Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

Supramolecular adducts between macrocyclic Gd(iii) complexes and polyaromatic systems: a route to enhance the relaxivity through the formation of hydrophobic interactions

The set-up of reversible binding interactions between the hydrophobic region of macrocyclic GBCAs (Gadolinium Based Contrast Agents) and SO₃⁻/OH containing pyrene derivatives provides new insights for pursuing relaxivity enhancements of this class of MRI contrast agents. The strong binding affinity allows attaining relaxation enhancements up to 50% at pyrene/GBCA ratios of 3 : 1. High resolution NMR spectra of the Yb-HPDO3A/pyrene system fully support the formation of a supramolecular adduct based on the set-up of hydrophobic interactions. The relaxation enhancement may be accounted for in terms of the increase of the molecular reorientation time (τ_R) and the number of second sphere water molecules. This effect is maintained in blood serum and in vivo, as shown by the enhancement of contrast in T_1w-MR images obtained by simultaneous injection of GBCA and pyrene derivatives in mice.

The set-up of reversible binding interactions between the hydrophobic region of macrocyclic gadolinium based contrast agents and SO₃⁻/OH containing pyrene derivatives provides new insights for pursuing relaxivity enhancement of MRI contrast agents.     

A dominance-based rough set approach applied to evaluate the credit risk of sovereign bonds

4OR - Even though sovereign bonds represent low-risk alternatives that give investors a healthy income, the risk assessment process for these bonds is still considered subjective because of the...     

Ligand dynamics and reactivity in trimetallic clusters

The general relationships between trinuclear cluster reactivity and the ligand dynamical processes in these systems are explored. Three specific mechanistic studies are presented: (1) the rate and stereochemistry of ligand addition to ₃-imidoyl complexes, (2) the factors influencing the rate of carbon-hydrogen bond activation in ₃-alkyne complexes, and (3) the origin of anomalously large kinetic deuterium isotope effect in metal to ligand and ligand to metal hydrogen transfer in trinuclear and binuclear complexes. In all three cases, the current state of the mechanistic studies are summarized and the possible rate of specific ligand dynamical processes in controlling the mechanism are put forth.     

Structural investigation of 3,5‐disubstituted isoxazoles by 1H‐nuclear magnetic resonance

HIV‐1 integrase (IN) is a very promising and validated target for the development of therapeutic agents against AIDS. In an effort to design and synthesize biological isosteric analogs of β‐diketoacid‐containing inhibitors of IN, we prepared a series of substituted isoxazole carboxylic acids. Several of these compounds inhibited catalytic activities of purified IN at micromolar concentration range. With an aim to prepare a large number of analogues based on the isoxazole pharmacophore we focused our study on a series of 3,5‐disubstituted isoxazole isomers. For a rapid structural analysis we discovered a convenient ¹H‐nmr method for distinguishing between isomeric structures based on their H‐4 assignments. This “finger print” approach to isomer identification will be useful in combinatorial chemistry settings where a mixture can be further derivatized.     

Alkyl metal asymmetric reduction. 11. The reaction of α,β-unsaturated ketones with β-branched trialkylaluminium compounds.

The reduction of a series of α,β-unsaturated ketones has been studied under various experimental conditions, by using β-branched trialkylalanes. Asymmetric induction phenomena are observed when optically active trialkylalanes are used.     

Construction of a singular elliptic-harmonic measure

The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated harmonic measure on the boundary is not absolutely continuous with respect to the ordinary surface measure.     

Transition metal-catalysed sequences of nucleophilic addition

Summary In presence of nickel or palladium catalysts, nucleophiles can attack vinylcyclopropanes with concomitant ring cleavage. With palladium catalysts in presence of appropriate substituents the terminal carbon atom of the resulting open chain is able to add to two molecules of a conjugated diene giving rise to long-chain unsaturated compounds.     

On the growth and shape of sodium taurodeoxycholate micellar aggregates: a spin-label and quasielastic light scattering investigation

Electron spin resonance (ESR) and quasielastic laser scattering (QELS) measurements have been carried out on sodium taurodeoxycholate (NaTDC) micellar aqueous solutions. Computer simulation of the ESR line shape has been used to quantitatively analyze the rotational dynamics of the cholestan-spin label (CSL) dissolved by the NaTDC micellar aggregates as a function of temperature and NaCl concentration. The local reorientation of CSL has been accounted for motionally-averaged g- and A-tensors assuming fast oscillation around the spin-probe long molecular axis. The overall Brownian tumbling of CSL-micelle complexes has been modeled by an axially symmetric rotational tensor. Good agreement with experimental spectra is obtained. Best-fit rotational parameters and QELS data suggest that, in the circumstance of large aggregation, NaTDC micelles have cylindrical shape and micellar growth occurs along the cylinder axis.     

Reaction of trans-[Pt(H)2(PCy3)2] with C60 reductive elimination of H2 and formation of [Pt(PCy3)2(η-C60)]

Reaction of trans-[Pt(H)₂(PCy₃)₂], 1, with [60]fullerene at room temperature affords [Pt(PCy₃)₂(η²-C₆₀)], 2, in nearly quantitative yield. The most probable reaction pattern is the insertion of a fullerene 6,6 junction onto a Pt-H bond yielding an η¹ alkyl derivative which, after hydrogen extrusion, gives 2. On the other hand, addition of 1 to different electron-deficient olefins, such as dimethyl maleate and fumarate, furnishes mixtures of both η¹ metal—alkyl and η² metal—olefin derivatives. If tetrachloroethylene is used as 2π component, trans-[PtCl(H)(PCy₃)₂] forms exclusively.