On an Riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid

In this paper we prove that the system of generalized eigenvectors of the operator (I+εK)⁻¹d⁴/dx⁴ forms a Riesz basis of L²(]−L,L[) where K is the integral operator with kernel the Hankel function of the first kind and order 0. This operator was introduced in J. Sound Vibration 177 (1994) 259-275. We give positive answers to the hypotheses posed in that article.     

A remarkable accelerating effect of iodide ions in the photostimulated phosphonylation of bromoaromatic compounds

We find that 1 equiv. of NaI greatly accelerates the photostimulated substitution (S_RN¹ mechanism) of bromobenzene, bromotoluenes and bromopyridines by diethylphosphite ion, in acetonitrile/tetrahydrofuran mixtures. Consequently, bromoaromatic compounds are suitable for preparative use.     

Mutagenic, antimutagenic and antioxidant activities of a new polyphenolic and a flavonoid substances isolated from Anagallis monelli

A new polyphenolic natural substance: 2,5-dihydroxy-benzoic acid 3'-formyl-5'-hydroxy-phenyl ester (1), Anamighrinal and 3-(O-alpha-L-rhamnosyl) quercetin (2) have been isolated from the methanolic aerial part extract of the plant Anagallis monelli by chromatographic separation. Their structures have been deduced essentially by one and two NMR spectroscopic procedures and mass spectrometry. Antioxidant, mutagenic, antimutagenic activities, of the natural products were realised and positive results were recorded.     

Structural and textural features of TiO<Subscript>2</Subscript>/SAPO-34 nanocomposite prepared by the sol–gel method

This paper focuses on the synthesis of nanocomposite materials, TiO₂/SAPO-34, using the sol–gel method, which involves preparing a mixture between as-synthesized or calcined SAPO-34 zeolite and TiO₂ gel under hydrothermal crystallization and then calcining it at 400 °C for the formation of the TiO₂ anatase phase. The structural and textural features of the obtained materials were determined by various physico-chemical techniques such as thermogravimetric analysis, X-ray diffraction, scanning electronic microscopy, nitrogen sorption at 77 K, energy dispersive X-ray analysis and ultraviolet–visible spectrometry. The DRX results showed that calcination at 400 °C of the mixture between the calcined SAPO-34 and TiO₂ gel led to the collapse of the original framework of zeolite, but formed the anatase TiO₂ in a nano-spherical morphology; however, the use of as-synthesized SAPO-34 supports provides a mixture phase between SAPO-34 and TiO₂ anatase after calcination. The photocatalytic properties of the SAPO-34/TiO₂ and TiO₂-type materials were tested for the removal of methylene blue (MB) dye. The MB degradation proved to increase as a function of contact time, catalyst mass and the initial concentration of MB.     

Simultaneous analysis of polychlorinated biphenyls and organochlorine pesticides in water by headspace solid-phase microextraction with gas chromatography-tandem mass spectrometry

Headspace solid-phase microextraction combined with gas chromatography-ion trap tandem mass spectrometry (HS-SPME-GC-ITMS-MS) method has been developed and studied for the simultaneous determination of 15 organochlorine pesticides (OCPs) and 20 polychlorinated biphenyls (PCBs) in aqueous samples. To perform the HS-SPME polydimethylsiloxane (PDMS) (7, 30 and 100 microm film thickness) and polydimethylsiloxane-divinylbenzene (PDMS-DVB) fibers were initially compared on the basis of their absorption capacities for the selected compounds, and PDMS 100 microm film thickness was selected to accomplish the rests of essays. The influence of various parameters on OCPs and PCBs extraction efficiency by HS-SPME was thoroughly studied using GC-electron capture detector (ECD). Parameters such as collision induced dissociation (CID) resonant excitation amplitude and RF storage level were optimized to increase specificity and sensibility for ITMS-MS analysis. The performance of proposed HS-SPME-GC-ITMS-MS methodology with respect to linearity, reproducibility and limit of detection (LOD) was evaluated by water spiked with target compounds. The linear range of most compounds was found to be between 0.01 and 1 ng mL(-1) and the limits of detection were between 0.4 and 26 pg mL(-1). The reproducibility of the method (n = 6), expressed as relative standard deviation (RSD), was between 5 and 21%. Finally, developed procedure was applied to determine selected OCPs and PCBs in river water samples in concentration below 0.1 ng mL(-1) can be easily carried out with ultra-selectivity and precision.     

Development of an Innovative Nitrite Sensing Platform Based on the Construction of an Electrochemical Composite Sensor of Polymer Coated CNTs and Decorated with Magnetite Nanoparticles

Electrochemical determination of nitrite in real water samples is achieved using simple and efficient electrochemical sensor. The sensor is fabricated by electrodeposition of a thin layer of poly(3,4-ethylenedioxythiophene) sandwiched by drop-casting two thin layers of CNTs and iron oxide nanoparticles (Fe₃O₄) over a GC electrode surface. Voltammetry determination of nitrite in tap water and wastewater samples in the concentration range (0.5–150 μM) is successfully achieved with detection limits of 22 and 24 nM, respectively. Practical application of the GC/CNT/PEDOT/Fe₃O₄ sensor is efficiently assessed in real water samples for nitrite determination with acceptable recoveries, excellent anti-interference ability and long-term stability.     

Conceptual polymorphism of entropy into the history: extensions of the second law of thermodynamics towards statistical physics and chemistry during nineteenth–twentieth centuries

After the birth of thermodynamics’ second principle—outlined in Carnot's Réflexions sur la puissance motrice du feu (1824)—several studies provided new arguments in the field. Mainly, they concerned the thermodynamics’ first principle—including energy conceptualisation—, the analytical aspects of the heat propagation, the statistical aspects of the mechanical theory of heat. In other words, the second half of nineteenth century was marked by an intense interdisciplinary research activity between physics and chemistry: new disciplines applied to the heat developed in the form of analytical, mechanical and statistical theories. Inside all these theories, entropy—the brand-new function that Clausius coined in his Mechanical theory of heat—started to play a central epistemic role. In the present paper, we analyse some steps of the historical process of conceptualisation of such function from 1850 to 1902. Particularly, we retrace the historical–foundational path that—starting from Clausius’ Second Law—lead Boltzmann and Gibbs to their distinguished formulations of statistical entropy. As usual, our research has been unrolled through the analyses of primary sources and by leaning on critical readings of the secondary literature. As for the methodological approach, text analysis of historical documents constituted our privileged modus operandi. This paper is the expression of a collaborative historical research program focused on the thermodynamic foundations of physics–chemistry relationship; early results have already been published by the same authors upon the concepts of reversibility––and––thermal equilibrium.

     

Ck-regularity for the $$\bar \partial $$ -equation with a support condition

Let D be a C ^d q-convex intersection, d ≥ 2, 0 ≤ q ≤ n ? 1, in a complex manifold X of complex dimension n, n ≥ 2, and let E be a holomorphic vector bundle of rank N over X. In this paper, C ^k -estimates, k = 2, 3,...,∞, for solutions to the \(\bar \partial \)-equation with small loss of smoothness are obtained for E-valued (0, s)-forms on D when n ? q ≤ s ≤ n. In addition, we solve the \(\bar \partial \)-equation with a support condition in C ^k -spaces. More precisely, we prove that for a \(\bar \partial \)-closed form f in C _0,q ^k (X D,E), 1 ≤ q ≤ n ? 2, n ≥ 3, with compact support and for ε with 0 < ε < 1 there exists a form u in C _0,q?1 ^k?ε (X D,E) with compact support such that \(\bar \partial u = f\) in \(X\backslash \bar D\). Applications are given for a separation theorem of Andreotti-Vesentini type in C ^k -setting and for the solvability of the \(\bar \partial \)-equation for currents.     

General Energy Decay for a Viscoelastic Equation of Kirchhoff Type with Acoustic Boundary Conditions

This paper is concerned with a viscoelastic equation of Kirchhoff type with acoustic boundary conditions in a bounded domain of \(\mathbb {R}^{n}.\) We show that, under suitable conditions on the initial data, the solution exists globally in time. Then, we prove the general energy decay of global solutions by applying a lemma of Martinez, which allows us to get our decay result for a class of relaxation functions wider than that usually considered.     

The Effect of Conducting Boundaries on Weakly Nonlinear Darcy–Bénard Convection

We consider convection in a uniform fluid-saturated porous layer which is bounded by conducting plates and heated from below. The primary aim is to determine the identity of the postcritical convection planform as a function of the thicknesses and conductivities of the bounding plates relative to that of the porous layer. This work complements and extends an early paper by Riahi (J Fluid Mech 129:153–171, 1983) who considered a situation where the porous layer is bounded by infinitely thick conducting media. We present regions in parameter space wherein convection in the form of rolls is unstable and within which cells with square planform form the preferred pattern.