Dynamic uniqueness for stochastic chains with unbounded memory

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail $\sigma$-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-${?}^2$ summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are ${?}^2$ summable. Finally, if we weaken the condition for DU, asking for coincidence on the future $\sigma$-algebra for almost every pair of pasts, we obtain a condition that is equivalent to $\beta$-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-${?}^2$ summability condition on the kernel is equivalent to the $\beta$-mixing of the compatible stationary chain.     

An efficient splitting technique for two‐layer shallow‐water model

We consider the numerical approximation of the weak solutions of the two‐layer shallow‐water equations. The model under consideration is made of two usual one‐layer shallow‐water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one‐layer shallow‐water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow‐water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non‐negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015     

A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes d_ε is equal to or much larger than the size of the holes ε. Such a diluted porous medium is interesting because it contains some cases where we have a non-negligible effect on the solution when(ε, d_ε) →(0, 0).Smaller distances were avoided for mathematical reasons and for these large distances, the geometry of the holes does not affect or rarely affect the asymptotic result. Very recently, it was shown for the 2D-Euler equations that a porous medium is non-negligible only for inter-holes distances much smaller than the sizes of the holes.For this result, the boundary regularity of holes plays a crucial role, and the permeability criterion depends on the geometry of the lateral boundary. In this paper, we relax slightly the regularity condition, allowing a corner, and we note that a line of irregular obstacles cannot slow down a perfect fluid in any regime such thatε ln d_ε→ 0.     

Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.     

Photoinduced magnetization in copper octacyanomolybdate

This article describes the studies of a photomagnetic cyanide-bridged Cu-Mo bimetallic assembly, Cu(II)(2)[Mo(IV)(CN)(8)].8H(2)O (Cu(II), S = (1)/(2); Mo(IV), S = 0) (1), which has an intervalence transfer (IT) band from Mo(IV)-CN-Cu(II) to Mo(V)-CN-Cu(I) around 480 nm. Wide-angle X-ray scattering and X-ray spectroscopic studies provide precise information about the 3D connectivity and the local environment of the transition metal ions. Irradiating with blue light causes solid 1 to exhibit a spontaneous magnetization (Curie temperature = 25 K). The thermal reversibility is carefully studied and shows the long-time stability of the photoinduced state up to 100 K. Photoreversibility is also observed; i.e., the magnetization is induced by irradiation with light below 520 nm, while the magnetization is reduced by irradiation with light above 520 nm. The UV-vis absorption spectrum after irradiation shows a decrease of the IT band and the appearance of the reverse-IT band in the region of 600-900 nm (lambda(max) = 710 nm). This UV-vis absorption spectrum is recovered to the original spectrum by irradiation with 658-, 785-, and 840-nm light. In this photomagnetic effect, the excitation of the IT band causes an electron transfer from Mo(IV) to Cu(II), producing a ferromagnetic mixed-valence isomer of Cu(I)Cu(II)[Mo(V)(CN)(8)].8H(2)O (Cu(I), S = 0; Cu(II), S = (1)/(2); Mo(V), S = (1)/(2)) (1'). 1' returns to 1 by irradiation of the reverse-IT band, which obeys the scheme for the potential energy surface in mixed-valence class II compounds.     

A selective synthesis of hydroxyborate anions as novel anchors for zirconocene catalysts

A new family of hydroxytris(pentafluorophenyl)borate anions [B(C6F5)3OH](-) associated with organic and aprotic cations c+ (imidazolium, pyrrolidinium and phosphonium) has been prepared by a general one-pot synthesis that implies the chloride borate analogues [B(C6F5)3Cl](-)[c]+. The [c]+[B(C6F5)3OH](-) salts have been isolated and fully characterized. The borate anion [B(C6F5)3OH](-) has been shown to protonate the Zr-Me bond in the Cp2ZrMe2 complex forming CH4 and the first published example of anionic [Cp2Zr(Me)OB(C6F5)3](-) species. Standard spectroscopic methods demonstrate the covalent character of the Zr metal center and the anionic character of the boron atom. This protonolysis methodology using [B(C6F5)3OH](-) anion affords a new route for the incorporation of a covalently bonded anionic functionality on organometallic complexes. This provides a new way to immobilize transition metal complexes in ionic liquids.     

Adsorption of L-lysine on Cu(110): a RAIRS study from UHV to the liquid phase

The adsorption of L-lysine on a Cu(110) surface has been investigated under UHV conditions from the sublimation of a crystalline phase. The adsorption was characterized by Fourier transform reflection absorption infrared spectroscopy (FT-RAIRS) during exposure and Auger electron spectroscopy (AES). At room temperature, the lysine molecules' adsorption geometry varies as a function of the exposure. At low coverage, the molecules are adsorbed via the oxygen atoms of the deprotonated carboxylate group and the nitrogen atom of the amino group. At high coverage, close to the monolayer, the molecules reorient to be anchored to the surface via one oxygen of a sideways-tilted carboxylate moiety. This first step is followed by the growth of multilayers of nonoriented molecules. In contrast, adsorption on an oxygen-modified copper surface leads to a rather disordered layer. The results are compared with the adsorption carried out on a polycrystalline copper surface after immersion in solutions of lysine at various pH values. The adsorption was monitored by polarization modulation infrared spectroscopy (PM-IRRAS). The chemistry of the adsorbed molecules is function of the starting chemical form of the lysine molecules imposed by the pH of the solution. The combination of the two techniques and various sets of adsorption conditions will give important insight into the adsorption of biomolecules on metal surfaces and the influence of water and surface oxygen.