Ion-Interaction Approach: Pressure Effect on the Solubility of Some Minerals in Submarine Brines and Seawater

The pressure dependence of salt solubility in multiple electrolyte solutions was estimated to 1000 atm. The activity coefficients, thermodynamic solubility products, degrees of saturation, and mineral solubility were calculated with high precision only up to 300 atm because of the absence of compressibility data for mixed electrolyte solutions. The ion-interaction approach developed during the last 2 decades allows the prediction of various thermodynamic properties, including volumetric ones for multiple-solute natural solutions. This approach was applied to the estimation of the depth dependence of solubility for certain evaporite minerals in natural brines. The influence of pressure on solubility products, mean activity coefficients, and degrees of saturation of minerals, such as, halite (NaCl), anhydrite (CaSO₄), gypsum (CaSO₄·2 H₂O), celestite (SrSO₄), and barite (BaSO₄) were calculated for in situ depths in the Orca Basin (Gulf of Mexico), the Tyro and Bannock II depressions (the Mediterranean Sea), and for average seawater.     

Stereoselective synthesis of decaprenylphosphoryl β-d-arabinofuranose

Decaprenylphosphoryl β-d-arabinofuranose (DPA) is known to be a key arabinose donor in mycobacteria. In order to study the biosynthesis of the major polysaccharides from the mycobacterial cell wall, it was necessary to develop a practical and stereoselective synthetic scheme for DPA. This goal was achieved by coupling of a suitably protected β-d-arabinofuranosyl phosphate intermediate with an activated form of decaprenol and subsequent deprotection.     

Poly(N‐isopropylacrylamide) Phase Diagrams: Fifty Years of Research

In 1968, Heskins and Guillet published the first systematic study of the phase diagram of poly(N‐isopropylacrylamide) (PNIPAM), at the time a “young polymer” first synthesized in 1956. Since then, PNIPAM became the leading member of the growing families of thermoresponsive polymers and of stimuli‐responsive, “smart” polymers in general. Its thermal response is unanimously attributed to its phase behavior. Yet, in spite of 50 years of research, a coherent quantitative picture remains elusive. In this Review we survey the reported phase diagrams, discuss the differences and comment on theoretical ideas regarding their possible origins. We aim to alert the PNIPAM community to open questions in this reputably mature domain.     

Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture

Let H be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold X and a real algebraic bundle \({\mathcal {E}}\) on X. Let \(\mathfrak {h}\) be the Lie algebra of H. Let \(\mathcal {S}(X,{\mathcal {E}})\) be the space of Schwartz sections of \({\mathcal {E}}\). We prove that \(\mathfrak {h}\mathcal {S}(X,{\mathcal {E}})\) is a closed subspace of \(\mathcal {S}(X,{\mathcal {E}})\) of finite codimension. We give an application of this result in the case when H is a real spherical subgroup of a real reductive group G. We deduce an equivalence of two old conjectures due to Casselman: the automatic continuity and the comparison conjecture for zero homology. Namely, let \(\pi \) be a Casselman–Wallach representation of G and V be the corresponding Harish–Chandra module. Then the natural morphism of coinvariants \(V_{\mathfrak {h}}\rightarrow \pi _{\mathfrak {h}}\) is an isomorphism if and only if any linear \(\mathfrak {h}\)-invariant functional on V is continuous in the topology induced from \(\pi \). The latter statement is known to hold in two important special cases: if H includes a symmetric subgroup, and if H includes the nilradical of a minimal parabolic subgroup of G.     

Tuning the critical temperature of cuprate superconductor films with self-assembled organic layers

Control over the T(c) value of high-T(c) superconductors by self-assembled monolayers is demonstrated (T(c) = critical temperature). Molecular control was achieved by adsorption of polar molecules on the superconductor surface (see scheme) that change its carrier concentration through charge transport or light-induced polarization.     

Causality and strict causality for symmetric bilinear systems

It is shown that if W is a symmetric bilinear operator on a Hilbert resolution space, then the causality and strict causality of W is equivalent to the causality and strict causality of the bipower map $\text{W}\text{?}$ induced by W.     

Martin’s axiom does not imply that every two ℕ1-dense sets of reals are isomorphic

Assuming the consistency of ZFC we prove the claim in the title by showing the consistency with ZFC of: There exists a set of realsA such that every function fromA toA is order preserving on an uncountable set. We prove related results among which is the consistency with ZFC of: Every function from the reals into the reals is monotonic on an uncountable set. I would like to thank the United States-Israel Binational Science Foundation for supporting this research by a grant.