Galerkin method for nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation with integral condition

In this paper, we are going to deal with the nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation. Galerkin method was the main used tool for proving the solvability of the given nonlocal problem.     

Batch and continuous fixed-bed column adsorption of Cs+ and Sr2+ onto montmorillonite–iron oxide composite: Comparative and competitive study

A montmorillonite–iron oxide composite (MIOC) was prepared to assess its effectiveness in the removal of Cs⁺ and Sr²⁺ from aqueous solution. A comparative and competitive adsorption study was conducted in single and binary systems. Used materials have been characterized by X-ray diffraction (XRD) and Infrared spectroscopy. Adsorption of Cs⁺ and Sr²⁺ as a function of contact time and pH was investigated, adsorption data of single metal solutions were well fitted to the Freundlich–Langmuir isotherm models. Equilibrium isotherms for the binary removal of Cs⁺ and Sr²⁺ by MIOC have been analyzed by using non modified and extended Langmuir models with a satisfactory R ² values. Neutral solution pH was found to be favorable for both single and binary systems. The adsorption model analysis revealed that MIOC was more selective for Sr than Cs. The maximum adsorption capacities for individual Cs⁺ and Sr²⁺ solutions were 52.6 and 55.5 mg g^?1, respectively. While the maximum uptakes in the binary system were 41.6 and 47.6 mg g^?1 for Cs⁺ and Sr²⁺, respectively. Column adsorption experiments were carried out at room temperature under the effect of various operating parameters such as bed depth, initial cation concentration and flow rate, Breakthrough curves were well fitted to the Thomas model. Desorption experiments were also conducted to assess the possibility for the reuse of adsorbent and the recovery of cations.     

Autotandem Catalysis: Inexpensive and Green Access to Functionalized Ketones by Intermolecular Iron-Catalyzed Amidoalkynylation/Hydration Cascade Reaction via N-Acyliminium Ion Chemistry

Iron-based catalysts were applied in cascade-type reactions for the synthesis of different carbonyl compounds. The reactions proceeded by a new iron-catalyzed cascade of alkynylation/hydration by using both the σ- and π-Lewis acid properties of iron salts. The alkynylation reactions of several endo and exocyclic acetoxylactams were achieved with three different catalysts including FeCl₃ ⋅ 6H₂O, FeCl₃, and Fe(OTf)₃ showing the efficiency of σ-Lewis acidity of iron (III) salts in catalyzing the alkynylation reaction. We also demonstrated that the reaction sequence could be shortened by the direct use of hydroxylactams, leading to an environmentally friendly protocol, avoiding the need to perform unnecessary lengthy steps. A combination of the hard/soft iron Lewis acid properties was then used to implement an unprecedented tandem intermolecular alkynylation/intramolecular hydration sequence allowing expedient access to a new carbonyl structures from trivial materials.     

Spontaneous Oxidative Addition of σ-SiSi Bonds at Gold

Gold can do it! The activation of disilanes at gold was observed experimentally and analyzed theoretically. Upon chelation with two or even only one phosphine donor, the oxidative addition of σ-Si?Si bonds proceeds readily at low temperatures. These results show an unexpected similarity between gold and the other late transition metals towards σ?bond activation.     

Chemical composition, antibacterial and antioxidant activities of the essential oils from Thymus satureioides and Thymus pallidus

This study was designed to examine the in vitro antibacterial and antioxidant activities of the essential oils (EOs) of Thymus satureioides (T.s) and T. pallidus (T.p). EOs were isolated by steam distillation and analyzed by capillary gas chromatography and gas chromatography coupled to mass spectrometry (GC-MS). The major constituents of the volatile fraction of T. satureioides were bomeol (29.5%), carvacrol (9.1%), and beta-caryophyllene (8.2%), while those of T. pallidus were camphor (29.8%), dihydrocarvone (17.6%), bomeol (7.6%) and camphene (7.5%). The essential oils were tested against a panel of Gram+ and Gram- bacteria by using agar diffusion and broth dilution methods. The data indicated that the Gram-positive Bacillus subtilis was the most sensitive strain producing an average inhibition zone of 51.7 mm. Furthermore, Pseudomonas aeruginosa, known as a resistant strain, was also sensitive. The samples were also subjected to screening for their possible antioxidant activity by using the 2,2-diphenyl-l-picrylhydrazyl (DPPH) assay. The IC50 values of the oil of T. satureioides and T. pallidus were 0.32 and 11.6 mg/mL, respectively.     

Synthesis, characterization and solution behaviour of phosphoryl complexes of tin tetrafluoride

The preparation and characterization of a series of octahedral complexes [SnF₄L₂] (L = (Me₂N)₃PO (1), L = (R₂N)₂P(O)F; R = Me (2); Et (3) or L = R₂NP(O)F₂; R = Me (4); Et (5)) are described. These new adducts have been characterised by multinuclear (¹⁹F, ³¹P and ¹¹⁹Sn) NMR, IR spectroscopy and elemental analysis. The NMR data particularly the ¹⁹F NMR spectra showed that the complexes exist in solution as mixtures of cis and trans isomers. The solution behaviour of the complexes studied by variable temperature NMR in the presence of excess ligand indicated that, unlike in the SnCl₄ analogues, the ligand exchange at room temperature is slow for 1–3 and fast only for 4 and 5. The metal–ligand exchange barriers in [SnF₄L₂] and [SnCl₄L₂] systems were estimated and compared. The results indicate that in addition to the difference in the Lewis acidity between SnF₄ and SnCl₄ the nature of the substituents (fluorine atoms) on the phosphorus atom of the ligand can contribute considerably to the lability of the complex obtained.     

Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size

This Note presents the derivation of the 2nd-order asymptotic expansion of the eigenvalues and the eigenfunctions of the operator associated to an interior elliptic equation supplemented by a Dirichlet boundary condition on a domain consisting of two cavities linked by a hole of small size. The asymptotic expansion is carried out with respect to the size of the hole. The main feature of the method is to yield a robust numerical procedure making it possible to compute the eigenvalues without resorting to a refined mesh around the hole. To cite this article: A. Bendali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Experimental confirmation of Kelvin's equilibria

We experimentally corroborate the core analytical deductions of Thomson's 124-year-old theorem, vis-à-vis the stability of a ring of N vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular N-gons are stable for Nor=8. The N相似文献   

Oxidative Addition of Carbon–Carbon Bonds to Gold

The oxidative addition of strained C? C bonds (biphenylene, benzocyclobutenone) to DPCb (diphosphino‐carborane) gold(I) complexes is reported. The resulting cationic organogold(III) complexes have been isolated and fully characterized. Experimental conditions can be adjusted to obtain selectively acyl gold(III) complexes resulting from oxidative addition of either the C(aryl)? C(O) or C(alkyl)? C(O) bond of benzocyclobutenone. DFT calculations provide mechanistic insight into this unprecedented transformation.