Around independence and domination in metric abstract elementary classes: assuming uniqueness of limit models

We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability‐like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.     

Fatty Acid Carboxylate‐ and Anionic Surfactant‐Controlled Delivery Systems That Use Mesoporous Silica Supports

We report the preparation of a MCM‐41 mesoporous material that contains the dye [Ru(bipy)₃]Cl₂ (bipy=bipyridine) inside the mesopores and functionalised with suitable binding groups at the entrance of the pores. Solids S1 – S3 were obtained by the reaction of the mesoporous material with N‐methyl‐N′‐propyltrimethoxysilylimidazolium chloride, N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]thiourea, or N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]urea, respectively. A study of the dye delivery of these systems in buffered water (pH 7.0, 2‐[4‐(2‐hydroxyethyl)piperazin‐1‐yl]ethanesulfonic acid (HEPES), 10^?3 mol dm^?3) in the presence of a family of carboxylate ions was carried out. In the interaction of the anions with the surface of the solids, the response depends on the characteristics of the binding groups (i.e., imidazolium, urea and thiourea) at the pore outlets and their specific interaction with the corresponding anion. The interaction of long‐chain carboxylate ions with the binding sites at the surface of the solids resulted in a remarkable inhibition of the delivery of the dye. This inhibition was observed clearly for the dodecanoate anion, whereas the octanoate, decanoate, cholate, deoxycholate, glycodeoxycholate and taurocholate anions induced a certain pore blockage that varied according to the solid studied. The interaction of smaller anions, such as acetate, butanoate, hexanoate and octanoate, with the solids had no effect on the dye release process. The possible use of the gating system for the chromo‐fluorogenic detection of anionic surfactants through selective dye delivery inhibition was also explored. Molecular dynamic simulations that use force‐field methods have been made to theoretically study the capping carboxylate mechanism. The calculations are in agreement with the experimental results, thus allowing a representation of the dye delivery inhibition in the presence of long‐chain carboxylate ions.     

A Colorimetric Sensor Array for the Detection of the Date‐Rape Drug γ‐Hydroxybutyric Acid (GHB): A Supramolecular Approach

γ‐Hydroxybutyric acid (GHB), a colourless, odourless and tasteless chemical, has become one of the most dangerous illicit drugs of abuse today. At low doses, this drug is a central nervous system depressant that reduces anxiety and produces euphoria and relaxation, sedating the recipient. There is an urgent need for simple, easy‐to‐use sensors for GHB in solution. Here, we present a colorimetric sensor array based on supramolecular host–guest complexes of fluorescent dyes with organic capsules (cucurbiturils) for the detection of GHB.     

On the effect of the BSSE on intermolecular potential energy surfaces. Comparison of a priori and a posteriori BSSE correction schemes

A comparative study of geometrical parameters is performed on the complexes HF–HF, H₂O–H₂O, and HF–H₂O using 12 different basis sets at the RHF, MP2, and DFT (BLYP and B3LYP) levels of theory. The equilibrium geometries were obtained from uncorrected, a posteriori (counterpoise, CP) and a priori (Chemical Hamiltonian Approach, CHA) BSSE‐corrected potential energy surfaces. The calculation of equilibrium geometries using the CP and CHA schemes is described in details. The effect of the BSSE on various intermolecular parameters is discussed and the performance of the applied theoretical models is critically evaluated from the BSSE point of view. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 765–786, 2001     

On Cullen numbers which are both Riesel and Sierpiński numbers

We describe an algorithm to determine whether or not a given system of congruences is satisfied by Cullen numbers. We use this algorithm to prove that there are infinitely many Cullen numbers which are both Riesel and Sierpiński. (Such numbers should be discarded if you are searching prime numbers with Proth?s theorem.)     

The Homogeneous Geometries of Real Hyperbolic Space

We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.