On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle

We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph.     

Tris(triphenylphosphine)rhodium cyano and triphenylcyanoborate complexes: Structures and a DFT study

The structures of [Rh(CN)(PPh₃)₃](EtOH) (1), [Rh(NCBPh₃)(PPh₃)₃] (2), and [Rh(CNBPh₃)(PPh₃)₃] (3) are reported together with a density functional theory (DFT) study of the model compounds [Rh(NCBH₃)(PH₃)₃] and [Rh(CNBH₃)(PH₃)₃]. Compound 1 crystallizes in space group Pc with a = 10.4798(15) Å, b = 12.5410(18) Å, c = 19.974(3) Å and = 112.215(6)°; compound 2 crystallizes in space group with a = 12.929(2) Å, b = 14.362(2) Å, c = 17.575(3) Å and = 92.544(3)°, = 90.214(3)°, = 113.831(3)°; compound 3 crystallizes in space group with a = 12.915(2), b = 14.296(2), c = 17.664(3) Å and = 92.469(3)°, = 90.088(3)°, = 113.768(3)°. All three complexes show slight tetrahedral distortion from ideal square planar geometry (largest for 1). Differences in the reactivity and stability of 2 and 3 are interpreted according to the results of a density functional theory study.     

Automatic flow procedure for the determination of glycerol in wine using enzymatic reaction and spectrophotometry

An automatic flow procedure for the determination of glycerol in wines by employing a flow system based on multicommutation and enzymatic reaction is described. Glycerol dehydrogenase was immobilized on aminopropyl glass beads and packed into a column that was coupled to the flow system. The NADH produced by the enzymatic reaction was monitored by spectrophotometry at 340 nm and its radiation absorption presented a relationship with glycerol concentration. The system manifold comprised a set of three-way solenoid valves controlled by a microcomputer, which was furnished with electronic interfaces and runs a software that was designed to carry out on-line sample dilution, reagent addition, and data acquisition. The procedure allows the determination of glycerol in wine samples without any prior pretreatment. The procedure presented as profitable features a linear response range between 2.0 and 10.0 g l⁻¹ glycerol (R=0.998), a detection limit of 0.006 g l⁻¹ glycerol, a relative standard deviation of 1.8% (n=14) for a typical wine sample presenting 5.3 g l⁻¹ glycerol, a sampling throughput of 33 determinations per hour, and a NAD⁺ consumption of 0.8 mg per determination. The results were compared with those obtained using a reference method and no significant difference at 90% confidence level was observed.     

Fast and efficient preparation of Baylis-Hillman-derived (E)-allylic azides and related compounds in aqueous medium

A practical access to alkyl- and aryl-substituted (E)-2-(azidomethyl)alkenoates and related azido compounds from the corresponding allylic bromides in aqueous acetone is described. An alternative method to obtain the starting bromides based on heterogeneous catalysis under mild conditions was also investigated.     

Analysis of the antioxidant activity of an indole library: cyclic voltammetry versus ROS scavenging activity

The electrochemical behavior of an indole library of compounds, including several tryptophan and tryptamine derivatives previously demonstrated to be active against several reactive oxygen species (ROS), was investigated. For this purpose, a voltammetry study was undertaken and the oxidation potential was correlated to the scavenging activity reported for the studied indoles. All the compounds showed an oxidation potential peak lower than that observed for indole (Epox = 1.035 V), but higher than that described for the antioxidant melatonin (Epox = 0.715 V). The electrochemical behavior showed a high correlation with the scavenging activity of peroxyl radical, for selected compounds.     

Unexpected reactivity of trifluoromethylated olefins with indole: a mechanistic investigation

Several trifluoromethylated compounds were reacted with indole sodium salt, leading to monofluorinated compounds. The unexpected products formation was rationalized by DFT calculations.     

Hydrogen‐bonding controls the solid‐state and enantiomeric comformations of the amino alcohol ligand 2‐[(2‐hydroxyethyl)amino]cyclohexanol

The crystal structure of the title compound, C₈H₁₇NO₂, consists of (R,R) and (S,S) enantiomeric pairs packed in adjacent double layers which are characterized by centrosymmetric hydrogen‐bonded dimers, generated via N—H...O and O—H...O interactions, respectively. Intermolecular interactions, related to acceptor and donor molecule chirality, link the achiral double layers into tubular columns, which consist of a staggered hydrophilic inner core surrounded by a hydrophobic cycloalkyl outer surface and extend in the [011] direction.     

Vibrational analysis of d-PCL(530)/siloxane-based hybrid electrolytes doped with two lithium salts

The present study has been focused on environmentally friendly sol–gel-derived electrolytes based on a di-urethane cross-linked d-PCL(530)/siloxane network [where d represents di, PCL identifies the poly(ε-caprolactone) biopolymer, and 530 is the average molecular weight in grams per mole] doped with a wide range of concentration of lithium perchlorate and lithium bis(trifluoromethanesulfonyl)imide. Fourier Transform Infrared and Raman spectroscopies have been applied to evaluate the extent of ionic association. Characteristic bands of the PCL(530) segments, of the urethane cross-links, and of the anions have been examined to gain insight into the cation/biopolymer, cation/anion, and cation/cross-link interactions. In both electrolyte systems, “free” ions and contact ions have been identified. The addition of salt modifies the hydrogen-bonded array of the host matrix, causing the destruction/formation of the urethane/urethane aggregates.