Problems for Ordinary Differential Equations with Transmission Conditions

We investigate a boundary-functional problem with transmission conditions for ordinary differential-operator equation in Sobolev spaces with a weight. We prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel basis of a system of root functions of the problem. Obtained results in the article are new even in case of Sobolev spaces without the weight.     

Valid inequalities based on simple mixed-integer sets

In this paper we use facets of simple mixed-integer sets with three variables to derive a parametric family of valid inequalities for general mixed-integer sets. We call these inequalities two-step MIR inequalities as they can be derived by applying the simple mixed-integer rounding (MIR) principle of Wolsey (1998) twice. The two-step MIR inequalities define facets of the master cyclic group polyhedron of Gomory (1969). In addition, they dominate the strong fractional cuts of Letchford and Lodi (2002).     

Does bisphenol A bioaccumulate on zebrafish? Determination of tissue bisphenol A level

Bisphenol A (BPA) is a high-production-volume industrial chemical mainly used in the production of polycarbonates and epoxy resins utilized in the manufacture of containers, bottles, toys, and medical devices. It has systemic effects as an endocrine disruptor even at low doses. To analyze its quantity in biological materials, sensitive and reproducible methods have to be used. Different doses and duration (90 and 900 μg/L, 24 and 120 h, and 21 days) of BPA exposure to whole body zebrafish were analyzed after specific homogenization of tissue, and then a modified method HPLC was used. The mobile phase was acetonitrile and water using a gradient method of reversed-phase C18 column, and excitation = 227 nm/emission = 313 nm. The calibration curve for BPA using HPLC-fluorescence detection method was between a concentration range of 1 and 1000 ng/mL and linear, and r² = 0.999. The mean and standard error of mean values were 4.29 ± 1.05, 2.50 ± 0.92, and 2.53 ± 0.68 for control; 10.43 ± 2.61, 11.46 ± 3.24, and 8.55 ± 3.11 for BPA-90 μg/L; and 17.78 ± 4.39, 21.55 ± 4.37, and 25.32 ± 3.25 for BPA-900 μg/L (24 h, 120 h, and 21 days, respectively). Although some statistical significance among dose/time was observed between two different dose-treated groups, statistical significance was not found in dose/time results within the group. However, the positive result of BPA in the control group can be explained by low-dose, chronic exposure or prevalence of endocrine-disrupting chemicals.     

Kinetics of catalytic Meerwein-Ponndorf-Verley reduction of aldehydes and ketones using boron triethoxide

Catalytic Meerwein-Ponndorf-Verley (MPV) reduction of various aliphatic, aromatic, and unsaturated aldehydes and ketones to corresponding alcohols (analyzed by GC-MS) in the presence of boron triethoxide (B(OEt)₃) were studied. Kinetics of this reduction reaction was also studied and the respective rate constants were determined. It was found that B(OEt)₃ catalyzes the reduction of aliphatic aldehydes and ketones to alcohols at room temperature while aromatic aldehydes and ketones were not reduced under the same conditions. In addition, MPV reduction using B(OEt)₃ was found to be chemoselective as unsaturated aldehydes and ketones afforded the corresponding alcohols without affecting unsaturated groups. The mechanism proposed involves a six-membered transition state in which both the alcohol and the carbonyl are coordinated to the same boron centre of a boron alkoxide catalyst.     

Solvent-free microwave extraction and hydrodistillation of essential oils from endemic Origanum husnucanbaseri H. Duman, Aytac & A. Duran: comparison of antibacterial activity and contents

The essential oils (EOs) obtained by solvent-free microwave extraction (SFME) and hydrodistillation (HD) from endemic Origanum husnucanbaseri H. Duman, Aytac & A. Duran were investigated using the gas chromatography-mass spectrometry system. The main constituents of both oils obtained from SFME and HD from O. husnucanbaseri are borneol (15.2-12.8%), α-terpineol (12.3-10.8%) and trans-sabinene hydrate (11.8-9.92%). The EO obtained from SFME contained substantially higher amounts of oxygenated compounds and lower amounts of monoterpenes than that from HD. The antibacterial activities of the EOs from SFME and HD were evaluated by the disc diffusion method against six bacterial strains. The EO extracted by SFME was more effective than the EO extracted by HD against the tested bacteria, except for Klebsiella pneumoniae American type culture collection (ATCC) 13883. Streptococcus pyogenes ATCC 19615 and Staphylococcus aureus ATCC 25923 in particular were more sensitive against the EO extracted by SFME.     

On‐site analysis of Chinese Cloisonné enamels from fifteenth to nineteenth centuries

A selection of 22 rare Chinese cloisonné enamels, from fifteenth century to nineteenth century A.D ., has been studied on‐site in the storage rooms of the musée des Arts décoratifs in Paris. The Raman signatures of the transparent and/or opacified glass matrix are discussed and compared with those that were previously recorded on glazed pottery, enameled and stained glasses. Enamels mostly belong to lead‐based potash‐lime glasses. Three different compositions, lead‐potash‐lime (fifteenth, sixteenth, eighteenth and nineteenth century), soda‐rich (sixteenth–seventeenth century) and soda‐lime (seventeenth century) are identified according to the wavenumber maxima of the Si O stretching and bending multiplets. Most of the pigment signatures are similar to those recorded on ceramic glazes and glass enamels, which proves the link between the technologies but a specific opacifier is observed: fluorite (CaF₂). Naples Yellow pigment variations give characteristic signatures. Additionally, a comparison is made with Limoges enamels (sixteenth–nineteenth century A.D. ). Copyright © 2009 John Wiley & Sons, Ltd.     

Selenium speciation in dill (Anethum graveolens L.) by ion pairing reversed phase and cation exchange HPLC with ICP-MS detection

In the present work, speciation of selenium in dill (Anethum graveolens L.), supplemented with sodium selenite during its growth, was performed using ion pairing reversed phase and cation exchange chromatography. Heptafluorobutyric acid (HFBA) was used as the ion-pairing agent in reversed phase chromatography. In cation exchange chromatography, two different gradient programs were employed for the identification of selenospecies using pyridinium formate as the mobile phase. Low molecular weight selenocompounds were extracted from root, stem and dill leaf with 0.1 M HCl. Enzymatic digestion was used for the extraction of selenospecies related to high molecular weight compounds. The chromatograms obtained from different parts of the plant revealed major differences in the type of selenospecies as well as their concentrations. The major selenospecies found in different parts of the plant is Se-methyl-selenocysteine (MeSeCys). Another major Se species identified is Se-methyl-selenomethionine (MeSeMet), which has the highest relative concentration in the root indicating possible Se volatilization from that part of the plant. Selenomethionine (SeMet) is present in minor quantities in all parts of the plant.     

Approximation by nonlinear integral operators via summability process

In this paper, we study the approximation properties of nonlinear integral operators of convolution-type by using summability process. In the approximation, we investigate the convergence with respect to both the variation semi-norm and the classical supremum norm. We also compute the rate of approximation on some appropriate function classes. At the end of the paper, we construct a specific sequence of nonlinear operators, which verifies the summability process. Some graphical illustrations and numerical computations are also provided.     

Lattice closures of polyhedra

Mathematical Programming - Given $$P\subset {\mathbb {R}}^n$$, a mixed-integer set $$P^I=P\cap ({\mathbb {Z}}^{t}\times {\mathbb {R}}^{n-t}$$), and a k-tuple of n-dimensional integral vectors...