg(-1) i.p.) - induced catalepsy in mice (p?相似文献   

A Functional Equation Whose Unknown is \mathcal{P}([0,1]) Valued

We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it depends continuously on the boundary datum, and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means of a Randomly Reinforced Urn with different reinforcement distributions having equal means. The general solution to the functional equation defines a new parametric collection of distributions on [0,1] generalizing the Beta family.     

A highly crystalline microporous hybrid organic-inorganic aluminosilicate resembling the AFI-type zeolite

ECS-14, a crystalline microporous hybrid organic-inorganic aluminosilicate, has been synthesized by using 1,4-bis-(triethoxysilyl)-benzene (BTEB) as a source of silica. Its structure contains a system of linear channels with 12-membered ring openings, running along the [001] direction, resembling the pore architecture of the AFI framework type.     

Power series and analyticity over the quaternions

We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a power series \({\sum\nolimits_{n \in \mathbb{N}} q^n a_n}\) in its domain of convergence, which is a ball B(0, R) centered at 0. At each \({p \in B(0,R)}\), f admits expansions in terms of appropriately defined power series centered at p, namely \({\sum\nolimits_{n \in \mathbb{N}} (q-p)^{*n} b_n}\). The expansion holds in a ball Σ(p, R ? |p|) defined with respect to a (non-Euclidean) distance σ. We thus say that f is σ-analytic in B(0, R). Furthermore, we remark that Σ(p, R ? |p|) is not always a Euclidean neighborhood of p; when it is, we say that f is strongly analytic at p. It turns out that f is strongly analytic in a neighborhood of \({B(0,R) \cap \mathbb{R}}\) that can be strictly contained in B(0, R). We then relate these notions of analyticity to the class of quaternionic functions introduced in Gentili and Struppa (Adv. Math. 216(1):279–301, 2007), and recently extended in Colombo et al. (Adv. Math. 222(5):1793–1808, 2009) under the name of slice regular functions. Indeed, σ-analyticity proves equivalent to slice regularity, in the same way as complex analyticity is equivalent to holomorphy. Hence the theory of slice regular quaternionic functions, which is quickly developing, reveals a new feature that reminds the nice properties of holomorphic complex functions.     

Cyclochiral resorcin[4]arenes as effective enantioselectors in the gas phase

The effect of cyclochirality of rccc‐2,8,14,20‐tetra‐n‐decyl‐4,10,16,22‐tetra‐O‐methylresorcin[4]arene (C) on the enantiodiscrimination of a number of chiral bidentate and tridentate aromatic and aliphatic biomolecules (G) has been investigated by nano‐electrospray ionization (nano‐ESI)‐Fourier transform ion cyclotron resonance mass spectrometry. The experimental approach is based on the formation of diastereomeric proton‐bound [C·H·G]⁺ complexes by nano‐ESI of solutions containing an equimolar amount of quasi‐enantiomers (C) together with the chiral guest (G) and the subsequent measurement of the rate of the G substitution by the attack of several achiral and chiral amines. In general, the heterochiral complexes react faster than the homochiral ones, except when G is an aminoalcoholic neurotransmitter whose complexes, beyond that, exhibit the highest enantioselectivity. The kinetic results were further supported by both collision‐induced dissociation experiments on some of the relevant [C₂·H·G]⁺ three‐body species and Density functional theory (DFT) calculations performed on the most selective systems. Copyright © 2012 John Wiley & Sons, Ltd.