Silver(I) oxide mediated highly selective monotosylation of symmetrical diols. Application to the synthesis of polysubstituted cyclic ethers

[reaction: see text] The reaction of symmetrical diols and oligo(ethylene glycol)s with a stoichiometric amount of p-toluenesulfonyl chloride in the presence of silver(I) oxide and a catalytic amount of potassium iodide led selectively to the monotosylate derivatives in high yields. Polysubstituted cyclic ethers were obtained readily upon treatment of the corresponding diols with an excess of silver oxide. The high selectivity was explained on the basis of the difference in acidity between the two hydroxy groups, which undergo an intramolecular hydrogen bonding.     

Variation de la L-norme de la 1-forme de torsion sur une variété hermitienne compacte

Let (M,g) be a complex compact hermitian manifold with dimension complex dim_C = m ≥ 2, we study in this paper the critical points of the functional: in the set of the hermitian metrics with total volume equal to one, where θ is 1 — form of torsion of the Chern connexion and r is a real number such that 1 ≤ r ≤ m. We show that the critical points of this functional are exactly a semi-kählerian metric.     

Hygrometric Determination of Water Activities and Osmotic and Activity Coefficients of NH4Cl–KCl–H2O at 25°C

Relative humidities have been measured for mixed aqueous electrolyte system of ammonium and potassium chlorides by the hygrometric method at total molalities from 0.3 to 6 mol-kg^–1for ionic-strength fractions yof NH₄Cl of 1/3, 1/2, and 2/3 at 25°C. The data allow the calculation of new water activities and osmotic coefficients. The proposed ECA (extended composed additivity) rule of calculation of water activity in mixed aqueous electrolyte solutions from the water activities of a single component is extended to this system. The experimental results and the predictions of the ECA rule are compared with the Robinson–Stokes, Reilly–Wood–Robinson, the Pitzer, and the Lietzke–Stoughton II models. Predictions made using these models are, in general, consistent with our results. From these measurements, the Pitzer mixing ionic parameters are determined and used to predict the solute activity coefficients in the mixture for different ionic-strength fractions.     

Hygrometric Determination of the Water Activities of the Aqueous Solutions of the Mixed Electrolyte NaCl–CaCl2–H2O at 25°C

The mixture {yNaCl + (1 – y)CaCl₂}(aq) has been studied with the hygrometric method at the temperature 25°C. The water activities were measured at total molalities from 0.25 mol-kg^–1 to near saturation for different ionic-strength fractions y of NaCl with y = 0.33, 0.50, and 0.67. The obtained data allow the calculation of osmotic coefficients. The experimental results are compared with the predictions of the Zdanovskii–Stokes–Robinson (ZSR), Kusik and Meissner (KM), Robinson and Stokes (RS), Lietzke and Stoughton (LS II), Reilly–Wood–Robinson (RWR), and Pitzer models. From the measured osmotic coefficients, the Pitzer ionic mixing parameters _{Na Ca} and _{Na Ca} Cl are determined and are used to predict the solute activity coefficients in the mixtures. The excess Gibbs energy is also determined. These results are compared with those given in the literature.     

Lyapunov Stability of Differential Inclusions with Lipschitz Cusco Perturbations of Maximal Monotone Operators

Set-Valued and Variational Analysis - We give new criteria for weak and strong invariant closed sets for differential inclusions in $\mathbb {R}^{n}$ , and which are simultaneously governed by...     

On Brøndsted–Rockafellar’s Theorem for convex lower semicontinuous epi-pointed functions in locally convex spaces

Mathematical Programming - In this work we give an extension of the Brøndsted–Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous...     

Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier-Stokes equations

The focus of this contribution is the examination of the influence of different interpolation orders (especially for the pressure field) by solving the stationary incompressible Navier-Stokes equations with least-squares finite elements. We consider two different div-grad first-order systems which result in a three-field formulation with stresses, velocitites and pressure, see e.g. SCHWARZ & SCHRÖDER [1] and BOCHEV & GUNZBURGER [2]. Additionally, a numerical example is presented to show the performance of the considered formulations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Straightforward Bienaymé and copper catalyzed N-arylation sequence to access diverse 5H-pyrido[2′,1′:2,3]imidazo[4,5-b]indoles and analogues

A two-step sequence is reported giving access to diverse 5H-pyrido[2′,1′:2,3]imidazo[4,5-b]indoles and analogues via a Bienaymé multicomponent reaction followed by N-arylation. The desired polycylic scaffolds were obtained in high yield using copper iodide in association with TMEDA in aqueous or dioxane media.