Concentration on minimal submanifolds for a singularly perturbed Neumann problem

We consider the equation −ε²Δu+u=up in Ω⊆RN, where Ω is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of ∂Ω, for N?3 and for k∈{1,…,N−2}. We impose Neumann boundary conditions, assuming 1<p<(N−k+2)/(N−k−2) and ε→⁰⁺. This result settles in full generality a phenomenon previously considered only in the particular case N=3 and k=1.     

A new class of functionalized terpyridyl ligands as building blocks for photosensitized supramolecular architectures. Synthesis, structural, and electronic characterizations

A new class of triarylpyridinio-derivatized [4'-(p-phenyl)(n)]terpyridyl ligands, R(1)(2)R(2)TP(+)-(p)(n)tpy, was designed as a novel category of electron-acceptor (A)-substituted proto-photosensitizing molecules. The first elements of this versatile family of ligands (i.e., n = 0, 1 and R(1) = R(2) = H), H(3)TP(+)-tpy and H(3)TP(+)-ptpy, were synthesized as well as their Ru(II) and Os(II) complexes to form the related acceptor-functionalized M(tpy)(2)(2+) and M(ptpy)(2)(2+) photosensitizer components denoted P0 and P1, respectively. Within the P1 series of compounds, an electron-donor (D)-substituted ligand, Me(2)N-ptpy, was also involved and associated with H(3)TP(+)-ptpy, giving rise to various combinations (up to 10 polyad systems). The two resulting series of nanometer-scale rigid rod-like photosensitized supramolecular architectures are of potential interest for long-range photoinduced electron transfer purposes. The main structural features of such supermolecules were determined by comparing the results obtained from (i) single-crystal X-ray analysis of the two free ligands together with that of the P0A/Ru and P1A(2)/Ru complexes and (ii) a detailed solution (1)H NMR study of the P0 series and, more specifically, of the P0A/Ru dyad (ROESY experiment). It is shown that the pseudoperpendicular conformation of the covalently linked A and P subunits found in the solid state is persistent in fluid medium; i.e., A is not conjugated with P (P0 and P1). The first insights regarding the consequences upon intercomponent couplings of combined substituent effects and conjugation (case of D-based polyads)-or absence of conjugation-are discussed in the light of ground-state electronic properties of the compounds.     

Calculation of effective index for different dielectric waveguides structures made of PVCi/PMATRIFE polymers at telecom-wavelength \lambda =1.55\,\upmu m

In this paper, a number of polymeric waveguide structures have been analyzed by using two distinct techniques which are: effective index method (EIM) and numerical simulation based on finite difference method (FDM). The main aim of this investigation is the calculation of effective indexes (EI) of the following structures: rib, ridge and buried channel waveguides at telecom wavelength $\lambda =1.55\,\upmu \hbox {m}$ for different dimensions of waveguide cores varying from 1.5–4  $\upmu \hbox {m}$ . Moreover, other optical propagation characteristics such as: confinement factor, normalized and propagation constant have been studied in TE polarisation. Otherwise the effect of the structure parameters and dimensions on the dispersion characteristics has been investigated. On the other hand, the optical field distribution has been computed using commercial software named OlympIOs. The polymers applied in the design of waveguide structures are the PVCi (n = 1,562 $\lambda = {1.55}\,\upmu $ m) used as core layer and the PMATRIFE (n = 1,409 $\lambda = 1.55\,\upmu $ m) used as substrate or cladding layer. The results obtained using EIM and simulation based on FDM show that effective index and field confinement factor of TE fundamental mode increase monotonously with the increasing dimension of core. The obtained results are in good agreement with published data based on other numerical methods.     

Horseradish Peroxidase Nanopatterned Electrodes by Click Chemistry: Application to the Electrochemical Detection of Paracetamol

We propose the fabrication of nanostructured glassy carbon (GC) electrodes modified with horseradish peroxidase (HRP) for the detection of paracetamol. This was accomplished by inducing the nanostructuration of GC via the adsorption of polystyrene nanospheres (900 nm diameter) followed by electropolymerization of N‐(10‐azidodecyl)pyrrole. The nanospheres were then removed and nanostructured polypyrrole‐GC was submitted to click reaction in presence of ethynyl‐biotin that was further coupled to HRP‐avidin. The electrode was then used to sense the electrochemical reduction of the enzymatically generated electroactive oxidized species of acetaminophen (NAPQI) in the presence of hydrogen peroxide. The nanostructured electrode with HRP exhibits a fast response towards NAPQI reduction and improved performances in terms of sensitivity and limit of detection compared to non structured electrode.     

Preparation and Characterization of Electrodes Modified with Pyrrole Surfactant,Multiwalled Carbon Nanotubes and Metallophthalocyanines for the Electrochemical Detection of Thiols

Our aim was to prepare hybrid electrodes active towards the electrooxidation of thiols by the co‐immobilization of native carbon nanotubes (CNTs) and cobalt phthalocyanine (CoPc) from aqueous solutions. This strategy was adopted to avoid the oxidation of CNTs that can induce a modification of their exceptional properties. To do so, a hydrosoluble pyrrole surfactant was used to get homogeneous aqueous dispersions of CNTs and CoPc and to trap both materials on the electrode via the electropolymerization of the pyrrole surfactant. The hybrid electrodes exhibit a good electrocatalytic activity towards the oxidation of L ‐cysteine and glutathione. Their performances in terms of limit of detection (0.01 mM) are compatible with the detection of these thiols in biological samples.     

The surface oxidation behavior of Ni–45.16%Ti shape memory alloys at different temperatures

The isothermal oxidation behavior of Ni–45.16%Ti (composition in atomic percent) alloy was investigated by thermogravimetric analysis, and differential scanning calorimeter (DSC) methods. It was found that Ni-rich NiTi alloy exhibits a different oxidation behavior at temperatures above 400 °C in oxygen atmosphere. The alloy was exposed to oxygen atmosphere isothermally, i.e., between 400 and 800 °C, for 1 h. A gravimetric method was used to determine the oxidation kinetics and it was seen that the oxidation constant increases significantly with isothermal temperature. The activation energy of oxidation reaction for NiTi alloy was determined to be 65.47 kJ mol^?1. According to DSC measurements, the transformation temperature of alloy (M _s, M _f, A _s and A _f) was increased and also R phase disappeared above 500 °C. The formal oxides were determined by means of SEM–EDX measurements and obtained oxides are TiO and TiO₂ oxides.     

$${\overline{1}}$$ 1 ¯ -Evaluating linear functionals on function spaces

Positivity - Let C(X) denotes the Riesz algebra of all real valued continuous functions on a Tychonoff space X, and let L be a vector subspace of C(X). A linear functional $$H:L\rightarrow {\mathbb...     

Effect of organic modifier and temperature on the resolution of betamethasone and dexamethasone using a porous graphitic carbon column: application to their identification and confirmation in human urine by LC-ESI-MS/MS

The effects of temperature, organic modifier and the type of acid on the retention factor, the resolution and peak shape of betamethasone and dexamethasone are described. The study is performed using narrow bore porous graphitic carbon (PGC) columns online with diode-array detector (DAD) and ESI MS/MS. The results show that temperature affects the retention behaviour of the two compounds and ACN yields the best separation while no effect is obtained by changing the type of organic acid. The developed method is applied for the confirmation of dexamethasone and betamethasone in human urine.     

q-Oscillator Algebra And d-Orthogonal Polynomials

In this paper we express the matrix coefficients of the Fock representation of a q-oscillator algebra in terms of the d-orthogonal Al-Salam Carlitz polynomials. Also, we derive a generating functions, recurrence relations and q-difference equations for these d-orthogonal polynomials.     

Experimental and theoretical study of AC electrical conduction mechanisms of semicrystalline parylene C thin films

The electrical conduction mechanisms of semicrystalline thermoplastic parylene C (-H(2)C-C(6)H(3)Cl-CH(2)-)(n) thin films were studied in large temperature and frequency regions. The alternative current (AC) electrical conduction in parylene C is governed by two processes which can be ascribed to a hopping transport mechanism: correlated barrier hopping (CBH) model at low [77-155 K] and high [473-533 K] temperature and the small polaron tunneling mechanism (SPTM) from 193 to 413 K within the framework of the universal law of dielectric response. The conduction mechanism is explained with the help of Elliot's theory, and the Elliot's parameters are determined. From frequency- and temperature-conductivity characteristics, the activation energy is found to be 1.27 eV for direct current (DC) conduction interpreted in terms of ionic conduction mechanism. The power law dependence of AC conductivity is interpreted in terms of electron hopping with a density N(E(F)) (~10(18) eV cm(-3)) over a 0.023-0.03 eV high barrier across a distance of 1.46-1.54 ?.