Mu-Chlorido-Bridged Dimanganese(II) complexes of the schiff base derived from [2+2] condensation of 2,6-diformyl-4-methylphenol and 1,3-bis(3-aminopropyl)tetramethyldisloxane: structure, magnetismo, electrochemical behaviour, and catalytic oxidation of secondary alcohols

The reaction of 2,6-diformyl-4-methylphenol with 1,3-bis(3-aminopropyl)tetramethyldisiloxane in the presence of MnCl2 in a 1:1:2 molar ratio in methanol afforded a dinuclear -chlorido-bridged manganese(II) complex of the macrocyclic [2+2] condensation product (H2L), namely, [Mn2Cl2(H2L)(HL)]Cl center dot 3H(2)O (1). The latter afforded a new compound, namely, [Mn2Cl2(H2L)(2)][MnCl4]center dot 4CH(3)CN center dot 0.5CHCl(3 center dot)0.4H(2)O (2), after recrystallisation from 1:1 CHCl3/CH3CN. The co-existence of the free and complexed azomethine groups, phenolato donors, mu-chlorido bridges, and the disiloxane unit were well evidenced by ESI mass spectrometry and FTIR spectroscopy and confirmed by X-ray crystallography. The magnetic measurements revealed an antiferromagnetic interaction between the two high-spin (S = 5/2, g = 2) manganese(II) ions through the mu-chlorido bridging ligands. The electrochemical behaviour of 1 and 2 has been studied, and details of their redox properties are reported. Both compounds act as catalysts or catalyst precursors in the solvent-free low-power microwave-assisted oxidation of selected secondary alcohols, for example, 1-phenylethanol, cyclohexanol, 2- and 3-octanol, to the corresponding ketones in the absence of solvent. The highest yield of 72% was achieved for 1-phenylethanol by using a maximum of 1% molar ratio of catalyst relative to substrate.

Tetranuclear COPPER(II) complexes with macrocyclic and open-chain disiloxane ligands as catalyst precursors for hydrocarboxylation and oxidation of alkanes and 1-phenylethanol

Two new tetranuclear complexes [Cu-4(mu-O)(L-1)-Cl-4] and [Cu-4(mu(4)-O)(L-2)(2)Cl-4] (2), where H2L1 is a macrocyclic ligand resulting from [2+2] condensation of 2,6-diformy1-4-methylphanol (DFF) and 1,3-bis(aminopropy1)tetramethyldisiloxane, and HL2 is a 1:2 condensation product: of DFF with trimethylsilyl p-aminobenzoate, have been prepared. The structures of the products were established by Xray diffraction. The complexes have been characterised by FTIR, UV/Vis spectroscopy, ES1 mass-spectrometry and magnetic susceptibility measurements. The latter revealed that the letrftriuclear complexes can be descr bed as two ferromagnetically coupled dinuclear units, in which the two copper(II) ions interact antiferromacinetically. The ccimpi.iunds act as homogeneous catalyst precursors for a number of single-pot reactions, including (I) hydrocarbaxylation, with CO, H2O and K2S2O8, of a variety of linear and cyclic (n = 5-8) alkanes into the corresponding Cn+1 carboxylic acids, (ii) peroxidative oxidation of cyclohexane, and (iii) solvent-free microwave-assisted oxidation of 1-phenyletha.nol.

µ-Chlorido-bridged dimanganese(II) complexes of the schiff base derived from [2+2] condensation of 2,6-diformyl-4-methylphenol and 1,3-bis(3-aminopropyl)tetramethyldisiloxane: structure, magnetismo, electrochemical behaviour, and catalytic oxidation of secondary alcohols

The reaction of 2,6-diformyl-4-methylphenol with 1,3-bis(3-aminopropyl)tetramethyldisiloxane in the presence of MnCl2 in a 1:1:2 molar ratio in methanol afforded a dinuclear -chlorido-bridged manganese(II) complex of the macrocyclic [2+2] condensation product (H2L), namely, [Mn2Cl2(H2L)(HL)]Cl center dot 3H(2)O (1). The latter afforded a new compound, namely, [Mn2Cl2(H2L)(2)][MnCl4]center dot 4CH(3)CN center dot 0.5CHCl(3 center dot)0.4H(2)O (2), after recrystallisation from 1:1 CHCl3/CH3CN. The co-existence of the free and complexed azomethine groups, phenolato donors, mu-chlorido bridges, and the disiloxane unit were well evidenced by ESI mass spectrometry and FTIR spectroscopy and confirmed by X-ray crystallography. The magnetic measurements revealed an antiferromagnetic interaction between the two high-spin (S = 5/2, g = 2) manganese(II) ions through the mu-chlorido bridging ligands. The electrochemical behaviour of 1 and 2 has been studied, and details of their redox properties are reported. Both compounds act as catalysts or catalyst precursors in the solvent-free low-power microwave-assisted oxidation of selected secondary alcohols, for example, 1-phenylethanol, cyclohexanol, 2- and 3-octanol, to the corresponding ketones in the absence of solvent. The highest yield of 72% was achieved for 1-phenylethanol by using a maximum of 1% molar ratio of catalyst relative to substrate.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Validation of a new reference values’s database for semiquantification of 123I‐FP‐CIT SPECT scans in one nuclear medicine department

The DatScanTM and its Semiquantification (SQ) can provide advantages in the diagnosis of Parkinsonian Syndromes (PS). To improve the SQ is recommended the creation of adapted database (DB) with reference values for the Nuclear Medicine Departments. Previously to this work was created a adapted database (DBRV) to Nuclear Medicine Department's protocol and population of Infanta Cristina's Hospital located in Badajoz, for patients between the ages of 60 and 75, and reference values of the SQ were calculated. Aim: To evaluate the discrimination capacity of a department's adapted DB reference's values of healthy controls for DatScanTM.