A molecular orbital study of trans-polyenes to 18 double bonds

Calculations involving molecular orbitals have appeared in the chemical literature over the past few years, but all have used smalltrans-polyenes. We now report extended Huckel molecular orbital calculations ontrans-polyenes of up to 18 double bonds (36 carbons and 38 hydrogen atoms). Information obtained from these calculations include total energies, bond gaps, and net charges on each atom. Also found is that the band gap approaches 1.41 eV as the number of double bonds approaches infinity. This value is quite close to reported experimental values. Data are also presented for polyenes assuming equal C-C bond lengths.     

Influence of HCl on the stability of liquid lamellae between two colliding bubbles in aqueous solutions ofn-fatty acids

The effect of HCl on life time of liquid lamellae created between two colliding bubbles in aqueous solutions ofn-fatty acids were studied. The results show, that the addition of HCl has a pronounced influence on life time of the lamellae. At low fatty acid concentration the lifetime of the lamellae in the acidified solution is higher than in the nonacidified solution, but at higher fatty acid concentration the effect reverses. The analysis of these experimental results show that the characteristic influence of HCl on lamellae lifetime can be explained by the formation of distinct association states of the fatty acids in the liquid phase at different concentration ranges. The results are discussed with respect to bubble coalescence in gas-liquid contactors.     

Production and energetic use of biogas from energy crops and wastes in Germany

The production of biogas for reducing fossil CO₂ emissions is one of the key strategic issues of the German government and has resulted in the development of new process techniques and new technologies for the energetic use of biogas. Progress has been made in cultivating energy crops for biogas production, in using new reactor systems for anaerobic digestion, and in applying more efficient technologies for combined heat and power production. Recently, integration of fuel cells within the anaerobic digestion process was started, and new technologies for biogas upgrading and conversion to hydrogen were tested. This article describes the trends in Germany for achieving more efficient energy production.     

Racemic and Quasi‐Racemic X‐ray Structures of Cyclic Disulfide‐Rich Peptide Drug Scaffolds

Cyclic disulfide‐rich peptides have exceptional stability and are promising frameworks for drug design. We were interested in obtaining X‐ray structures of these peptides to assist in drug design applications, but disulfide‐rich peptides can be notoriously difficult to crystallize. To overcome this limitation, we chemically synthesized the L ‐ and D ‐forms of three prototypic cyclic disulfide‐rich peptides: SFTI‐1 (14‐mer with one disulfide bond), cVc1.1 (22‐mer with two disulfide bonds), and kB1 (29‐mer with three disulfide bonds) for racemic crystallization studies. Facile crystal formation occurred from a racemic mixture of each peptide, giving structures solved at resolutions from 1.25 Å to 1.9 Å. Additionally, we obtained the quasi‐racemic structures of two mutants of kB1, [G6A]kB1, and [V25A]kB1, which were solved at a resolution of 1.25 Å and 2.3 Å, respectively. The racemic crystallography approach appears to have broad utility in the structural biology of cyclic peptides.     

The enumerative geometry of surfaces and modular forms

Let be a surface, and let be a holomorphic curve in representing a primitive homology class. We count the number of curves of geometric genus with nodes passing through generic points in in the linear system for any and satisfying .

When , this coincides with the enumerative problem studied by Yau and Zaslow who obtained a conjectural generating function for the numbers. Recently, Göttsche has generalized their conjecture to arbitrary in terms of quasi-modular forms. We prove these formulas using Gromov-Witten invariants for families, a degeneration argument, and an obstruction bundle computation. Our methods also apply to blown up at 9 points where we show that the ordinary Gromov-Witten invariants of genus constrained to points are also given in terms of quasi-modular forms.     

Calcium

Ohne Zusammenfassung