Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

A bound for minimal graphs with a normal at infinity

It is shown that a minimal graph with a normal at infinity is in a-priori bounded vertical distance from its approximating halfcatenoid. This is used to show that the exterior contact angle problem is wellposed under natural geometric conditions on the domain, while the exterior Dirichlet problem can be solvable only for data which satisfy an oscillation bound.This paper was written under the support of the Deutsche Forschungsgemeinschaft while the author was visiting the department of mathematics at Stanford University.This article was processed by the author using the LaT_EX style filepljour1 from Springer-Verlag.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.     

A liquid chromatography-mass spectrometry method for the quantification of both etoricoxib and valdecoxib in human plasma

A practicable and selective liquid chromatography-mass spectrometry assay for the determination of two cyclooxygenase-2 inhibitors, etoricoxib and valdecoxib, in human plasma is presented. The analytical technique is based on reversed-phase high-performance liquid chromatography (HPLC) coupled to atmospheric pressure chemical ionisation (APCI) mass spectrometry (Finnigan Mat LCQ ion trap). Mass analysis was performed in the positive ion mode. The ion trap was operated in the tandem MS mode (MS2) and the transitions of etoricoxib (m/z 359.2 --> 280.3) and valdecoxib (m/z 315.1 --> 235.1) were followed by selected reaction monitoring. Retention times of etoricoxib and valdecoxib were 1.05 and 1.08 min, respectively. The method was validated over a linear range 10-2500 and 5-1000 microg/L using the other substrate as internal standard. After validation, the method was used to study the pharmacokinetic pro fi le of etoricoxib or valdecoxib in a healthy volunteer after administration of a single oral dose (valdecoxib, 20 mg; etoricoxib, 90 mg). The presented method was suf fi cient to cover more than 90% of the area under the plasma concentration time curve.     

Gilmicolin and Mycorrhizinol,Two New Metabolites of Gilmaniella humicolaBARRON

The structure of gilmicolin and mycorrhizinol, two new metabolites isolated from culture filtrates of Gilmaniella humicola BARRON , have been shown to be 3 and 15 respectively by spectral and chemical studies. The X-ray analysis of gilmicolin ( 3 ) is also reported.     

Approaching supramolecular functionality

Functional molecules require a high degree of complexity which is difficult to achieve by covalent synthesis. This article discusses supramolecular approaches to the creation of larger architectures through noncovalent bonds, self-assembly, and template strategies. It highlights selected examples for the structural and conformational control of function and attempts to identify difficulties and challenges which may arise in future.