Absolutely monotonic functions related to Euler’s gamma function and Barnes’ double and triple gamma function

It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler’s gamma function are Laplace transformations of positive multiples of absolutely monotonic functions. Applications concerning positivity of sums involving Bernoulli numbers are given.     

An extension of Vietoris's inequalities

We establish a best possible extension of a famous Theorem of Vietoris about the positivity of a general class of cosine sums. Our result refines and sharpens several earlier generalizations of this Theorem, and settles some open questions regarding the possibility of further improvement of it. Some new inequalities for trigonometric sums are given. We show that our results have applications within the context of positive sums of Gegenbauer polynomials and quadrature methods. We also obtain some existing estimates for the location of zeros of certain trigonometric polynomials under a weakened condition on their coefficients. 2000 Mathematics Subject ClassificationPrimary—42A05; Secondary—42A32,26D05, 26D15, 33B15, 33C45 Dedicated to Richard Askey on the occasion of his 70th birthday     

On a trigonometric sum of Vinogradov

The trigonometric sum

     

Occurrence and distribution of selected pharmaceutical compounds on sewage-impacted section of River Acheloos,Western Greece

The occurrence of eight pharmaceutical compounds (PhCs), two metabolites and caffeine was investigated in River Acheloos, located in Western Greece, during a twelve-month monitoring period (March 2007–February 2008). Solid-phase extraction (SPE) was used for the extraction and pre-concentration of the target pollutants and gas chromatography mass spectrometry (GC–MS) for the detection and quantification. Recoveries were determined between 74.0–100.4% for distilled water and 72.6–95.1% for the river water, whereas the relative standard deviation was less than 9.4% for distilled water and 8% for the river water, respectively. The limits of detection ranged between 1–40 ng L^?1. Two pharmaceuticals (paracetamol and carbamazepine), caffeine and the metabolite (salicylic acid), have been detected in all the analysed samples. Maximum concentration levels determined in river samples reached 305 ng L^?1 recorded for paracetamol. The concentrations of target compounds were significantly higher in the samples collected at the sampling station situated after the wastewater treatment plant (WWTP) of Agrinio City compared to the samples collected in upper and lower parts of the river. Seasonal variations were attributed mainly to river flow variations and removal percentages by WWTP. Risk quotient method for median environmental concentrations revealed minimal to median risk with the exception of triclosan, ibuprofen and diclofenac, which presented high risk when maximum environmental concentrations were used.     

A multi-step reaction model for ignition of fully-dense Al-CuO nanocomposite powders

A multi-step reaction model is developed to describe heterogeneous processes occurring upon heating of an Al-CuO nanocomposite material prepared by arrested reactive milling. The reaction model couples a previously derived Cabrera-Mott oxidation mechanism describing initial, low temperature processes and an aluminium oxidation model including formation of different alumina polymorphs at increased film thicknesses and higher temperatures. The reaction model is tuned using traces measured by differential scanning calorimetry. Ignition is studied for thin powder layers and individual particles using respectively the heated filament (heating rates of 10³–10⁴ K s^?1) and laser ignition (heating rate ～10⁶ K s^?1) experiments. The developed heterogeneous reaction model predicts a sharp temperature increase, which can be associated with ignition when the laser power approaches the experimental ignition threshold. In experiments, particles ignited by the laser beam are observed to explode, indicating a substantial gas release accompanying ignition. For the heated filament experiments, the model predicts exothermic reactions at the temperatures, at which ignition is observed experimentally; however, strong thermal contact between the metal filament and powder prevents the model from predicting the thermal runaway. It is suggested that oxygen gas release from decomposing CuO, as observed from particles exploding upon ignition in the laser beam, disrupts the thermal contact of the powder and filament; this phenomenon must be included in the filament ignition model to enable prediction of the temperature runaway.     

Regulation of catalytic behaviour of hydrolases through interactions with functionalized carbon-based nanomaterials

The interaction of enzymes with carbon-based nanomaterials (CBNs) is crucial for the function of biomolecules and therefore for the design and development of effective nanobiocatalytic systems. In this study, the effect of functionalized CBNs, such as graphene oxide (GO) and multi-wall carbon nanotubes (CNTs), on the catalytic behaviour of various hydrolases of biotechnological interest was monitored and the interactions between CBNs and proteins were investigated. The enzyme–nanomaterial interactions significantly affect the catalytic behaviour of enzymes, resulting in an increase up to 60 % of the catalytic efficiency of lipases and a decrease up to 30 % of the esterase. Moreover, the use of CNTs and GO derivatives, especially those that are amine-functionalized, led to increased thermal stability of most the hydrolases tested. Fluorescence and circular dichroism studies indicated that the altered catalytic behaviour of enzymes in the presence of CBNs arises from specific enzyme–nanomaterial interactions, which can lead to significant conformational changes. In the case of lipases, the conformational changes led to a more active and rigid structure, while in the case of esterases this led to destabilization and unfolding. Kinetic and spectroscopic studies indicated that the extent of the interactions between CBNs and hydrolases can be mainly controlled by the functionalization of nanomaterials than by their geometry.     

Series and product representations for some mathematical constants

We present several series and product representations for γ, π, and other mathematical constants. One of our results states that, for all real numbers μ s>0, we have

Site‐Selective C−H Oxygenation via Aryl Sulfonium Salts

Herein, we report a two‐step process forming arene C?O bonds in excellent site‐selectivity at a late‐stage. The C?O bond formation is achieved by selective introduction of a thianthrenium group, which is then converted into C?O bonds using photoredox chemistry. Electron‐rich, ‐poor and ‐neutral arenes as well as complex drug‐like small molecules are successfully transformed into both phenols and various ethers. The sequence differs conceptually from all previous arene oxygenation reactions in that oxygen functionality can be incorporated into complex small molecules at a late stage site‐selectively, which has not been shown via aryl halides.