A simple route to 6- and 7-fluoro-substituted naphthalene-1-carboxylic acids

A simple one-pot method for the synthesis of 6-fluoro- and 6,7-difluoro-1-naphthoic acid is described. 6-Fluoro-1-naphthoic acid can be converted into 7-fluoro-1-naphthoic acid in three straightforward steps.     

Heteroaryl substituted ansa‐titanocene anti‐cancer drugs derived from fulvenes and titanium dichloride

Starting from 2‐furylfulvene (1a) , 2‐thiophenylfulvene (1b) , and 1‐methyl‐2‐pyrrolylfulvene (1c), [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐furyl)ethanediyl] titanium dichloride (2a) , [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐thiophenyl)ethanediyl] titanium dichloride (2b) , and [1,2‐di(cyclopentadienyl)‐1,2‐bis‐(1‐methyl‐2‐pyrrolyl)ethanediyl] titanium dichloride (2c) were synthesized. When titanocenes (2a–c) were tested against pig kidney carcinoma cells (LLC‐PK), inhibitory concentrations (50%) of 4.5 × 10^?4 M , 2.9 × 10^?4 M and 2.0 × 10^?4 M respectively were observed. Copyright © 2005 John Wiley & Sons, Ltd.     

Electronic structure and electron dynamics at the GaSb(0 0 1) surface studied by femtosecond pump-and-probe pulsed laser photoemission spectroscopy

Transiently excited electron states at the GaSb(0 0 1) surface have been studied by means of time- and angle-resolved photoemission spectroscopy based on a femtosecond laser system. A normally unpopulated surface electron state has been found at ∼250 meV above the valence band maximum with a strong confinement at the center of the surface Brillouin zone. The lifetime of transiently excited carriers at the intergap surface states has been found to be ∼11 ps, associated with rapid carrier diffusion.     

Prescriptions for gravitational initial data as judged by a simple radiating model

Several methods of prescribing initial data for gravitational and matter fields, which are intended to eliminate extraneous radiation that is not produced by the matter source, are analysed in a simple exactly soluble radiating model. The model consists of an harmonic oscillator coupled to a scalar field along future light cones of Minkowski space time. In particular we analyze the asymptotic regime of the oscillator and find it is characterized essentially by two distinct decay modes. They differ in the way they behave both in the limit of small coupling constant and in a certain Newtonian limit. As a criterion to select initial data for the field with no extra radiation, we require that these initial data sets should put the oscillator from the start into the asymptotic regime. The underlying hypothesis here is that initial transients result from excitation of the oscillator by incoming radiation. We then see that the requirement of a uniform Newtonian limit leads to unique data for the scalar field for each arbitrary data set for the oscillator. We further find that this unique data set indeed satisfies our criterion.     

Metrics on products of surfaces with non-positive sectional curvature

Let (S _i, g_i),i=1, 2 be two compact riemannian surfaces isometrically embedded in euclidean spaces. In this paper we show that ifM=S ₁×S₂,then for any functionF: M→R, the graph ofF, i.e. the manifold {(x, F(x)): x∈M}, does not have positive sectional curvature.     

Ueber einen neuen Apparat zur directen Bestimmung der Kohlens?ure

Ohne Zusammenfassung     

Wavelet expansions forBMOρ (w)‐functions

We give necessary and sufficient conditions on the wavelet coefficients of a function for being a member of some BMO_φ (w) space. We achieve this characterization for a wide variety of wavelet systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Newtonian limit of general relativity

We establish rigorous results about the Newtonian limit of general relativity by applying to it the theory of different time scales for non-linear partial differential equations as developed in [4, 1, 8]. Roughly speaking, we obtain a priori estimates for solutions to the Einstein's equations, an intermediate, but fundamental, step to show that given a Newtonian solution there exist continuous one-parameter families of solutions to the full Einstein's equations — the parameter being the inverse of the speed of light — which for a finite amount of time are close to the Newtonian solution. These one-parameter families are chosen via aninitialization procedure applied to the initial data for the general relativistic solutions. This procedure allows one to choose the initial data in such a way as to obtain a relativistic solution close to the Newtonian solution in any a priori given Sobolev norm. In some intuitive sense these relativistic solutions, by being close to the Newtonian one, have little extra radiation content (although, actually, this should be so only in the case of the characteristic initial data formulation along future directed light cones).Our results are local, in the sense that they do not include the treatment of asymptotic regions; global results are admittedly very important — in particular they would say how differentiable the solutions are with respect to the parameter — but their treatment would involve the handling of tools even more technical than the ones used here. On the other hand, this local theory is all that is needed for most problems of practical numerical computation.