Existence and uniqueness of positive solutions for the Neumann p-Laplacian

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory reaction which satisfies only a unilateral growth restriction. Using the principal eigenvalue of an eigenvalue problem involving the Neumann p-Laplacian plus an indefinite potential, we produce necessary and sufficient conditions for the existence and uniqueness of positive smooth solutions.     

Performance of interventions with manipulator-driven real-time MR guidance: implementation and initial in vitro tests

The purpose of this work was to implement and assess the performance of interventions inside a cylindrical magnetic resonance imaging (MRI) scanner with an MR-compatible manipulator system and manipulator-driven real-time MR guidance. The interventional system is based on a seven degree-of-freedom MR-compatible manipulator, which offers man-in-the-loop control either with a graphical user interface or with a master/slave device. The position and the orientation of the interventional tool are sent to an MR scanner for a manipulator-driven dynamic update of the imaging plane to track, visualize and guide the motion of an end-effector. Studies on phantoms were performed with a cylindrical 1.5-T scanner using an operator-managed triggered gradient-recalled echo (GRE) or a computer-managed dynamic True Fast Imaging with Steady Precession (TrueFISP). Targets were acquired with an accuracy of 3.2 mm and with an in-plane path orientation of 2.5 degrees relative to the prescribed one. Path planning, including negotiation of obstacles and needle bending, was successfully performed. The signal-to-noise ratio (SNR) of TrueFISP was 25.3+/-2.1 when the manipulator was idle and was 18.6+/-2.4 during its operation. The SNR of triggered GRE (acquired only when the manipulator was idle) was 61.3+/-1.8. In conclusion, this study shows the feasibility of performing manually directed interventions inside cylindrical MR scanners with real-time MRI.     

Simultaneous determination of the endocrine disrupting compounds nonylphenol, nonylphenol ethoxylates, triclosan and bisphenol A in wastewater and sewage sludge by gas chromatography-mass spectrometry

An integrated analytical method for the simultaneous determination of 4-n-nonylphenol (4-n-NP), nonylphenol monoethoxylate (NP1EO), nonylphenol diethoxylate (NP2EO), bisphenol A (BPA) and triclosan (TCS) in wastewater (dissolved and particulate phase) and sewage sludge was developed based on gas chromatography-mass spectrometry. Chromatographic analysis was achieved after derivatization with bis(trimethylsilyl)trifluoroacetamide (BSTFA). Extraction from water samples was performed by solid-phase extraction (SPE). The optimization of SPE procedure included the type of sorbent and the type of the organic solvent used for the elution. Referred to solid samples, the target compounds were extracted by sonication. In this case the optimization of the extraction procedure included the variation of the amount of the extracted biomass, the duration and the temperature of sonication and the type of the extraction organic solvent. The developed extraction procedures resulted in good repeatability and reproducibility with relative standard deviations (RSDs) less than 13% for all the tested compounds for both types of samples. Satisfactory recoveries were obtained (>60%) for all the compounds in both liquid and solid samples, except for 4-n-NP, which gave recoveries up to 35% in wastewater samples and up to 63% in sludge samples. The limits of detection (LODs) of the target compounds varied from 0.03 (4-n-NP) to 0.41 microg l(-1) (NP2EO) and from 0.04 (4-n-NP) to 0.96 microg kg(-1) (NP2EO) for liquid and solid samples, respectively. The developed methods were successfully applied to the analysis of the target compounds in real samples.     

Formal extension and quotients of the invariant holonomic system

Let be a semisimple Lie algebra and a Cartan subalgebra of . Fix . Let be the invariant holonomic system (see [R. Hotta, M. Kashiwara, The invariant holonomic system on a semisimple Lie algebra, Invent. Math. 75 (1984) 327–358]). First we investigate its formal extension . In the sequel we calculate the characteristic variety of some simple quotients of and its Fourier transform .     

Universality is a Σ 1 1 -complete property

Our purpose in this article is to prove that if ? ∞ < a < b < ∞, then the set of all sequences with terms in C([a, b], ?) which posses a universal element is Σ ₁ ¹ -complete in C([a, b], ?)^?.     

A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potential

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). By combining variational with degree theoretic techniques, we prove a multiplicity theorem. In the process, we also prove a result of independent interest relating and local minimizers, of a nonsmooth locally Lipschitz functional.      

Synthesis,characterization, crystal structure and antiproliferative activity of platinum(II) complexes with 2-acetylpyridine-4-cyclohexyl-thiosemicarbazone

New platinum complexes have been synthesized by the reaction of Na₂PtCl₄ with 2-acetylpyridine-4-cyclohexyl-thiosemicarbazone, HAc4CyclHexyl (1). The new complexes [Pt(Ac4CyclHexyl)Cl] (2) and [Pt(Ac4CyclHexyl)₂] (3) have been characterized by elemental analyses and spectroscopic studies. The crystal structure of the complex [Pt(Ac4CyclHexyl)Cl] · DMF has been solved by single-crystal X-ray diffraction. The anion of Ac4CyclHexyl coordinates in a planar conformation to the central platinum(II) through the pyridyl N, azomethine N and thiolato S atoms. The crystal packing is determined by double intermolecular hydrogen interactions, π–π, Pt–C and Pt–π contacts. The cytotoxic activities of 1–3 have been evaluated for antiproliferative activity in vitro against the cells of three human cancer cell lines: MCF-7 (human breast cancer cell line), T24 (bladder cancer cell line), A-549 (non-small cell lung carcinoma) and a mouse L-929 (a fibroblast-like cell line cloned from strain L). The compounds 1–3 display IC₅₀ values in a μM range better than that of the antitumor drug cisplatin and are considered as agents with potential antitumor activity candidates for further stages of screening in vitro and/or in vivo.     

Chitosan derivatives as biosorbents for basic dyes

The scope of this study was to prepare and evaluate chitosan derivatives as biosorbents for basic dyes. This was achieved by grafting poly (acrylic acid) and poly (acrylamide) through persulfate induced free radical initiated polymerization processes and covalent cross-linking of the prepared materials. Remacryl Red TGL was used as the cationic dye. Equilibrium sorption experiments were carried out at different pH and initial dye concentration values. The experimental equilibrium data for each adsorbent-dye system were successfully fitted to the Langmuir, Freundlich and pH-dependent Langmuir-Freundlich sorption isotherms. Thermodynamic parameters of the adsorption process such as DeltaG degrees, DeltaH degrees, and DeltaS degrees were calculated. The negative values of free energy reflected the spontaneous nature of adsorption. The typical dependence of dye uptake on temperature and the kinetics of adsorption indicated the process to be chemisorption. The grafting modifications greatly enhanced the adsorption performance of the biosorbents, especially in the case of powdered cross-linked chitosan grafted with acrylic acid, which exhibited a maximum adsorption capacity equal to 1.068 mmol/g. Kinetic studies also revealed a significant improvement of sorption rates by the modifications. Diffusion coefficients of the dye molecule were determined to be of the order 10(-13) - 10(-12) m2/s. Furthermore, desorption experiments affirmed the regenerative capability of the loaded material.     

Per(6-guanidino-6-deoxy)cyclodextrins: synthesis, characterisation and binding behaviour toward selected small molecules and DNA

Per(6-guanidino-6-deoxy)-cyclodextrins , and are novel derivatives, resulting from homogeneous introduction of the guanidino group at the primary side of alpha-, beta- and gamma-cyclodextrins. The products were obtained from the corresponding amino derivatives, as direct guanidinylation of the known bromo-cyclodextrins provided mixtures. The new compounds were fully characterized by NMR spectroscopy and other analytical methods, and their interaction with guest molecules was studied. Strong complexation with 4-nitrophenyl phosphate () disodium salt was observed (K(binding) approximately 5 x 10(4) M(-1)), whereas the non-phosphorylated substrate nitrobenzene () formed a very weak complex. 2D ROESY spectra revealed cavity inclusion in both cases, however the orientation of was opposite to that of , such that the phosphate group is oriented toward the primary side facing the guanidine groups. The strong affinity of towards the phosphorylated guest suggested that interaction with DNA was possible. The new compounds were found to completely inhibit the migration of ultra pure calf thymus DNA during agarose gel electrophoresis, whereas no effects were observed with guanidine alone or with the plain cyclodextrins. Further, the condensation of DNA into nanoparticles in the presence of was demonstrated by atomic force microscopy, confirming strong electrostatic interaction between the biopolymer and the multicationic products . The strong guanidine-phosphate interactions between and DNA were therefore attributed to the clustering of the guanidine groups in the primary area of the cyclodextrin. Cavity effects could not be assessed.     

An analytical method for the simultaneous trace determination of acidic pharmaceuticals and phenolic endocrine disrupting chemicals in wastewater and sewage sludge by gas chromatography-mass spectrometry

This article presents an analytical method based on solid-phase extraction (SPE) and gas chromatography coupled with mass spectrometry for the simultaneous determination of the most frequently used acidic pharmaceutical residues, ibuprofen, diclofenac, naproxen and ketoprofen (KFN), and phenolic endocrine disruptors, bisphenol (BPA), triclosan (TCS), nonylphenol, nonylphenol monoethoxylate and nonylphenol diethoxylate, in wastewater and sewage sludge samples. In the first phase of the study, each compound has been characterized individually and afterwards in mixture as a trimethylsilyl derivative in order to identify the characteristic ions (m/z ratio) constituting the mass spectrum and to choose the ions for quantification and confirmation. Subsequently, derivatization was evaluated by testing different variables such as the volume of the derivatization solvent bis(trimethylsilyl)trifluoroacetamide and the effect of each catalyst, pyridine and 1% trimethyl chlorosilane, in the derivatized solution. For the analysis of wastewater samples, two commercial SPE cartridges, C18 and Oasis HLB, were compared for their extraction efficiency of the target compounds. The key parameter of extraction procedure included the effect of pH (2.5, 5.3 and 7) of the loading solution. For solid samples, parameters such as the extracted biomass, the volume of the extraction organic solvent and the effect of matrix interferences in chromatographic analysis were evaluated. By using C18 cartridges as purification procedure and ultrasound sonication, satisfactory mean relative recoveries with BPA-d16 and meclofenamic acid as surrogates were obtained ranging from 91% to 117% for wastewater and 84% to 107% for sewage sludge samples. Nine-point calibration of the standard mixture was performed by linear regression analysis with a correlation coefficient >0.99 for all the tested compounds. Limits of detection for the developed methods were established between 0.3 (KFN) and 14.8 (BPA) ng L⁻¹, and 15.0 (TCS) and 32.9 (BPA) ng g⁻¹ for wastewater and sewage sludge, respectively. Application to real samples of the wastewater treatment plant in Athens, the capital of Greece, demonstrated the presence of all tested compounds in most of the samples.