Calculated ultraviolet exposure levels for a healthy vitamin D status

The dangers of overexposure to sunlight have been well publicized, but less attention has been given to an acknowledged benefit of exposure to UV radiation; that being the cutaneous synthesis of vitamin D3. Here we define a standard vitamin D dose on the basis of recently recommended requirements for vitamin D that take account of its risk reduction role in a variety of diseases, and present a web-based tool that enables the reader to calculate associated exposure times for any time and place using either default values or user-selected conditions. Either it is not possible to synthesize vitamin D3 at high latitudes in winter, or the exposure time required to reach a standard dose is sometimes impractical. Where solar UV is sufficient, a risk-benefit analysis of sunburn vs. vitamin D3 synthesis shows that the best time for brief sun exposure is in the middle of the day. For low solar elevation angles common at high latitudes, a fine line exists between adequate UV exposure for vitamin D3 synthesis and a risk of sun burn.     

Regioselectivity in aqueous palladium catalysed hydroxycarbonylation of styrene: a catalytic and mechanistic study

Regioselectivity control was studied in palladium catalysed hydroxycarbonylation of styrene in neat water with water-soluble phosphines, mostly trisulfonated triphenylphosphine, TPPTS, but also N-bis(N',N'-diethyl-2-aminoethyl)-4-aminomethylphenyl-diphenylphosphine, N3P. The factor giving the highest changes in regioselectivity in the TPPTS system, under similar reaction conditions, is the temperature. In the N3P case, only a minor variation in the n/i ratio as a function of temperature is observed. Insitu normal- and high-pressure NMR experiments were performed to obtain further information about the catalytic cycle and the reaction intermediates. Two palladium hydride intermediates, a palladium eta3-benzylic complex and both the branched and linear palladium acyl complexes were identified in the HP NMR experiments. The hydroxycarbonylation in water using styrene as a substrate operates using a hydride mechanism for pathways leading to both linear and branched product. Insertion of styrene in the palladium-hydride bond gives an eta3-benzyl compound. A high CO pressure gives a kinetic preference for the iso-acyl in the next step. In the TPPTS system, at moderate temperatures, the hydrolysis of the iso-acyl is faster than its conversion to the thermodynamically more stable n-acyl. A low n/i therefore requires high pressures and reasonably low temperatures. The N3P ligand always favours the linear product since isomerisation of the iso-acyl to the n-acyl in this system is fast under all conditions investigated.     

A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues

In this paper, we derive “universal” inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin–Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain.     

Spectral asymptotics of periodic elliptic operators

We demonstrate that the structure of complex second-order strongly elliptic operators H on with coefficients invariant under translation by can be analyzed through decomposition in terms of versions , , of H with z-periodic boundary conditions acting on where . If the s emigroup S generated by H has a H?lder continuous integral kernel satisfying Gaussian bounds then the semigroups generated by the have kernels with similar properties and extends to a function on which is analytic with respect to the trace norm. The sequence of semigroups obtained by rescaling the coefficients of by converges in trace norm to the semigroup generated by the homogenization of . These convergence properties allow asymptotic analysis of the spectrum of H. Received September 1, 1998; in final form January 14, 1999