Bochner-Weitzenböck formulas and curvature actions on Riemannian manifolds

Gradients are natural first order differential operators depending on Riemannian metrics. The principal symbols of them are related to the enveloping algebra and higher Casimir elements. We give formulas in the enveloping algebra that induce not only identities for higher Casimir elements but also all Bochner-Weitzenböck formulas for gradients. As applications, we give some vanishing theorems.

     

In vivo isotropic 3D diffusion tensor mapping of the rat brain using diffusion-weighted 3D MP-RAGE MRI

The purpose of this study was to examine the potential of diffusion-weighted (DW) three-dimensional (3D) MP-RAGE MRI for diffusion-tensor mapping of the rat brain in vivo. A DW-3D-MP-RAGE (3D-DWI) sequence was implemented at 2.0 T using six gradient orientations and a b value of 1000 s/mm2. In this sequence, the preparation sequence with a "90 degrees RF-motion proving gradient (MPG): MPG-180 degrees RF-MPG-90 degrees RF" pulse train (DW driven equilibrium Fourier transform) was used to sensitize the magnetization to diffusion. A centric k-space acquisition order was necessary to minimize saturation effects (T1 contamination) from tissues with short relaxation time. The image matrix was 128x128x128 (interpolated from 64x64x64 acquisitions), which resulted in small isotropic DW image data (voxel size: 0.273x0.273x0.273 mm3). Moreover, 3D-DWI-derived maps of the fractional anisotropy (FA), relative anisotropy (RA) and main-diffusion direction were completely free of susceptibility-induced signal losses and geometric distortions. Two well-known commissural fibers, the corpus callosum and anterior commissure, were indicated and shown to be in agreement with the locations of these known stereotaxic atlases. The experiment took 45 min, and shorter times should be possible in clinical application. The 3D-DWI sequence allows for in vivo 3D diffusion-tensor mapping of the rat brain without motion artifacts and susceptibility to distortion.     

Monoamine oxidase inhibitory naphthoquinone and/or naphthalene dimers from Lemuni Hitam (Diospyros sp.), a Malaysian herbal medicine.

From the extract of a Malaysian herbal medicine, Lemuni Hitam (Diospyros sp.), which exhibited monoamine oxidase (MAO) inhibition, three new naphthoquinone and/or naphthalene dimers (lemuninols A-C, 1-3) were isolated together with 4,6-dihydroxy-5-methoxy-2-methyl-naphthalene (8) and six known monomers (4-7, 9 and 10). The structures were determined by spectroscopic methods including 2D-NMR techniques. Among them, lemuninol A showed 45% inhibition of MAO (mouse liver) at 5.0 x 10(-6) g/ml, and lemuninols B and C and a naphthoquinone (9) indicated weak activity. Some related quinones were also tested for their MAO inhibitory activities.     

Numerical analysis of fatigue striations

A computational model was developed to numerically analyse fatigue striations. The inclined strip yield model with continuous distributions of infinitesimal dislocations was utilized to express the crack tip plasticity in this model. The fatigue crack tip blunting process was approximated by sequential activation of two slip lines under loading, and crack closure during unloading was taken into account. The plastic zone at a growing fatigue crack tip at the maximum load was independent of the crack growth up to ten cycles while the reversed plastic zone decreased in a size to one twentieth of that at the maximum load as the crack grew. The ratio of these plastic zone sizes and also the crack tip opening displacement were quite different from the simple prediction by J.R. Rice for a stationary crack. The computed striation spacings were compared with the observed ones and moderate agreement between them obtained.     

On the Threshold of Long-Range Magnetic Order: UNi2/3Rh1/3Al and UCoAl Study

We present a comparative study of magnetism in UCoAl and UNi_2/3Rh_1/3Al single crystals. UCoAl is commonly believed to be an itinerant 5 f-electron metamagnet with B _c < 1 T with uniaxial anisotropy. Pressure and alloying effects on the ground state point to competing ferromagnetic and antiferromagnetic interactions to be responsible for the non-magnetic ground state. UNi_2/3Rh_1/3Al is a solid solution between an antiferromagnet (UNiAl) and a ferromagnet (URhAl) and may have a similar underlying microscopic mechanism of the non-magnetic ground state. Possible analogies between the two compounds are discussed.     

Semi-micro liquid chromatography of aromatic amino acid metabolites using isocratic elution and column switching

The concentrations of catecholamine-related compounds in body fluids reflect sympathetic nerve functions. Measuring the enzyme activity of these metabolic pathways will improve diagnosis since a variety of symptoms are reported. An isocratic elution system with two column switching valves was developed using three types of semi-micro columns for fast chromatographic analysis of catecholamine related compounds. Columns are a pentyl-bonded phase, 50 x 2.1 mm i.d., a phenylhexyl-bonded phase, 100 x 2.1 mm i.d. and an octadecyl-bonded phase, 100 x 2.1 mm i.d. The separation of 20 standard compounds was achieved within 25 min using reversed-phase ion-pair liquid chromatography with an electrochemical detector. This new system was applied for analysis of catecholamine-related compounds in pig brain, since pigs are a widely used animal model for transgenic manipulation of neural genes, and MHPG (or VMA), DOPAC, DOPA, NE, EP, DA, 5HTP and 5HIAA were quantified.