Activity Coefficients of Electrolytes from Liquid Membrane Cells. XII. Magnesium,Lanthanum, and Tris(ethylenediamine)cobalt(III) Salts of the 1,5-Naphthalenedisulfonate Anion at 298.15 K

Activity coefficients of the highly charged electrolytes Mgds, La₂ds₃, and [Co(en)₃]₂ds₃ (en = ethylenediamine, ds²⁻=1,5-naphthalenedisulfonate anion), were determined at 298.15 K using liquid-membrane cells. These salts are found not to display large negative deviations from the Debye-Hückel limiting slope in the dilute regions, which characterize the corresponding sulfate salts. Theoretical calculations based on the primitive model (charged hard spheres in an unstructured dielectric medium) reproduce the behavior of these salts correctly up to concentrations of 0.01 mol⋅kg⁻¹ or more (0.1 mol⋅kg⁻¹ for Mgds), although ds²⁻, far from resembling a charged sphere, is a planar ion with charges distant from one another. The Pitzer model parameter values are reported for the activity and osmotic coefficients.     

Étude thermodynamique de la complexation de l'argent par la pipéridine et ses dérivés méthylés

Enthalpies of silver complexes formation with piperidine, 2-methylpiperidine, 3-methylpiperidine, 4-methylpiperidine and 2,6-dimethylpiperidine are determined at 25°C by means of direct calorimetry, in aqueous medium with 0.5 M KNO₃ as a constant ionic strength.Free energies from a previous work and corresponding entropies are also given in this paper.All the thermodynamic functions are discussed in relation to the substituent position. Particularly, a linear relationship is found between complexation enthalpies and proton ionization enthalpies already determined in a previous study.     

Complexation metallique des imides. I. Grandeurs thermodynamiques de formation des complexes de Ag(I), Cd(II), NI(II), Cu(II) avec la succinimide

Thermodynamic values for the formation of Ag⁺, Cd²⁺, Ni²⁺ and Cu²⁺ complexes with succinimide were determined at 25°C in aqueous medium 0.5 M KNO₃. The stability constants were calculated from pH metric measurements and the related enthalpies from direct calorimetric determinations. An interpretation of the results is given, based on the character of the established bonds.     

Exact join detection for convex polyhedra and other numerical abstractions

Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification and optimization of hardware and software systems. In such application fields though, general convex polyhedra are just one among many, so-called, numerical abstractions, which range from restricted families of (not necessarily closed) convex polyhedra to non-convex geometrical objects. We thus tackle the problem from an abstract point of view: for a wide range of numerical abstractions that can be modeled as bounded join-semilattices—that is, partial orders where any finite set of elements has a least upper bound—we show necessary and sufficient conditions for the equivalence between the lattice-theoretic join and the set-theoretic union. For the case of closed convex polyhedra—which, as far as we know, is the only one already studied in the literature—we improve upon the state-of-the-art by providing a new algorithm with a better worst-case complexity. The results and algorithms presented for the other numerical abstractions are new to this paper. All the algorithms have been implemented, experimentally validated, and made available in the Parma Polyhedra Library.     

Can smooth LTB models mimicking the cosmological constant for the luminosity distance also satisfy the age constraint?

The central smoothness of the functions defining a LTB solution plays a crucial role in their ability to mimic the effects of the cosmological constant. Even if non-smoothness is not physically inconsistent with the theory of general relativity, smoothness is still an important geometrical property characterizing the solution of the Einstein’s equations. So far attention has been focused on $C^{1}$ models while in this paper we approach it in a more general way, investigating the implications of higher order central smoothness conditions for LTB models reproducing the luminosity distance of a $\Lambda CDM$ Universe. Our analysis is based on a low red-shift expansion, and extends previous investigations by including also the constraint coming from the age of the Universe and re-expressing the equations for the solution of the inversion problem in a manifestly dimensionless form which makes evident the freedom to accommodate any value of $H_0$ as well. Higher order smoothness conditions strongly limit the number of possible solutions respect to the first order condition. Neither a $C^{1}$ or a $C^{i}$ LTB model can both satisfy the age constraint and mimic the cosmological constant for the luminosity distance. This implies that it is not necessary to include any additional observable to distinguish mathematically the theoretical predictions of a smooth LTB model from a $\Lambda CDM$ . One difference is in the case in which the age constraint is not included and the bang function is zero, in which there is a unique solution for $C^1$ models but no solution for the $C^{i}$ case. Another difference is in the case in which the age constraint is not included and the bang function is not zero, in which the solution is undetermined for both $C^1$ and $C^{i}$ models, but the latter ones have much less residual parametric freedom. Our results imply that any LTB model able to fit luminosity distance data and satisfy the age constraint is either not mimicking exactly the $\Lambda CDM$ red-shift space theoretical predictions or it is not smooth.     

Condensation cascades and methylgroup transfer reactions during the formation of arsane,methyl- and dimethylarsane by aqueous borohydride and (methyl) arsenates

The formation of volatile products during the reaction of As(iii), As(v), MeAsO(OH)₂, and Me₂AsO(OH) with aqueous NaBH₄ has been investigated, and the formation of arsanes, diarsanes, and triarsanes has been detected. The presence of triarsanes is reported here for the first time. Diarsanes and triarsanes are likely formed in condensation cascade reactions, whereas trimethylarsane arises via the transfer of a methyl group. The formation of volatile by-products is considerably reduced by increasing the acidity of the medium and the concentration of NaBH₄ or by the addition of thiols, such as cysteine. A reaction scheme is proposed which reconciles the evidence reported herein and elsewhere in the literature that is valid for both analytical (trace analysis) and non-analytical reaction conditions.     

Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term

We investigate the asymptotic behaviour as p → ∞ of sequences of positive weak solutions of the equation $$\left\{\begin{array}{l}-\Delta_p u = \lambda\,u^{p-1}+ u^{q(p)-1}\quad {\rm in}\quad \Omega,\\ u = 0 \quad {\rm on}\quad \partial\Omega,\end{array} \right.$$ where λ > 0 and either 1 < q(p) < p or p < q(p), with ${{\lim_{p\to\infty}{q(p)}/{p}=Q\neq1}}$ . Uniform limits are characterized as positive viscosity solutions of the problem $$\left\{\begin{array}{l}\min\left\{|\nabla u (x)| - \max\{\Lambda\,u (x),u ^Q(x)\}, -\Delta_{\infty}u (x)\right\} = 0 \quad {\rm in} \quad \Omega,\\ u = 0\quad {\rm on}\quad \partial\Omega.\end{array}\right.$$ for appropriate values of Λ > 0. Due to the decoupling of the nonlinearity under the limit process, the limit problem exhibits an intermediate behavior between an eigenvalue problem and a problem with a power-like right-hand side. Existence and non-existence results for both the original and the limit problems are obtained.