Asymptotics of collision integral matrix elements in the isotropic case

The method of nonlinear moments, when used to solve the Boltzmann equation, necessitates the calculation of collision integral matrix elements. The matrix elements are hard to calculate numerically, especially at large indices. The asymptotics of the matrix elements are constructed. In terms of the model of pseudopower particle interaction, a formula free of summation is derived. This makes it possible to find the asymptotic behavior of linear and nonlinear elements when two indices are large. For an arbitrary interaction cross section, asymptotic expansions of linear and nonlinear matrix elements in one index are obtained. For Maxwellian molecules, asymptotic formulas are derived for three large indices.     

Scaling by Binormalization

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.     

Homoconjugated ketones with extended unsaturation: Wavelength-selective,regioselective, diastereoselective,and enantiospecific photochemical transformations of methyl 7-oxospiro[5.5]undeca-1,3-and -2,4,-diene-2-carboxylate

The title molecules were shown to photorearrange with remarkable selectivity. Wavelength variation steers the rearrangement modes, of which the [1,2]-acyl shift was found to be largely regioselective, diastereoselective, and enantiospecific. Chemical intercorrelation of products and mechanistic studies were carried out all along. The potential significance of these photochemical processes in selective synthetic schemes is discussed.     

Cobalt(II) and cobalt(III) dipicolinate complexes: solid state,solution, and in vivo insulin-like properties

The synthesis and characterization of Co(II) and Co(III) 2,6-pyridinedicarboxylate (dipic(2-)) complexes are reported. Solid-state X-ray characterizations were performed on [Co(H(2)dipic)(dipic)].3H(2)O and [Co(dipic)(mu-dipic)Co(H(2)O)(5)].2H(2)O. Two coordination modes not previously observed in dipicolinate transition metal complexes were observed in these complexes; one involves metal coordination to the short C-O (C=O) bond, and the other involves metal coordination to a protonated oxygen atom. Solution studies, including paramagnetic NMR and UV-vis spectroscopy, were done showing the high stability and low lability of the Co(III) complex, whereas the Co(II) complexes exhibited ligand exchange in the presence of excess ligand. The [Co(dipic)(2)](2-) complex has pH dependent lability and in this regard is most similar to the [VO(2)dipic](-) complex. The [Co(dipic)(2)](2-) was found to be effective in reducing the hyperlipidemia of diabetes using oral administration in drinking water in rats with STZ-induced diabetes. Oral administration of VOSO(4) was used as a positive control for metal efficacy against diabetes. In addition to providing a framework to evaluate structure-function relationships of various transition metal complexes in alleviating the symptoms of diabetes, this work describes novel aspects of structural and solution cobalt chemistry.     

Dynamic light scattering and cryogenic transmission electron microscopy investigations on metallo-supramolecular aqueous micelles: evidence of secondary aggregation

Metallo-supramolecular diblock copolymers consisting of a polystyrene (PS) block connected to a poly(ethylene oxide) (PEO) block by a bis(terpyridine)ruthenium complex (PS₂₀-[Ru]-PEO _y ) were used to prepare aqueous micelles. The length of the PS block was kept constant, while two PEOs of different molecular weight were used. The resulting hydrated micelles and aggregates were characterized by a combination of cryogenic transmission electron microscopy (cryo-TEM) and dynamic light scattering measurements. The results were compared to those obtained for a covalent counterpart (PS₂₂-b-PEO₇₀). Cryogenic transmission electron microscopy allowed visualization of the PS core of the micelles. Moreover, the aggregates result from clustering of individual micelles.     

A comparison principle for functions of a uniformly random subspace

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid.     

Separation of angular and energy relaxations of nonequilibrium electrons in a solid

We demonstrate that the collision integral of the kinetic equation for the interaction of hot electrons with phonons can be split into substantially different parts that correspond to elastic and inelastic collisions. In particular, this applies to electrons with energies of about 1 eV that propagate in semiconductors. The difference in the characteristic energy and momentum relaxation times makes it possible to separate the angular and energy relaxation processes. If the differential cross section of elastic scattering depends, not on the scattering angle, but on the directions of incident and scattered electrons (which is observed, e.g., for the interaction of an electron with piezoelectric lattice vibrations in A^IIIB^V compounds), the Laplacian in the equation that describes the spatial and energy distributions of electrons can be replaced by an elliptical operator; i.e., the electron diffusion turns out to be anisotropic.