The Number of Lattice Points Above the Catenary

For fixed c > 1 and for arbitrary and independent a,b ≧ 1 let Z ²|b( cosh(x/a)−c) ≦ y < 0}. We investigate the asymptotic behaviour of R(a,b) for a,b → ∞. In the special case b = o(a ^5/6) the lattice rest has true order of magnitude . This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of nitrogen adsorption on the mid-infrared spectrum of water clusters

Experimental Fourier-transform infrared spectra and DFT calculated infrared spectra are compared to investigate the effect of adsorbed nitrogen on the OH-stretch band complex of water clusters. Using a collisional cooling experiment, pure as well as partially and completely N(2)-covered water clusters consisting of 20-200 water molecules have been generated in thermal equilibrium in the aerosol phase within the temperature range of 5-80 K. Computational IR-spectra simulations have been performed for discrete pure and N(2)-covered water clusters including 10, 15, 20, and 30 water molecules. The adsorbed N(2) molecules especially affect the three-coordinated water molecules at the cluster surface which could be observed as a blue shift of the companion O-H band at 2900 cm(-1) and a red shift of the dangling O-H band at 3700 cm(-1) by about 20 cm(-1) in both cases. The most striking effect of the N(2) adsorbate is an intensity increase of the dangling O-H band by a factor of 3-5. Furthermore, the onset temperature of nitrogen adsorption at the water cluster surface was experimentally found to be roughly 30 K for cluster sizes of about 100 water molecules. Experimental and computational results are in good agreement. The presented results are based on and support the work of V. Buch, J. P. Devlin, and co-workers (e.g., J. Phys. Chem. B, 1997; J. Phys. Chem. A, 2003; Int. Rev. Phys. Chem., 2004).     

Oxide- and zeolite-supported molecular metal complexes and clusters: physical characterization and determination of structure, bonding, and metal oxidation state

This article is a review of the physical characterization of well-defined site-isolated molecular metal complexes and metal clusters supported on metal oxides and zeolites. These surface species are of interest primarily as catalysts; as a consequence of their relatively uniform structures, they can be characterized much more precisely than traditional supported catalysts. The properties discussed in this review include metal nuclearity, oxidation state, and ligand environment, as well as metal-support interactions. These properties are determined by complementary techniques, including transmission electron microscopy; X-ray absorption, infrared, Raman, and NMR spectroscopies; and density functional theory. The strengths and limitations of these techniques are assessed in the context of results characterizing samples that have been investigated thoroughly and with multiple techniques. The depth of understanding of well-defined metal complexes and metal clusters on supports is approaching that attainable for molecular analogues in solution. The results provide a foundation for understanding the more complex materials that are typical of industrial catalysts.     

Real-time Imaging of Nascent DNA in Live Cells by Monitoring the Fluorescence Lifetime of DNA-Incorporated Thiazole Orange-Modified Nucleotides

A modified 2′-deoxycytidine triphosphate derivative ( dC^TOTP ) bearing a thiazole orange moiety tethered via an oligoethylene glycol linker was designed and synthesized. The nucleotide was incorporated into DNA by DNA polymerases in vitro as well as in live cells. Upon incorporation of dC^TOTP into DNA, the thiazole orange moiety exhibited a fluorescence lifetime that differed significantly from the non-incorporated (i.e. free and non-covalently intercalated) forms of dC^TOTP . When dC^TOTP was delivered into live U-2 OS cells using a synthetic nucleoside triphosphate transporter, it allowed us to distinguish and monitor cells that were actively synthesizing DNA in real time, from the very first moments after the treatment. We anticipate that this probe could be used to study chromatin organization and dynamics.     

DISTANCE-DEPENDENT FLUORESCENCE QUENCHING OF TRYPTOPHAN BY ACRYLAMIDE

Abstract We used GHz frequency-domain fluorometry to investigate the time-dependent intensity decays of N -acetyl -L-trytophanamide (NATA) when collisionally quenched by acrylamide in propylene glycol at 20°C. The intensity decays of NATA became increasingly heterogeneous in the presence of acrylamide. The NATA intensity decays were not consistent with the Collins-Kimball radiation boundary condition (RBC) model for quenching. The steady-state Stern-Volmer plots show significant upward curvature. At low temperature in vitrified propylene glycol (-60%), where translational diffusion cannot occur during the lifetime of the excited state, quenching of NATA by acrylamide was observed. The Smoluchowski and RBC quenching models do not predict any quenching in the absence of translational diffusion. Hence, these frequency-domain and steady-state data indicate a through-space quenching interaction between NATA and acrylamide. The rate for quenching of NAT A by acrylamide appears to depend exponentially on the fluorophore-quencher separation distance. Comparison of the time-resolved and steady-state data provides a sensitive method to determine the distance dependence of the fluorophore-quencher interaction. The distance-dependent rate of quenching also explains the upward curvature of the Stern-Volmer plot, which is often observed for quenching by acrylamide. These results suggest that the distance-dependent quenching rates need to be considered in the interpretation of quenching data of proteins by acrylamide.     

LINEAR DICHROISM STUDY OF METALLOPORPHYRIN TRANSITION MOMENTS IN VIEW OF RADIATIONLESS INTERACTIONS WITH TRYPTOPHAN IN HEMOPROTEINS

We measured the linear dichroism of several metalloporphyrins embedded in stretched polyvinyl alcohol (PVA) films to estimate the orientation of the absorption transition moments, which in hemoproteins are relevant to the radiationless energy transfer between tryptophan and heme. The metalloporphyrins were derivatives of protoporphyrin IX (PPIX), namely Fe³⁺-PPIX (ferric-heme) and Fe²⁺CO-PPIX (CO-heme), Mg-PPIX (Mg-heme) and Zn-PPIX (Zn-heme). Measurements were conducted between 300 and 700 nm. In all cases the linear dichroism was wavelength dependent, indicating the presence of several transition moments with different orientations. We focused our attention on the near-UV (300–380 nm) and Soret (380450 nm) absorption bands. Deconvolution in terms of Gaussian components gave three components between 380 and 450 nm and only one in the 300–380 nm region. Deconvolution of the near-UV and Soret spectra of oxy-, deoxy- and carbonmonoxyhemoglobin gave very similar results, suggesting a very similar orientation of the various transition moments in the free and protein-embedded hemes. It should be stressed that the single 300–380 nm band is the only one responsible for the overlap integral that regulates the energy transfer from tryptophan to heme in hemoproteins (Gryczynski et al., Biophys. J . 63, 648–653, 1992). The dichroism of this single band indicated that its transition moment is oriented at about 60 from the α-γ meso-axis of the heme moiety. We conclude that the heme should be considered a linear oscillator when it acts as acceptor of energy transfer from tryptophans.     

On the distribution of distances between specified nodes in increasing trees

We study the quantity distance between nodejand nodenin a random tree of sizen chosen from a family of increasing trees. For those subclass of increasing tree families, which can be constructed via a tree evolution process, we give closed formulæ for the probability distribution, the expectation and the variance. Furthermore we derive a distributional decomposition of the random variable considered and we show a central limit theorem of this quantity, for arbitrary labels 1≤j<n and n→∞.Such tree models are of particular interest in applications, e.g., the widely used models of recursive trees, plane-oriented recursive trees and binary increasing trees are special instances and are thus covered by our results.     

An asymptotic series for an integral

The Ramanujan Journal - Let $$f(z)=\sum _{n=0}^{\infty }a_{n}{\mathbf {e}}(nz),g(z)=\sum _{n=0}^{\infty }b_{n}{\mathbf {e}}(nz)\ ({\mathbf {e}}(z)=e^{2\pi \sqrt{-1}z})$$ be holomorphic modular...