Estimation and testing in generalized mean-reverting processes with change-point

In this paper, we study an inference problem in generalized Ornstein–Uhlenbeck processes with an unknown change-point when the drift parameter is suspected to satisfy a linear restriction. The testing problem studied generalizes a very recent problem about testing the existence of a change-point. To this end, we derive the asymptotic properties of the unrestricted estimator (UE) and the restricted estimator for the drift parameters, and we construct some shrinkage estimators (SEs). Further, we derive a test for testing the uncertain restriction and establish its asymptotic power. Moreover, we derive the asymptotic distributional risk of the proposed estimators and we prove that SEs dominate the UE. Finally, we present some numerical results which confirm the consistency of the proposed test as well as the superiority of the SEs over UE.     

Scattered and hereditarily irresolvable spaces in modal logic

When we interpret modal ? as the limit point operator of a topological space, the Gödel-Löb modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices S _α , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining a simple proof of the Abashidze–Blass theorem. On the other hand, when we interpret ? as closure in a topological space, the Grzegorczyk modal system Grz defines the class HI of hereditarily irresolvable spaces. We also give a partition of HI into α-slices H _α , where α ranges over all ordinals. For a subset A of a hereditarily irresolvable space X and an ordinal α, we introduce the α-representation of A, give an axiomatization of the α-representation of A, and characterize H _α in terms of α-representations. We prove that ${X \in {\bf H}_{1}}When we interpret modal ◊ as the limit point operator of a topological space, the G?del-L?b modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices S _α , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining a simple proof of the Abashidze–Blass theorem. On the other hand, when we interpret ◊ as closure in a topological space, the Grzegorczyk modal system Grz defines the class HI of hereditarily irresolvable spaces. We also give a partition of HI into α-slices H _α , where α ranges over all ordinals. For a subset A of a hereditarily irresolvable space X and an ordinal α, we introduce the α-representation of A, give an axiomatization of the α-representation of A, and characterize H _α in terms of α-representations. We prove that X ? H₁{X \in {\bf H}_{1}} iff X is submaximal. For a positive integer n, we generalize the notion of a submaximal space to that of an n-submaximal space, and prove that X ? H_n{X \in {\bf H}_{n}} iff X is n-submaximal. This provides topological completeness and definability results for extensions of Grz. We show that the two partitions are related to each other as follows. For a successor ordinal α = β + n, with β a limit ordinal and n a positive integer, we have H_a ?Scat = S_b+2n-1 èS_b+2n{{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\beta+2n-1} \cup {\bf S}_{\beta+2n}} , and for a limit ordinal α, we have H_a ?Scat = S_a{{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\alpha}} . As a result, we obtain full and faithful translations of ordinal complete extensions of Grz into ordinal complete extensions of GL, thus generalizing the Kuznetsov–Goldblatt–Boolos theorem.     

Impact of grain-dependent boron uptake on the electrochemical and electrical properties of polycrystalline boron doped diamond electrodes

A combination of high-resolution electrical and electrochemical imaging techniques, in conjunction with cathodoluminescence (CL), is used to investigate the electrochemical behavior of oxygen-terminated highly doped polycrystalline boron doped diamond (BDD). The BDD has a dopant density approximately 5 x 10(20) atoms cm(-3), grain size ca. 5-40 microm, and thickness 500 microm. CL imaging demonstrates that boron uptake is nonuniform across the surface of BDD, and conducting atomic force microscopy (C-AFM) highlights how this impacts on the local conductivity. While C-AFM shows no evidence for enhanced grain boundary conductivity, two characteristic conductivity domains are found with resistances of ca. 100 kOmega and ca. 50 MOmega. With the use of scanning electrochemical microscopy (SECM), local heterogeneities are also observed in the electroactivity of the BDD surface, consistent with the two different types of conducting regions. Local currents of the magnitude expected for metal-like behavior are observed in some regions, suggesting degenerative doping of the grains (supported by CL studies). In other regions, slower electron transfer is apparent. However, even for the reduction of Ru(NH(3))(6)(3+), which occurs at potentials far negative of the flat-band potential for oxygen-terminated BDD, all areas of the surface show some electroactivity. This study highlights that the spatially heterogeneous conductivity and corresponding electroactivity of BDD are readily resolved using a combination of C-AFM, SECM, and CL.     

Enantioselective synthesis of ferrocenyl nucleoside analogues with apoptosis-inducing activity

[reaction: see text] As a contribution to bioorganometallic chemistry, an enantioselective synthesis of novel carbocyclic nucleoside analogues with a ferroceno-cyclopentene backbone was developed. Diastereoselective cuprate 1,4-addition or Mukaiyama-Michael addition to a planar-chiral enoate (ethyl (E)-2-[2-methoxycarbonyl-ferrocenyl]-acrylate) allowed for the introduction of different side chains (RCH(2)). Other important steps include a Dieckmann cyclization and the attachment of the nucleobase (NB) in an iron-assisted S(N)1 reaction. Some of the target compounds were shown to exhibit significant apoptosis-inducing activity (LD(50) = 10-20 microM) against tumor cells.     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

Modelling internal erosion of cohesionless soils using a microstructural parameter

Internal erosion processes are of vital importance for the risk management of geotechnical structures as well as for the understanding of the macroscopic mechanical and hydraulic properties of the subsoil in various man-made constructions. Here, a 4-phase continuum model is presented and numerically applied to illustrative applications. The role of interfacial area and related microstructural parameters is addressed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A <Emphasis Type="Italic">p</Emphasis>-adic RANSAC algorithm for stereo vision using Hensel lifting

A p-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developed. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised p-adic hierarchical classification algorithm imitiating the known LBG quantization method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the “true” solution of the problem.