On the general additive divisor problem

We obtain a new upper bound for the sum Σ _h≤H Δ _k (N, h) when 1 ≤ H ≤ N, k ∈ ℕ, k ≥ 3, where Δ _k (N, h) is the (expected) error term in the asymptotic formula for Σ _N<n≤2N d _k (n)d _k (n + h), and d _k (n) is the divisor function generated by ζ(s) ^k . When k = 3, the result improves, for H ≥ N ^1/2, the bound given in a recent work of Baier, Browning, Marasingha and Zhao, who dealt with the case k = 3.     

On fluid-structure interaction in transonic wind tunnels

This paper studies the interaction (influence) of perforated walls of transonic wind tunnels in two-dimensional investigations which employ the generalized method for solving Dirichlets problem formulated for the rectangle of the transonic wind tunnel work section. The algorithm has been applied to the aerodynamic experimental results from investigations of NACA 0012 airfoil obtained at the VTI – Aeronautical Institute and the Faculty of Mechanical Engineering in Belgrade to demonstrate in two-dimensional investigations the appropriateness of the presented advanced algorithm for the calculation of the interference of the transonic wind tunnel wall. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of Aliphatic Chain Length on Structural,Thermal and Electrochemical Properties of n-alkylene Benzyl Alcohols: A Study of the Odd–Even Effect

The century-old, well-known odd–even effect phenomenon is still a very attractive and intriguing topic in supramolecular and nano-scale organic chemistry. As a part of our continuous efforts in the study of supramolecular chemistry, we have prepared three novel aromatic alcohols (1,2-bis[2-(hydroxymethyl)phenoxy]butylene (Do4OH), 1,2-bis[2-(hydroxymethyl)phenoxy]pentylene (Do5OH) and 1,2-bis[2-(hydroxymethyl)phenoxy]hexylene (Do6OH)) and determined their crystal and molecular structures by single-crystal X-ray diffraction. In all compounds, two benzyl alcohol groups are linked by an aliphatic chain of different lengths (CH₂)_n; n = 4, 5 and 6. The major differences in the molecular structures were found in the overall planarity of the molecules and the conformation of the aliphatic chain. Molecules with an even number of CH₂ groups tend to be planar with an all-trans conformation of the aliphatic chain, while the odd-numbered molecule is non-planar, with partial gauche conformation. A direct consequence of these structural differences is visible in the melting points—odd-numbered compounds of a particular series display systematically lower melting points. Crystal and molecular structures were additionally studied by the theoretical calculations and the melting points were correlated with packing density and the number of CH₂ groups. The results have shown that the generally accepted rule, higher density = higher stability = higher melting point, could not be applied to these compounds. It was found that the denser packaging causes an increase in the percentage of repulsive H‧‧‧H interactions, thereby reducing the stability of the crystal, and consequently, the melting points. Another interesting consequence of different molecular structures is their electrochemical and antioxidative properties—a non-planar structure displays the highest oxidation peak of hydroxyl groups and moderate antioxidant activity.     

Field Effect and Local Gating in Nitrogen-Terminated Nanopores (NtNP) and Nanogaps (NtNG) in Graphene

Functionalization of electrodes is a wide-used strategy in various applications ranging from single-molecule sensing and protein sequencing, to ion trapping, to desalination. We demonstrate, employing non-equilibrium Green′s function formalism combined with density functional theory, that single-species (N, H, S, Cl, F) termination of graphene nanogap electrodes results in a strong in-gap electrostatic field, induced by species-dependent dipoles formed at the electrode ends. Consequently, the field increases or decreases electronic transport through a molecule (benzene) placed in the nanogap by shifting molecular levels by almost 2 eV in respect to the electrode Fermi level via a field effect akin to the one used for field-effect transistors. We also observed the local gating in graphene nanopores terminated with different single-species atoms. Nitrogen-terminated nanogaps (NtNGs) and nanopores (NtNPs) show the strongest effect. The in-gap potential can be transformed from a plateau-like to a saddle-like shape by tailoring NtNG and NtNP size and termination type. In particular, the saddle-like potential is applicable in single-ion trapping and desalination devices.     

Synthesis, structure, and biological evaluation of C-2 sulfonamido pyrimidine nucleosides

The C-2 sulfonamido pyrimidine nucleosides were prepared by opening the 2,2′- or 2,3′-bond in anhydronucleosides under nucleophilic attack of sulfonamide anions. Reaction of the sodium salt of p-toluenesulfonamide or 2-(aminosulfonyl)-N,N-dimethylnicotinamide with 2,2′-anhydro-1-(β-d-arabinofuranosyl)cytosine gave the C-2 sulfonamido derivatives in excellent yields. Ring opening of the less reactive 2,2′-anhydrouridine and 2,3′-anhydrothymidine could be accomplished with DBU/CH₃CN activation of p-toluenesulfonamide, giving moderate yields for C-2 sulfonamido derivatives. The action of acetic acid or ZnBr₂/CH₂Cl₂ on 5-methyl-N²-tosyl-1-(2-deoxy-5-O-trityl-β-d-threo-pentofuranosyl)isocytosine led to the cleavage of both the protection group and the nucleoside bond, yielding 5-methyl-N²-tosylisocytosine as the major product. Structures of the prepared C-2 sulfonamido nucleosides were confirmed by the 1D and 2D NMR experiments, and X-ray structural analysis of 4-imino-N²-tosylamino-1-(β-d-arabinofuranosyl)pyrimidine. Both methods confirmed β-configuration and anti-conformation of the 2-sulfonamido nucleosides. The investigated compounds displayed moderate inhibition of tumor cell growth in vitro, as determined by the MTT assay using six different human tumor cell lines.     

The average prime divisor of an integer in short intervals

Archiv der Mathematik -     

Relation between pore sizes of protein crystals and anisotropic solute diffusivities

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.