Local mode and normal mode interpretations of the CH and CD stretching vibrational manifolds of 1,1-dideuteroethene

The =CH2 AND =CD2 stretching vibrational overtones of H2C=CD2 have been studied up to V= 6 and V= 3, respectively. We report their interpretation in terms of a transition from normal to local modes, involving Fermi resonance with the C=C stretching and CH2 scissoring vibrations. We discuss the alternative representation of the vibrational Hamiltonian matrix in local mode and normal mode basis functions, and conclude that the normal mode basis offers greater flexibility in representing small anharmonic couplings with other modes.

Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds

In this paper we extend the well-known Leinfelder–Simader theorem on the essential selfadjointness of singular Schrödinger operators to arbitrary complete Riemannian manifolds. This improves some earlier results of Shubin, Milatovic and others.

The Brownian traveller on manifolds

We study the inuence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the at case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the at case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

Droplet shape of an anisotropic liquid

We investigate how a droplet of a complex liquid is modified by its internal nanoscale structure. As the liquid passes from an isotropic disordered state to an anisotropic layered morphology, the droplet shape switches from a smooth spherical cap to a terraced hyperbolic profile, which can be modeled as a stack of thin concentric circular disks with a repulsion between adjacent disk edges. Our ability to resolve the detailed shape of these defect-free droplets offers a unique opportunity to explore the underlying physics.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

Carbon suboxide: the vibrational dependence of the v7 bending potential function

Data on the vibrational energy levels and rotational constants of carbon suboxide for the low-wavenumber bending mode ν7 are reviewed, in the ground-state manifold, and in the ν2-, ν3-, ν4-, and ν2 + ν4-state manifolds. Following the procedure developed by Duckett, Mills, and Robiette [J. Mol. Spectrosc. 63, 249 (1976)] the data have been inverted to give the effective bending potential in ν7 for each of these five states. Values are obtained for various other parameters in the effective vibration-rotation Hamiltonian. The potential and rotational constants in ν2 + ν4 are given to a close approximation by linear extrapolation from the ground state through the ν2 and ν4 states.

Peroxynitrite-modified collagen-II induces p38/ERK and NF-kappa B-dependent synthesis of prostaglandin E-2 and nitric oxide in chondrogenically differentiated mesenchyrnal progenitor cells

Objective: Peroxynitrite (ONOO-) is formed in the inflamed and degenerating human joint. Peroxynitrite-modified collagen-II (PMC-II) was recently discovered in the serum of patients with osteoarthritis (OA) and rheumatoid arthritis (RA). Therefore we investigated the cellular effects of PMC-II on human mesenchymal progenitor cells (MPCs) as a model of cartilage and cartilage repair cells in the inflamed and degenerating joint. Design: MPCs were isolated from the trabecular bone of patients undergoing reconstructive surgery and were differentiated into a chondrogenic lineage. Cells were exposed to PMC-II and levels of the proinflammatory mediators nitric oxide (NO) and prostaglandin E-2 (PGE(2)) measured. Levels of inducible nitric oxide synthase (iNOS) and cyclooxygenase-2 (COX-2), phosphorylated mitogen activated protein kinases (MAPKs) and nuclear factor kappa B (NF-kappa B) activation were measured by enzyme linked immunosorbent assay (ELISA) together with specific MAPK and NF-kappa B inhibitors. Results: PMC-II induced NO and PGE(2) synthesis through upregulation of iNOS and COX-2 proteins. PMC-II also lead to the phosphorylation of MAPKs, extracellularly regulated kinase 1/2 (ERK1/2) and p38 [but not c-Jun NH2-terminal kinase (JNK1/2)] and the activation of proinflammatory transcription factor NF-kappa B. Inhibitors of p38, ERK1/2 and NF-kappa B prevented PMC-II induced NO and PGE(2) synthesis, NOS and COX-2 protein expression and NF-kappa B activation. Conclusion: iNOS, COX-2, NF-KB and MAPK are known to be activated in the joints of patients with OA and RA. PMC-II induced iNOS and COX-2 synthesis through p38, ERK1/2 and NF-KB dependent pathways suggesting a previously unidentified pathway for the synthesis of the proinflammatory mediators, NO and PGE(2), further suggesting that inhibitors of these pathways may be therapeutic in the inflamed and degenerating human joint. (c) 2005 OsteoArthritis Research Society International. Published by Elsevier Ltd. All rights reserved.