Convex-Concave Extensions

In this paper we introduce a new notion which we call convex-concave extensions. Convex-concave extensions provide for given nonlinear functions convex lower bound functions and concave upper bound functions, and can be viewed as a generalization of interval extensions. Convex-concave extensions can approximate the shape of a given function in a better way than interval extensions which deliver only constant lower and upper bounds for the range. Therefore, convex-concave extensions can be applied in a more flexible manner. For example, they can be used to construct convex relaxations. Moreover, it is demonstrated that in many cases the overestimation which is due to interval extensions can be drastically reduced. Applications and some numerical examples, including constrained global optimization problems of large scale, are presented.     

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.     

Analysis of Toxaphene (PCC) and Chlordane in Biological Samples by NCI Mass Spectrometry

Abstract

Several recent reports indicate that both toxaphene (polychlorocamphene, PCC) and chlordane are widespread pollutants in our environment. These insecticides, both complex mixtures of chlorinated hydrocarbons, are difficult to separate from each other. Thus the analyses of them in environmental samples are difficult and furthermore complicated by interferences from other chlorinated hydrocarbons such as PCB and DDT compounds. Mass fragmentography using the negative ions formed by chemical ionization proved to be useful to selectively detect the toxaphenes and the chlordanes without interferences from DDT. High concentrations of PCB still influence on the results and have to be removed in the clean-up procedure.     

Synthesis of functionalized cinnamaldehyde derivatives by an oxidative Heck reaction and their use as starting materials for preparation of Mycobacterium tuberculosis 1-deoxy-D-xylulose-5-phosphate reductoisomerase inhibitors

Cinnamaldehyde derivatives were synthesized in good to excellent yields in one step by a mild and selective, base-free palladium(II)-catalyzed oxidative Heck reaction starting from acrolein and various arylboronic acids. Prepared α,β-unsaturated aldehydes were used for synthesis of novel α-aryl substituted fosmidomycin analogues, which were evaluated for their inhibition of Mycobacterium tuberculosis 1-deoxy-D-xylulose 5-phosphate reductoisomerase. IC(50) values between 0.8 and 27.3 μM were measured. The best compound showed activity comparable to that of the most potent previously reported α-aryl substituted fosmidomycin-class inhibitor.     

Nitrogen-rich La-Si-Al-O-N oxynitride glass structures probed by solid state NMR

We investigate the local structures of oxynitride La-Si-(Al)-O-N glasses by ²⁹Si and ²⁷Al magic-angle spinning (MAS) solid state Nuclear Magnetic Resonance (NMR). The glasses studied span an unprecedented range of compositions, up to >50 at.% lanthanum and nitrogen out of the cations and anions, respectively, and achievable through a recently introduced glass preparation route. Transmission as well as scanning electron microscopy verified homogeneous samples over length-scales down to 20 nm. As the nitrogen content of the glasses increased, ²⁹Si NMR evidenced a progressive formation of Si-N bonds, with SiO₂N₂ tetrahedra dominating in the nitrogen-rich glass networks. In the oxygen-rich end of the series, aluminum is predominantly present in tetrahedral coordination as AlO₄, whereas the glasses with highest nitrogen contents have a major fraction of AlO₃N structural units. Trends in isotropic ²⁹Si and ²⁷Al chemical shifts and ²⁷Al quadrupolar couplings are compared with results of La-Si-Al-O glasses and are discussed in relation to the glass compositions and their proposed structures.