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.     

Solution conformation by NMR and molecular modeling of three sulfide-free somatostatin octapeptide analogs compared to angiopeptin

Summary The conformation in dimethylsulfoxide of the somatostatin derivative angiopeptin and of three disulfide-free analogs was estimated by two-dimensional nuclear magnetic resonance spectroscopy at room temperature. The resulting 3D molecular graphics were compared and shown to reflect the observed differences in the inhibition of restenosis after rat aorta balloon injury by these octapeptide inhibitors. Angiopeptin and its active analog 2 displayed a relatively rigid conformation of the cyclic hexapeptide backbone due to the presence of two well-defined hydrogen bonds, further stabilized by a third hydrogen bond outside the ring. No such constraints were detected for the two biologically inactive analogs, which, compared to 2, had a two-atom longer or shorter hexapeptide ring. The well-defined structure of compound 2 may serve as an improved pharmacophore for this new class of drugs.     

An Isolated Nitridyl Radical‐Bridged {Rh(N.)Rh} Complex

Photochemical activation of [(PNNH)Rh(N₃)] (PNNH=6‐di‐(tert‐butyl)phosphinomethyl‐2,2′‐bipyridine) complex 2 produced the paramagnetic (S=1/2), [(PNN)Rh?N^.‐Rh(PNN)] complex 3 (PNN^?=methylene‐deprotonated PNNH), which could be crystallographically characterized. Spectroscopic investigation of 3 indicates a predominant nitridyl radical (^.N^2?) character, which was confirmed computationally. Complex 3 reacts selectively with CO, producing two equivalents of [(PNN)Rh^I(CO)] complex 4 , presumably by nitridyl radical N,N‐coupling.     

Tritopic NHC Precursors: Unusual Nickel Reactivity and Ethylene Insertion into a C(sp3)–H Bond

The imidazolium chloride [C₃H₃N(C₃H₆NMe₂)N{C(Me)(=NDipp)}]Cl ( 1 ; Dipp=2,6‐diisopropyl phenyl), a potential precursor to a tritopic N^imineC^NHCN^amine pincer‐type ligand, reacted with [Ni(cod)₂] to give the Ni^I‐Ni^I complex 2 , which contains a rare cod‐derived η³‐allyl‐type bridging ligand. The implied intermediate formation of a nickel hydride through oxidative addition of the imidazolium C−H bond did not occur with the symmetrical imidazolium chloride [C₃H₃N₂{C(Me)(=NDipp)}₂]Cl ( 3 ). Instead, a Ni−C(sp³) bond was formed, leading to the neutral N^imineCHN^imine pincer‐type complex Ni[C₃H₃N₂{C(Me)(=NDipp)}₂]Cl ( 4 ). Theoretical studies showed that this highly unusual feature in nickel NHC chemistry is due to steric constraints induced by the N substituents, which prevent Ni−H bond formation. Remarkably, ethylene inserted into the C(sp³)−H bond of 4 without nickel hydride formation, thus suggesting new pathways for the alkylation of non‐activated C−H bonds.     

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.