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.     

Functional inequalities for the Teichmüller ring capacity

The geometric study of the action of quasiconformal mappings by means of conformal invariants often leads to inequalities for special functions. Examples of such special functions are the capacities of the Grötzsch and Teichmüller rings. Several new inequalities for these and related functions are given in the multidimensional case.     

Quantitative assessment of the enzymatic degradation of amorphous cellulose by using a quartz crystal microbalance with dissipation monitoring

The systematic evaluation of the degradation of an amorphous cellulose film by a monocomponent endoglucanase (EG I) by using a quartz crystal microbalance with dissipation monitoring (QCM-D) identified several important aspects relevant to the study the kinetics of cellulose degradation by enzymes. It was demonstrated that, to properly evaluate the mechanism of action, steady state conditions in the experimental set up need to be reached. Rinsing or diluting the enzyme, as well as concentration of the enzyme, can have a pronounced effect on the hydrolysis. Quantification of the actual hydrolysis was carried out by measuring the film thickness reduction by atomic force microscopy after the enzymatic treatment. The values correlated well with the frequency data obtained by QCM-D measurement for corresponding films. This demonstrated that the evaluation of hydrolysis by QCM-D can be done quantitatively. Tuning of the initial thickness of films enabled variation of the volume of substrate available for hydrolysis which was then utilized in establishing a correlation between substrate volume and hydrolytic activity of EG I as measured by QCM-D. It was shown that, although the amount of substrate affects the absolute rate of hydrolysis, the relative rate of hydrolysis does not depend on the initial amount of substrate in steady state system. With this experimental setup it was also possible to demonstrate the impact of concentration on crowding of enzyme and subsequent hydrolysis efficiency. This effort also shows the action of EG I on a fully amorphous substrate as observed by QCM-D. The enzyme was shown to work uniformly within the whole volume of swollen film, however being unable to fully degrade the amorphous film.     

An impedance QCM study on the partitioning of bioactive compounds in supported phospholipid bilayers

The interaction of two drugs of small molecular size, propranolol and tetracaine, and the membrane-perturbing peptide melittin with a phospholipid bilayer supported on a SiO2 surface was studied with the quartz crystal microbalance. All three bioactive compounds interacted with the lipid bilayer and changed its viscoelastic properties. Adsorbed mass of the compounds was analyzed with a viscoelastic model as a function of the concentration of the compounds in the aqueous phase, as well as the effect of the compounds on the bilayer viscoelasticity. The analysis was based on the interpretation of the impedance of the crystal, utilizing the 5th, 7th and 9th overtone of the fundamental 5 MHz resonance frequency.     

Synthesis, structural characterization, photophysical properties and theoretical analysis of gold(I) thiolate-phosphine complexes

A series of luminescent dinuclear neutral complexes of stoichiometry [(AuSPh)(2)(PPh(2)-(C(6)H(4))(n)-PPh(2))] (n = 1, 2, 3) as well as their tetranuclear cationic derivatives [(Au(2)SPh)(2)(PPh(2)-(C(6)H(4))(n)-PPh(2))(2)](PF(6))(2) are reported. Their crystal structures have been elucidated by X-ray studies. These studies indicate that, for the dinuclear species, only when n = 1 the molecules exhibit intermolecular aurophilic interactions. None of the tetranuclear species crystallizes in their molecular form, due to the formation of aggregates through Au···Au interactions. The origin of the luminescence has been analyzed by computational studies indicating that the presence or absence of aurophilic interactions does not affect the luminescent behavior and that intraligand charge transfer processes which involve the thiolate and the diphosphine are responsible for the emissions. The result is in contrast with the thiolate-gold charge transfer processes which dominate the photophysics of gold-thiolate compounds and reveals the influence of the phenylene spacers in the emissive behavior of these compounds.     

Coinage metal complexes of 2-diphenylphosphino-3-methylindole

Coordination of P,N indolyl-phosphine ligands to Au(I), Ag(I) and Cu(I) metal ions under weakly basic conditions results in easy deprotonation of the indolyl N-H function and effective formation of a family of homo- and heterobimetallic complexes MM'(PPh(2)C(9)H(7)N)(2) (M = M' = Au (2), Ag (5); M = Au, M' = Cu (3), Ag (4)). The latter (4) exists as an inseparable mixture of four different complexes, which are in equilibrium driven by slow dynamics. The reaction of silver(I) and copper(I) ions with PPh(2)(C(9)H(8)N) affords a rare tetranuclear Z-shaped cluster Ag(2)Cu(2)(PPh(2)C(9)H(7)N)(4) (6), which exhibits red luminescence in solid state (650 nm) and a weak dual emission in solution with the main component in the near-IR region (746 nm).     

Structural principles of semiconducting Group 14 clathrate frameworks

We have performed a comprehensive theoretical investigation of the structural principles of semiconducting clathrate frameworks composed of the Group 14 elements carbon, silicon, germanium, and tin. We have investigated the basic clathrate frameworks, together with their polytypes, intergrowth clathrate frameworks, and extended frameworks based on larger icosahedral building blocks. Quantum chemical calculations with the PBE0 hybrid density functional method provided a clear overview of the structural trends and electronic properties among the various clathrate frameworks. In agreement with previous experimental and theoretical studies, the clathrate II framework proved to be the energetically most favorable, but novel hexagonal polytypes of clathrate II also proved to be energetically very favorable. In the case of silicon, several of the studied clathrate frameworks possess direct and wide band gaps. The band structure diagrams and simulated powder X-ray patterns of the studied frameworks are provided and systematic preliminary evaluation of guest-occupied frameworks is conducted to shed light on the characteristics of novel, experimentally feasible clathrate compositions.