Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

Copper corrosion in buffered and non-buffered synthetic seawater: a comparative study

The electrochemical behaviour of copper in neutral buffered and non-buffered synthetic seawater and in pure chloride solutions has been studied by cyclic voltammetry, weight loss measurements, open circuit potential and scanning electron microscopy (SEM). Values of the repassivation potentials of Cu in non-buffered and buffered synthetic seawater, at 50 mV s^–1, were 0.12 and 0.46 V vs. SCE, respectively. The sharpness, heights and location of the different peaks as well as their charges were shown to be influenced by the composition of the solution, buffering conditions, deoxygenation, polarization potential and time. High chloride concentrations lead to higher oxidation charges. The anodic and the cathodic charges were shown to increase as the chloride concentration increases. The open circuit potential transients of copper in non-deoxygenated, non-buffered synthetic seawater indicate pitting from the beginning of the exposure, while in buffered solutions the pitting appeared only after a quite long exposure period, i.e. after 40 days. Corrosion rates of Cu samples after 3 months of immersion were higher in solutions of pure chloride (0.5 M) than in synthetic seawater. After six months the differences were even more noticeable. SEM images have showed a somewhat higher density of pits on copper samples immersed in the chloride solution (0.5 M), in comparison with those in synthetic seawater.     

Reaction of acetylenes with transition metals: VIII. π-allylpalladium complexes from acetylenes and alkenes

Coupling of diarylacetylenes with alkenes in the presence of dichlorobis(benzonitrile)palladium gives chloro(syn-1-chloro-anti-1-aryl-syn-3-alkyl)-π-allylpalladium complexes.     

Preparation of diverse BODIPY diesters

The synthesis and properties of a variety of substituted BODIPY diesters is presented. We find that certain substitution patterns afford appreciable yields of the target compounds and that electronic effects result in predicable differential fluorescent behavior. Challenges to further water solubilize these dyes and/or provide new points of attachment for biological tagging remain, these strategies are discussed.     

Columnar bis(pyridinium) ionic liquid crystals derived from 4-hydroxypyridine: synthesis,mesomorphism and emission properties

A series of flexibly linked bis(pyridinium) salts with various counterions (Br^?, PF₆^?, BF₄^? and OTf-) was designed and prepared starting from corresponding N-alkylated 4-pyridones precursors with mesogenic 3,4,5-tris(alkyloxy)benzyl moieties (alkyl = dodecyl or tetradecyl). These salts were investigated for their liquid crystalline properties by a combination of differential scanning calorimetry, polarising optical microscopy and temperature-dependent powder X-ray diffraction (XRD). Their thermal stability was checked by thermogravimetric analysis. All bis(pyridinium) salts, except the triflate salt with shorter terminal carbon chain, display an enantiotropic liquid crystalline behaviour with a hexagonal columnar (Col_h) phase assigned on the basis of its characteristic texture and XRD studies. It was found that these luminescent bis(pyridinium) salts show weak emission in dichloromethane solutions at room temperature and a pronounced red-shifted emission in solid state. The emission properties of these bis(pyridinium) salts do not depend significantly on the nature of counterion employed.     

Interpolation operators on a triangle with one curved side

We construct certain Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives on the border of a triangle with one curved side, as well as some of their product and Boolean sum operators. We study the interpolation properties and the order of accuracy (degree of exactness and precision set) of the constructed operators, respectively the remainders of the corresponding interpolation formulas. Finally, we give some numerical examples.     

Determination of different recreational drugs in hair by HS-SPME and GC/MS

A simple procedure combining headspace solid-phase microextraction (HS-SPME) and gas chromatography–mass spectrometry (GC/MS) to detect and quantify amphetamines, ketamine, methadone, cocaine, cocaethylene and ∆⁹-tetrahydrocannabinol (THC) in hair is described. This procedure allows, in a single sample, even scant, analysis of drugs requiring different analytical conditions. A hair sample (10 mg) is washed and subjected to acidic hydrolysis. Then the HS-SPME is carried out (10 min at 90 °C) for amphetamines, ketamine, methadone, cocaine and cocaethylene. For derivatization of analytes, the fibre is introduced into the headspace of another closed vial containing acetic anhydride. After a chromatographic run, an alkaline hydrolysis for THC analysis is carried out in the same vial containing the hair sample previously used. For adsorption, the solid-phase microextraction needle is inserted into the headspace of the vial and the fibre is exposed for 30 min at 150 °C. For derivatization of analytes, the fibre is introduced into the headspace of another closed vial containing N-methyl-N-(trimethylsilyl)trifluoroacetamide. The GC/MS parameters were the same for both chromatographic runs. The linearity was proved to be between 0.01 and 10.00 ng/mg. The repeatability (intra- and interday precision) was below 10% as the coefficient of variation for all compounds. The accuracy, as the relative recovery, was 96.2–103.5% (spiked samples) and 88.6–101.7% (quality control sample). The limit of detection ranged from 0.01 to 0.12 ng/mg, and the limit of quantification ranged from 0.02 to 0.37 ng/mg. Application of the procedure to real hair samples is described. To the best of our knowledge, the proposed procedure combining HS-SPME and GC/MS is the first one be to successfully applied to the simultaneous determination of most of the common recreational drugs, including THC, in a single hair sample.     

Surfaces Generation by Blending Interpolation on a Triangle with One Curved Side

We use some interpolation operators and some Bernstein type operators for construction of surfaces which satisfy some given conditions.     

Capillary Stokes drift: a new driving mechanism for mixing in AC-electrowetting

We studied the flow fields generated inside sessile drops that oscillate periodically between states of high and low contact angle under the influence of alternating electric fields of variable frequency and amplitude. Following the motion of dye patches, we show that the number of oscillation cycles required to achieve mixing scales logarithmically with the Péclet number as expected for chaotic mixing. High speed movies reveal an asymmetry of the drop shape between the spreading and receding phase of the oscillations. This results in net internal flow fields that we characterize by tracing the motion of colloidal seed particles. The strength and frequency dependence of the flow are explained in terms of Stokes drift driven by capillary waves that emanate from the oscillating contact line.