A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

Insights into brain microstructure from the T2 distribution

T2 weighting is particularly sensitive, but notoriously unspecific, to a wide range of brain pathologies. However, careful measurement and analysis of the T2 decay curve from brain tissue promise to provide much improved pathological specificity. In vivo T2 measurement requires accurate 180 pulses and appropriate manipulation of stimulated echoes; the most common approach is to acquire multiple echoes from a single slice. The T2 distribution, a plot of component amplitude as a function of T2, can be estimated using an algorithm capable of fitting a multi-exponential T2 decay with no a priori assumptions about the number of exponential components. T2 distributions from normal brain show peaks from myelin water, intra/extracellular water and cerebral spinal fluid; they can be used to provide estimates of total water content (total area under the T2 distribution) and myelin water fraction (MWF, fractional area under the myelin water peak), a measure believed to be related to myelin content. Experiments on bovine brain suggest that magnetization exchange between water pools plays a minor role in the T2 distribution. Different white matter structures have different MWFs. In normal white matter (NWM), MWF is not correlated with the magnetization transfer ratio (MTR) or the diffusion tensor fractional anisotropy (FA); hence it provides unique information about brain microstructure. Normal-appearing white matter (NAWM) in multiple sclerosis (MS) brain possesses a higher water content and lower MWF than controls, consistent with histopathological findings. Multiple sclerosis lesions demonstrate great heterogeneity in MWF, presumably due to varying myelin contents of these focal regions of pathology. Subjects with schizophrenia were found to have significantly reduced MWF in the minor forceps and genu of the corpus callosum when compared to controls, suggesting that reduced frontal lobe myelination plays a role in schizophrenia. In normal controls, frontal lobe myelination was positively correlated with both age and education; this result was not observed in subjects with schizophrenia. A strong correlation between MWF and the optical density from the luxol fast blue histological stain for myelin was observed in formalin-fixed brain, supporting the use of the MWF as an in vivo myelin marker.     

Synthesis of bisimines of pyrene and dibenz[a,h]anthracene

The preparation of 3b,4a,7b,8a-tetrahydro-4H,8H-pyreno[4,5-b:9,10-b']bisazirine and of 1a,6b,7a,12b-tetrahydro-1H,7H-dibenz[3,4:7,8]anthra[1,2-b:5,6-b']bisazirine is described. The corresponding diepoxides were reacted with sodium azide in aqueous acetone and the mixtures of trans-azido alcohols, so formed, were cyclized by tri-n-butylphosphine.     

On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

Über ebene affine Inzidenzgruppen

For a translation plane P with respect to f we consider the group of collineations generated by all elations fixing f and a point F of f. All subgroups or are determined which operate regularly on the points of the affine plane P. Group-theoretic and operating properties of the groups are stated especially for the finite and the Desarguesian cases. In the latter case the companion NL-near modules are constructed. Finally we characterize the groups within PGL(3, K) with commutative field K of finite characteristic.     

Direct 23Na NMR observation of mixed cations residing inside a G-quadruplex channel

We report direct (23)Na NMR observation for the presence of mixed cations (Na(+)/K(+), Na(+)/Rb(+), Na(+)/Sr(2+)) inside the G-quadruplex channel formed by the self-association of guanosine 5'-monophosphate at pH 8.     

New 4-(benzotriazol-1-yl)-1,2,3-triazole derivatives

A new 4-(benzotriazol-1-yl)-1,2,3-triazole structure was obtained by the diazotization reaction of either of 1-(2-aminophenyl)-4-carboxamido-5-amino-1H-1,2,3-triazole ( 1c ) or of the corresponding Dimroth isomer 1d . It underwent some common reactions to evaluate its chemical behaviour and structure. An analogous reaction sequence was carried out from the 2-nitro-4-methylphenyl azide, to assign the structure to the nitro derivatives prepared. The structure of the new compounds prepared was confirmed by chemical and spectroscopic methods.     

The Surface Energy of MgO: Multiscale Reconstruction from Thermal Groove Geometry

The surface energy of MgO is determined using experimental data collected from equilibrated thermal grooves circumscribing island grains. Local equilibrium assumptions at each groove require that the Herring equations be satisfied at each data site, thereby yielding a large and overdetermined system of equations involving the surface energy . This inverse problem is then solved using a new technique that is statistical in nature and multiscale in implementation. The resulting discrete solution represents a statistically significant representation of the surface energy of MgO as a function of surface orientation. Comparisons to results derived from a more traditional approach, along with suggested further applications, are discussed.     

New 1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidine derivatives II

The 7‐chloro‐3‐(2‐chlorobenzyl)‐ and 7‐chloro‐3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐d]pyrimidines ( 1 and 4 ), by nucleophilic replacement with some hydrazides, gave the corresponding 7‐hydrazidoderivatives ( 2a‐e and 5a‐e ). These, by heating in Dowtherm, underwent an intramolecular cyclization to form the new tricyclic 7‐substituted‐3‐(2‐chlorobenzyl)‐ and 3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidines ( 3a‐d and 6a‐d ). The 7‐hydrazino‐3‐(2‐chlorobenzyl)‐ and 7‐hydrazino‐3‐(2‐fluorobenzyl)‐triazolo‐pyrimidines ( 9a and 9b ) were also prepared via the corresponding mercapto ( 7a and 7b ) and thiomethyl ( 8a and 8b ) derivatives.     

Thermal analysis of glasses for proecological applications

Thermal behaviour and biochemical activity of potassium-silicate-phosphate glasses modified by addition of Ca, Mg, acting as ecological fertilisers of controlled release rate of the nutrients for plants were studied. It has been found that the biochemical activity of silicate-phosphate glasses depends on the nature and the number of components forming the glassy framework and is related to the thermal stability of glass demonstrated by the formation of new compounds during the process of crystallisation. It is proved that these seemingly different properties are determined by the same parameters which are the strengths bonds of glass network-formers and modifiers as well as their chemical affinity. This revised version was published online in July 2006 with corrections to the Cover Date.