The twelfth moment of central values of Hecke series

Let H_j(s) be the Hecke L-function attached to the Maass wave form for the jth eigenvalue of the hyperbolic Laplacian acting in the Hilbert space of automorphic functions for the full modular group. The following mean value estimate for the central values is proved:

     

Peak dispersion and contributions to plate height in nonaqueous capillary electrophoresis at high electric field strengths: propanol as background electrolyte solvent

Peak dispersion effects in nonaqueous capillary electrophoretic separations of aromatic anionic analytes were investigated in a propanolic background electrolyte solution. Poly(glycidylmethacrylate-co-N-vinylpyrrolidone) coating was applied to the capillary to suppress the electroosmotic flow and to improve the repeatability of the migration times. Electrical field strengths up to 2000 Vcm(-1) were applied in separations and the separation efficiencies were compared with theoretical values calculated on the basis of plate height theory. The contributions to the total plate height were calculated for injection plug length, diffusion, Joule heating, electromigration dispersion, analyte adsorption to the capillary wall, and detector slit aperture length. Analyte diffusion coefficients were measured by Taylor dispersion method, while distribution constants were measured chromatographically. Agreement between the calculated and empirical results was fairly good even though some approximations were required. In most cases the longitudinal diffusion contribution governed the total plate height, while the contribution of Joule heating was insignificant even at exceptionally high field strengths used. The relatively long detection slit aperture was found to influence the separation efficiency strongly, while the other dispersion sources that were investigated were of minor importance, except for adsorption in the case of one analyte. With all analytes, the dispersive effect of longitudinal diffusion was reduced as the field strength was increased, leading to enhanced migration velocities and faster separations.     

SPH simulation of oblique shocks in compressible flows

The Lagrangian smoothed particle hydrodynamics (SPH) method is used to simulate shock waves in inviscid, supersonic (compressible) flow. It is shown for the first time that the fully Lagrangian SPH particle method, without auxiliary grid, can be used to simulate shock waves in compressible flow. The wall boundary condition is treated with ghost particles combined with a suitable repulsive potential function, whilst corners are treated by a novel ‘angle sweep’ technique. The method gives accurate predictions of the flow field and of the shock angle as compared with the analytical solution. The study shows that SPH is a good potential candidate to solve complex aerodynamic problems, including those involving rarefied flows, such as atmospheric re‐entry. Copyright © 2016 John Wiley & Sons, Ltd.     

Investigation of endoglucanase selectivity on carboxymethyl cellulose by mass spectrometric techniques

The benefits of applying cellulose selective enzymes as analytical tools for chemical structure characterization of cellulose derivatives have been frequently addressed over the years. In a recent study the high selectivity of cellulase Cel45A from Trichoderma reesei (Tr Cel45A) was utilized for relating the chemical structure to the flow properties of carboxymethyl cellulose (CMC). However, in order to take full advantage of the enzymatic hydrolysis the enzyme selectivity on the cellulose substrate must be further investigated. Therefore, the selectivity of Tr Cel45A on CMC was studied by chemical sample preparation of the enzyme products followed by mass spectrometric chemical structure characterization. The results strongly suggest that, in accordance with recent studies, also this highly selective endoglucanase is able to catalyze hydrolysis of glucosidic bonds adjacent to mono-substituted anhydroglucose units (AGUs). Furthermore, the results also indicate that substituents on the nearby AGUs will affect the hydrolysis.     

Push-pull nitrile ligands exhibit specific hydration patterns

The reaction between K[PtCl(3)(Me(2)SO)] or prepared in this work cis- and trans-[PtCl(2)(NCNR(2))(Me(2)SO)] (R(2) = Me(2), 1; C(4)H(8)O, 2; C(5)H(10) 3) with an excess of NCNR(2) in water gives the cationic bischelate [Pt{κ(2)-N,N'-NH=C(NMe(2))OC(NMe(2))=NH}(2)](2+) (4(2+)) and the monochelates [PtCl{κ(2)-N,O-NH=C(NR(2))NC(NR(2))=O}(Me(2)SO)] (R(2) = C(4)H(8)O, 5; C(5)H(10), 6). Complex 4(2+) was released from the reaction mixture as 4·[PtCl(3)(Me(2)SO)](2)·(H(2)O)(2) or it was precipitated as 4·[A](2) (A = pic, 4·[pic](2); PF(6), 4·[PF(6)](2); BPh(4), 4·[BPh(4)](2)·(NH(2)CONMe(2))) by addition of picric acid, NaPF(6), or NaBPh(4), respectively, to the filtrate obtained after separation of 4·[PtCl(3)(Me(2)SO)](2)·(H(2)O)(2). In 2, the dialkylcyanamide ligand undergoes bond cleavage giving the known trans-[PtCl(2){N(H)C(4)H(8)O}(Me(2)SO)] (trans-7). All complexes were characterized by elemental analyses (C, H, N), high resolution ESI-MS, IR, (1)H and (13)C{(1)H} NMR spectroscopic techniques, including 2D NMR correlation experiments ((1)H,(1)H-COSY, (1)H,(13)C-HMQC/(1)H,(13)C HSQC, (1)H,(13)C-HMBC, and (1)H,(1)H-NOESY). The structures of cis-1, cis-3, 4·[PtCl(3)(Me(2)SO)](2)·(H(2)O)(2), 4·[BPh(4)](2)·(NH(2)CONMe(2)) and 5 were determined by a single-crystal X-ray diffraction.     

Assembly of the Au-diphosphine helical cage molecules via alkynyl-μ4-methylydine ligand transformation

The assembly of the gold(I)-diphosphine cages occurs via unprecedented transformation of the alkynyls into the μ(4)-methylydine ligands under basic conditions. These compounds demonstrate the equilibrium between the P?M helical isomers and serve as hosts to accommodate small molecules (CH(2)Cl(2) and CS(2)).     

Flavoured leptogenesis in the CTP formalism

Within the Closed Time Path (CTP) framework, we derive kinetic equations for particle distribution functions that describe leptogenesis in the presence of several lepton flavours. These flavours have different Standard-Model Yukawa couplings, which induce flavour-sensitive scattering processes and thermal dispersion relations. Kinetic equilibrium, which is rapidly established and maintained via gauge interactions, allows to simplify these equations to kinetic equations for the matrix of lepton charge densities. In performing this simplification, we notice that the rapid flavour-blind gauge interactions damp the flavour oscillations of the leptons. Leptogenesis turns out to be in the parametric regime where the flavour oscillations are overdamped and flavour decoherence is mainly induced by flavour sensitive scatterings. We solve the kinetic equations for the lepton number densities numerically and show that they interpolate between the unflavoured and the fully flavoured regimes within the intermediate parametric region, where neither of these limits is applicable.     

Inequalities for the generalized trigonometric and hyperbolic functions

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional p$p$-Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi?–Adamovi?’s inequality, Lazarevi?’s inequality, Huygens-type inequalities, Wilker-type inequalities, and Cusa–Huygens-type inequalities, are generalized to the case of generalized functions.