Obtuse cones in Hilbert spaces and applications to partial differential equations

The positive cone K in a partially ordered Hilbert space is said to be obtuse with respect to the inner product if the dual cone $\text{K}{}^1\text{? K}$. Obtuseness of cones with respect to non-symmetric bilinear forms is also defined and characterized. These results are applied to the generalized Sobolev space associated with an elliptic boundary value problem, in particular to the question of determining the non-negativity of the Green's function. A notion of strict obtuseness is defined, characterized and applied to the question of strict positivity of the Green's function. Applications to positivity preserving semi-groups are also given.     

Random partial diffuser as beam splitter in a new,common path interferometer

Use of a random partial diffuser is suggested as a beam spitter. An aberration-free reference beam coaxial with the test beam is obtained when the latter converges on the diffuser. Based on this principle, an interferometer has been realised for absolute measurements with a sensitivity equal to that of a Mach-Zehnder interferometer. A large variety of optical components can be tested by this simple and inexpensive interferometer which could replace the already existing ones in optical workshops.     

Temporal correlation vortices and topological dispersion

Interference measurements of a polychromatic partially coherent light source verify the existence of a temporal correlation vortex. Topological dispersion is found to destabilize this singularity.     

Properly designed modular asymmetric synthesis for enantiopure sulfinamide auxiliaries from N-sulfonyl-1,2,3-oxathiazolidine-2-oxide agents

Simple and practical asymmetric synthesis of functionally differentiated aminoindanol based endo-N-sulfonyl 1,2,3-oxathiazolidine-2-oxide as sulfinyl transfer agents are developed. The importance of these new and unique sulfinyl transfer reagents are exemplified by the expedient production of several sulfinamide ligands, including either enantiomer of (R)-tert-butanesulfinamide in excellent yields and enantiopurities.     

A survey on Zariski cancellation problem

In this survey article we describe known results and open questions on the Zariski cancellation problem, highlighting recent developments on the problem. We also discuss its close relationship with some of the other central problems on polynomial rings.     

Norm inequalities related to the matrix geometric mean

Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.     

Three Dimensional Branched Gold Nanostructures on Reduced Graphene Oxide Films Formed at a Liquid/Liquid Interface

Interfacing anisotropic gold nanostructures with graphene can open up new avenues for modifying the light–matter interaction of graphene. A chemical route is explored to synthesize branched gold nanostructures on reduced graphene oxide (rGO) layers by in situ reduction, assisted by binary surfactant mixtures containing tetraoctylammonium bromide with cetyltrimethy­lammonium bromide, sodium dodecylsulfate, or sodium citrate. The hybrid material self‐assembles at a liquid/liquid interface forming a free‐standing film. Electron microscopy studies reveal the morphology, microstructure, and crystallinity of the hybrids. The gold nanostructures are branched in three dimensions and possess various shapes, such as irregular stars, multipods, and spiky features, interspersed with rGO layers. The hybrids exhibit plasmon modes in the visible and near‐infrared region due to the shape anisotropy. The enhancement effect of the spiky features is also observed in the Raman spectra. The growth mechanism of the branched nanostructures is followed by kinetic studies and indicates that the formation of multiple twinned crystals is the key factor for branching.     

Simultaneous determination of centbutindole and its hydroxy metabolite in serum by high-performance liquid chromatography.

A high-performance liquid chromatographic assay has been developed and validated for the determination of centbutindole and its hydroxy metabolite in serum. The method involves extraction of serum samples with diethyl ether at pH greater than 8, back-extraction into 0.5 M hydrochloric acid and finally again with diethyl ether after addition of 2 M potassium hydroxide. Separation was accomplished by reversed-phase high-performance liquid chromatography on a cyano column with an acetonitrile-phosphate buffer system. The recovery of centbutindole and its metabolite was always greater than 80%. Calibration curves were linear over the concentration range 0.25-5 ng/ml for centbutindole and 0.05-1 ng/ml for the hydroxy metabolite. Although the lower limit of detection was 0.1 ng/ml for centbuntindole and 0.02 ng/ml for the hydroxy metabolite, the reliable limits of quantitation were 0.25 and 0.05 ng/ml, respectively, using 4 ml of serum.