Positive definite functions on the Heisenberg group

Work supported in part by the NSF     

Cotangent cohomology of Stanley-Reisner rings

Simplicial complexes X provide commutative rings A(X) via the Stanley- Reisner construction. We calculated the cotangent cohomology, i.e., T¹ and T² of A(X) in terms of X. These modules provide information about the deformation theory of the algebro geometric objects assigned to X.     

VNCl2(Pyridin)2 Synthese,IR-Spektrum und Kristallstruktur

VNCl₂(Pyridine)₂; Synthesis, I. R. Spectrum, and Crystal Structure VNCl₂(Pyridine)₂ is formed from the cyclothiazeno-vanadium(IV) complex [VCl(N₃S₂)(Pyridine)₂]₂ · 2 CH₂Cl₂ in boiling toluene in form of brown-red, hydrolysis sensitive crystal. It was characterized by its I.R. spectrum and an X-ray crystal structure determination. VNCl₂(Pyridine)₂crystallizes in the orthorhombic space group Pccn with four formula units per unit cell (668 observed independent reflexions, R = 0.055). Lattice constants: a = 1550, b = 924, c = 832 pm. Monomer molecules are situated on twofold rotation axes. They are stacked along the V?N axis to form columns V?N…V. The short VN bond of 160 pm corresponds to a triple bond, whereas the V…N distance of 256 pm indicates a weak interaction. The V? N(Pyridine) and V? Cl bond lengths are 213.0 and 233.5 pm, respectively.     

The non-selective voltage-activated cation channel in the human red blood cell membrane: reconciliation between two conflicting reports and further characterisation

Using the patch-clamp technique, the non-selective, voltage-activated cation channel in the human red blood cell (RBC) membrane was further characterised. Activity of the cation channel could be demonstrated at a range of salt concentrations with the current-voltage characteristics for monovalent cations going from linear to superlinear functions, depending on the cation concentration in the range of 100-500 mM. The non-selective voltage-activated cation channel was demonstrated to be permeable to the divalent cations Ca2+ and Ba2+, and even Mg2+. The current-voltage relations for the divalent cations were superlinear even at 75 mM salt concentration, but indicated outward rectification in contrast to the I-V curve for monovalent cations. The degree of activation at a given membrane potential depended strongly on the prehistory of the channel. The gating exhibited hysteretic-like behaviour, since the quasi steady-state deactivation and activation curves were displaced by approximately 25 mV. This result fully explains apparent discrepancies between V0.5-values previously obtained by slightly different experimental protocols. The possible physiological/pathophysiological role of the channel is discussed in the context of the demonstrated permeability for divalent cations.     

Laser-based detection of PAHs and BTXE-aromatics in oil polluted soil samples

Time-resolved laser-induced fluorescence spectroscopy and fiber optics are applied for the detection of aromatic hydrocarbons in oil contaminated water and soil samples. Time-integrated data accumulation of fluorescence intensities in an early and in a late time window with respect to the exciting laser pulse simplifies the method in such a way that it becomes very attractive for practical applications. For ultraviolet laser excitation at 337 nm and recording fluorescence signals at 400 nm, typical detection limits of the present set-up are 0.5 mg engine oil/L in water and 5 mg engine oil/kg in soil. A discrimination between BTXE-aromatics and PAHs in oil polluted soil or water samples is possible, when more than one laser wavelength in the ultraviolet is used for the excitation. The possibilities for a thermal discrimination between different aromatics are also discussed.     

Co-occurrence of two terpenoid isocyanide-formamide pairs in a marine sponge (Halichondria sp.)

From a marine sponge (Halichondria sp.) we have isolated amorphane sesquiterpenoids that are substituted at C-10 by isocyanide (1), formamide (2), and isothiocyanate (3), and diterpenoids that are 3,7,11,15- tetramethyl-1,6,10,14-hexadecatetraenes (geranyllinaloyl) bearing isocyanide (13), formamide (14), and isothiocyanate (16) functions at C-3.     

Janoxepin and brevicompanine B: antiplasmodial metabolites from the fungus Aspergillus janus

Two compounds janoxepin (1) and brevicompanine B (2) were isolated from the fungus Aspergillus janus and the structures elucidated by one- and two-dimensional NMR spectroscopic methods and mass spectrometry. Janoxepin is a novel oxepin derivative with a rare d-leucine incorporated. Brevicompanine B has previously only been isolated from Penicillium brevicompactum. Both compounds were tested in antimicrobial assays and found to be active against the malaria parasite Plasmodium falciparum 3D7 (IC₅₀-values of 28 and 35 mg/ml, respectively). However, no activity was observed in antifungal or antibacterial assays.     

Modeling chemoadaptive behavior: X-ray structure of the trimethylamine oxide-urea (1∶4) complex

The structure of a trimethylamine oxide (TMAO)-urea 14 complex was investigated by x-ray crystallographic methods. C₃H₉NO, 4CH₄N₂O, M_r=315.33, monoclinic P2₁/n, a=11.004(2), b=9.8259, c=15.419(2),=106.88(4), V=1595.4(2) å₃, Z=4, D_x=1.313(1) g cm^–3, monochromatized Cu (=1.5418 å),=8.94 cm^–1, F(OOO)=680, temperature = 110K, final R=0.067, for 1786 unique observed reflections. Based on these studies and comparison with related compounds a model of the interaction of urea and TMAO with proteins, especially enzymes, is proposed. This is important in the physiology of many organisms, especially elasmobranchs. The counteracting effect of TMAO on urea perturbation of protein structure and function is interpreted in terms of water structure as a balance between the structure breaking effect of urea and the structure-stabilizing effect of TMAO.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).