Applications of hybrid universality to multivariable zeta-functions

In the present paper, we obtain new results on universality as applications of hybrid universality and almost-periodicity in its half-plane of absolute convergence. By using these, we show the universality for Euler products of Igusa type, Euler-Zagier multiple zeta-functions and Tornheim-Hurwitz type of double zeta-functions.     

A dichotomy for the convex spaces of probability measures

We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has ‘small’ local character in M or else M contains a measure of ‘large’ Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions.     

On Riesz Transforms Characterization of <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> Spaces Associated with Some Schrödinger Operators

Let \(\mathcal Lf(x)=-\Delta f (x)+V(x)f(x)\), V?≥?0, \(V\in L^1_{loc}(\mathbb R^d)\), be a non-negative self-adjoint Schrödinger operator on \(\mathbb R^d\). We say that an L ¹-function f is an element of the Hardy space \(H^1_{\mathcal L}\) if the maximal function

$ \mathcal M_{\mathcal L} f(x)=\sup\limits_{t>0}|e^{-t\mathcal L} f(x)| $

belongs to \(L^1(\mathbb R^d)\). We prove that under certain assumptions on V the space \(H^1_{\mathcal L}\) is also characterized by the Riesz transforms \(R_j=\frac{\partial}{\partial x_j}\mathcal L^{-1\slash 2}\), j?=?1,...,d, associated with \(\mathcal L\). As an example of such a potential V one can take any V?≥?0, \(V\in L^1_{loc}\), in one dimension.

     

The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Morita context is constructed. This construction allows one to associate two pairs of adjoint functors with right adjoint functors having a common domain or a double adjunction to a Morita context. It is shown that, conversely, every Morita context arises from a double adjunction. The comparison functor between the domain of right adjoint functors in a double adjunction and the Eilenberg-Moore category of the associated Morita context is defined. The sufficient and necessary conditions for this comparison functor to be an equivalence (or for the moritability of a pair of functors with a common domain) are derived.     

Properties of β-sitostanol/DPPC monolayers studied with Grazing Incidence X-ray Diffraction (GIXD) and Brewster Angle Microscopy

Although the influence of structurally modified sterols on artificial membranes has been intensively investigated, studies on the properties of stanols, which are saturated analogs of sterols, are very rare. Therefore, we have performed Grazing Incidence X-ray Diffraction (GIXD) experiments aimed at studying in-plane organization of a plant stanol-β-sitostanol monolayer and its mixtures with 1,2-dipalmitoyl-sn-glycero-3-phosphocholine - DPPC at the air/water interface. The collected GIXD data, resulting in-plane parameters and BAM images provide information on molecular organization and in-plane ordering of the investigated films. It was found that the lateral organization of β-sitostanol/DPPC monolayers depends on their composition. The oblique structure of the in-plane lattice of tilted hydrophobic region of molecules, found for DPPC film, is maintained at 10 mol% of stanol in the system. However, at 30 and 90 mol% of stanol in the mixture, the arrangement of molecules is hexagonal and they are oriented perpendicularly to the interface. With the addition of stanol the extend of the in-plane order of the monolayers decreases. Moreover, in mixtures the ordered domains consist of both monolayer's components. Additionally, β-sitostanol film is of similar in-plane organization as the corresponding sterol monolayer (β-sitosterol) and stanol induces condensing effect on DPPC.     

Evaluation of 1‐arylpiperazine derivative of hydroxybenzamides as 5‐HT1A and 5‐HT7 serotonin receptor ligands: An experimental and molecular modeling approach

The synthesis and evaluation as 5‐HT_1A and 5‐HT₇ serotonin receptor ligands of the two sets of O‐substituted hydroxybenzamides, structurally related to 2‐{3‐[4‐(2‐methoxyphenyl)piperazin‐1‐yl]propoxy}benzamide ( 1 ), (K_i 5‐HT_1A = 21 nM, 5‐HT₇ = 234 nM) are reported. To affect the affinity for 5‐HT_1A and 5‐HT₇ receptors, an amide moiety ( 2 , 3 , 4 , 5 , 6 ) and a hydrocarbon chain length ( 7 , 8 , 9 , 10 ) were modified. The serotonergic activity of compounds 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 was generally higher in the case of 5‐HT_1A receptors compared with 5‐HT₇ ones; the most active 5‐HT_1A ligands being meta‐isomer 2 (K_i = 7 nM) and both analogs of 1 with the longest spacer, i.e., penta‐ and hexa‐methylene derivatives 9 and 10 (K_i = 4 and 3 nM, respectively). The observed biological properties of compounds 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 were elucidated using molecular modeling procedures. J. Heterocyclic Chem., (2010).     

Synthesis, antimicrobial and antiproliferative activity of novel silver(I) tris(pyrazolyl)methanesulfonate and 1,3,5-triaza-7-phosphadamantane complexes

Five new silver(I) complexes of formulas [Ag(Tpms)] (1), [Ag(Tpms)(PPh(3))] (2), [Ag(Tpms)(PCy(3))] (3), [Ag(PTA)][BF(4)] (4), and [Ag(Tpms)(PTA)] (5) {Tpms = tris(pyrazol-1-yl)methanesulfonate, PPh(3) = triphenylphosphane, PCy(3) = tricyclohexylphosphane, PTA = 1,3,5-triaza-7-phosphaadamantane} have been synthesized and fully characterized by elemental analyses, (1)H, (13)C, and (31)P NMR, electrospray ionization mass spectrometry (ESI-MS), and IR spectroscopic techniques. The single crystal X-ray diffraction study of 3 shows the Tpms ligand acting in the N(3)-facially coordinating mode, while in 2 and 5 a N(2)O-coordination is found, with the SO(3) group bonded to silver and a pendant free pyrazolyl ring. Features of the tilting in the coordinated pyrazolyl rings in these cases suggest that this inequivalence is related with the cone angles of the phosphanes. A detailed study of antimycobacterial and antiproliferative properties of all compounds has been carried out. They were screened for their in vitro antimicrobial activities against the standard strains Enterococcus faecalis (ATCC 29922), Staphylococcus aureus (ATCC 25923), Streptococcus pneumoniae (ATCC 49619), Streptococcus pyogenes (SF37), Streptococcus sanguinis (SK36), Streptococcus mutans (UA159), Escherichia coli (ATCC 25922), and the fungus Candida albicans (ATCC 24443). Complexes 1-5 have been found to display effective antimicrobial activity against the series of bacteria and fungi, and some of them are potential candidates for antiseptic or disinfectant drugs. Interaction of Ag complexes with deoxyribonucleic acid (DNA) has been studied by fluorescence spectroscopic techniques, using ethidium bromide (EB) as a fluorescence probe of DNA. The decrease in the fluorescence of DNA-EB system on addition of Ag complexes shows that the fluorescence quenching of DNA-EB complex occurs and compound 3 is particularly active. Complexes 1-5 exhibit pronounced antiproliferative activity against human malignant melanoma (A375) with an activity often higher than that of AgNO(3), which has been used as a control, following the same order of activity inhibition on DNA, i.e., 3 > 2 > 1 > 5 > AgNO(3)? 4.     

Weak intermolecular interactions in gas-phase nuclear magnetic resonance

Gas-phase nuclear magnetic resonance (NMR) spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO(2) dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D(2)-rare gas systems is considered.     

Geometric and magnetic properties of Pt clusters supported on graphene: relativistic density-functional calculations

The geometric and magnetic structures of small Pt(n) clusters (n = 1 - 5) supported on a graphene layer have been investigated using ab initio density functional calculations including spin-orbit coupling. Pt-Pt interactions were found to be much stronger than the Pt-C interactions promoting the binding to the support. As a consequence, the equilibrium structure of the gas-phase clusters is preserved if they are deposited on graphene. However, the clusters bind to graphene only via at most two Pt-C bonds: A Pt(2) dumbbell prefers an upright position, the larger clusters are bound to graphene only via one edge of the planar cluster (Pt(3) and Pt(5)) or via two terminal Pt atoms of a bent Pt(4) rhombus. Evidently, the strong buckling of the graphene layer induced by the Pt-C bonds prevents the formation of a larger number of cluster-support bonds. As the local spin and orbital magnetic moments are quenched on the Pt atoms forming Pt-C bonds, the magnetic structure of the supported clusters is much more inhomogeneous as in the gas-phase. This leads to noncollinear magnetic structures and a strongly reduced magnetic anisotropy energy.