On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

 The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L ¹ topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L ¹ to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term. (Accepted 25, October 2002) Published online March 14, 2003 Communicated by P.-L. Lions     

Detection of formate, rather than carbon monoxide, as the stoichiometric coproduct in conversion of fatty aldehydes to alkanes by a cyanobacterial aldehyde decarbonylase

The second of two reactions in a recently discovered pathway through which saturated fatty acids are converted to alkanes (and unsaturated fatty acids to alkenes) in cyanobacteria entails scission of the C1-C2 bond of a fatty aldehyde intermediate by the enzyme aldehyde decarbonylase (AD), a ferritin-like protein with a dinuclear metal cofactor of unknown composition. We tested for and failed to detect carbon monoxide (CO), the proposed C1-derived coproduct of alkane synthesis, following the in vitro conversion of octadecanal (R-CHO, where R = n-C(17)H(35)) to heptadecane (R-H) by the Nostoc punctiforme AD isolated following its overproduction in Escherichia coli. Instead, we identified formate (HCO(2)(-)) as the stoichiometric coproduct of the reaction. Results of isotope-tracer experiments indicate that the aldehyde hydrogen is retained in the HCO(2)(-) and the hydrogen in the nascent methyl group of the alkane originates, at least in part, from solvent. With these characteristics, the reaction appears to be formally hydrolytic, but the improbability of a hydrolytic mechanism having the primary carbanion as the leaving group, the structural similarity of the ADs to other O(2)-activating nonheme di-iron proteins, and the dependence of in vitro AD activity on the presence of a reducing system implicate some type of redox mechanism. Two possible resolutions to this conundrum are suggested.     

Dinuclear and Mononuclear Platinum(II) and Palladium(II) Complexes with Modified 2,2′‐Dipyridylamine Ligands Featuring a Cisplatin Analogous Structure Motif

In modern cancer therapy the clinical application of platinum‐based drugs is more and more limited by the occurrence of intrinsic or acquired resistances. In this context the potential use of dinuclear platinum complexes in chemotherapy is increasingly relevant. The novel complexes Pd(Bzdpa)Cl₂, Pd₂(C₄H₈(dpa)₂)Cl₄, and Pt₂(C₄H₈(dpa)₂)Cl₄ allow a direct comparison of mono‐ and dinuclear palladium and platinum complexes respectively deriving from a 2,2′‐dipyridylamine (Hdpa) ligand system. They were characterized by single crystal X‐ray analysis as well as infrared spectroscopy and elemental analysis. The cisplatin analogous mononuclear palladium complex Pd(Bzdpa)Cl₂ ( 1 ) (Bzdpa: (2,2′‐dipyridylbenzyl)amine) belongs to a range of 2,2′‐dipyridylamine‐based compounds which were extensively studied in our laboratories. 1 crystallizes in the orthorhombic space group Pna2₁ with a = 13.722(3), b = 13.457(3), c = 9.483(2), V = 1751.1(6) ų, and Z = 4. The metal binding motif of 1 was expanded by a flexible butyl‐linker to form the tetradentate C₄H₈(dpa)₂ ligand. The resulting isotypic dinuclear complexes Pd₂(C₄H₈(dpa)₂)Cl₄·2CH₃CN ( 2 ) and Pt₂(C₄H₈(dpa)₂)Cl₄·2CH₃CN ( 3 ) crystallize in the triclinic space group with a = 7.8427(2), b = 8.7940(2), c = 11.7645 (3), α = 79.219(2)°, β = 84.033(2)°, γ = 87.744(2)°, V = 792.58(3) ų ( 2 ) and a = 7.831(5), b = 8.814(5), c = 11.817(5), α = 79.271(5)°, β = 83.571(5)°, γ = 88.063(5)°, V = 796.3(8) ų ( 3 ), both with one centrosymmetrical molecule in the unit cell.     

Kupferbestimmung im Blute

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