Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Eu(III)-cyclen-phen conjugate as a luminescent copper sensor: the formation of mixed polymetallic macrocyclic complexes in water

The cationic cyclen based Eu(III)-phen conjugated 1.Eu was synthesised as a chemosensor for Cu(II), where the recognition in water at pH 7.4 gave rise to quenching of the Eu(III) luminescence and the formation of tetranuclear polymetallic Cu(II)-Eu(III) macrocyclic complexes in solution where Cu(II) was bound by three 1.Eu conjugates.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.     

The Formation of Luminescent Supramolecular Ternary Complexes in Water: Delayed Luminescence Sensing of Aromatic Carboxylates Using Coordinated Unsaturated Cationic Heptadentate Lanthanide Ion Complexes

The synthesis of four lanthanide ion complexes Eu?1, Eu?2, Tb?1 and Tb?2, from the heptadentate tri-arm cyclen (1,4,7,10-tetraazacyclododecane) ligands 1 and 2 that were made in one-pot syntheses is described. These coordinatively unsaturated complexes have two labile metal-bound water molecules, as demonstrated by X-ray crystallography. This was also confirmed by evaluating their hydration state (q～2) by measuring their lifetimes in D²O and H²O, respectively. The above complexes were all designed as being “photophysically silent” prior to the recognition of the anion, since they do not possess antenna that can participate in sensitisation of the Eu(III) or the Tb(III) excited state. However, the two water molecules can be displaced upon anion binding by the appropriate aromatic carboxylates to give ternary complexes in water, through either four- or six-member ring chelates (q～0), or possibly via a monodentate binding. In the case of Tb?1 and Tb?2, large luminescence enhancements were observed upon the formation of such ternary complexes with N,N-dimethylaminobenzoic acid at ambient pH. Such binding and luminescent enhancements were also observed for Tb?1 in the presence of salicylic acid. On all occasions, the anion recognition “switched” the emission “on” over two logarithmic units. At higher concentrations, the emission is reduced possibly due to quenching. In the case of aspirin, the binding was too weak to be measured, indicating that Tb?1 selectively detects salicylic acid, the active form of aspirin in water. In the case of Eu?1 and Eu?2, the affinity of these complexes towards such aromatic carboxylates was too weak for efficient ternary complex formation.     

Polaroid operators and Weyl's theorem

``Polaroid elements" represent an attempt to abstract part of the condition, ``Weyl's theorem holds" for operators.