A second-order accurate numerical method for a fractional wave equation

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k ² + h ², where k and h are the parameters for the time and space meshes, respectively.     

Isotopic production cross sections of residues in reactions induced by relativistic heavy ions with protons and deuterons

The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets.     

On solvability of differential equations with the Riesz fractional derivative

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy-type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well-known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory.     

A practical access to novel 2-amino-5-arylidene-1,3-thiazol-4(5H)-ones via sulfur/nitrogen displacement under solvent-free microwave irradiation

A new effective approach to the synthesis of a small library of 2-amino-5-arylidene-1,3-thiazol-4(5H)-ones was reported using solvent-free reaction conditions under microwave irradiation. In the first step, rhodanines were subjected to Knoevenagel condensation with aryl aldimines according to a facile one-pot protocol. Then the (5Z)-5-arylidene rhodanine derivatives were transformed directly into the corresponding 2-amino-1,3-thiazol-4(5H)-ones by sulfur/nitrogen displacement reaction under microwaves with retention of configuration and good overall yields.     

An approach to estimate the energy and strength of the intramolecular hydrogen bond in different conformers of 4‐methylamino‐3‐penten‐2‐one

The molecular structure and intramolecular hydrogen bond energy of 32 conformers of 4‐methylamino‐3‐penten‐2‐one were investigated at MP2 and B3LYP levels of theory using the standard 6–31G** basis set and AIM analyses. Furthermore, calculations for all the possible conformations of 4‐methylamino‐3‐penten‐2‐one in water solution were also carried out at B3LYP/6–31G** level of theory. The calculated geometrical parameters and conformational analyses in gas phase and water solution show that the ketoamine conformers of this compound are more stable than the other conformers (i.e., enolimine and ketoimine). This stability is mainly due to the formation of a strong N? H···O intramolecular hydrogen bond, which is assisted by π‐electrons resonance. Hydrogen bond energies for all conformers of 4‐methylamino‐3‐penten‐2‐one were obtained from the related rotamers method. The nature of intramolecular hydrogen bond existing within 4‐methylamino‐3‐penten‐2‐one has been investigated by means of the Bader theory of atoms in molecules, which is based on topological properties of the electron density. The results of these calculations support the results which obtained by related rotamers method. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Palladium-catalyzed Suzuki cross-coupling of aryl halides with aryl boronic acids in the presence of glucosamine-based phosphines

Carbohydrate-substituted phosphines are easily obtained in quite good yields by coupling of protected or non-protected d-glucosamine with the corresponding diphenylphosphino acid. These neutral ligands, in association with palladium acetate, are very active catalysts in the Suzuki cross-coupling reaction. The polyhydroxy phosphines are more active than the peracetylated phosphines. The process tolerates electron-rich as well as electron-poor substituents. Excellent turnovers, up to 97?000 are observed.     

Novel Copolymers of 2-Phenyl-1,1-dicyanoethylene with 4-Fluoro- and Pentafluorostyrene

Copolymerization of 2-phenyl-1,1-dicyanoethylene (PDE) with 4-fluorostyrene and pentafluorostyrene in solution with radical initiation (ABCN) at 70°C yielded random copolymers with PDE alternating units. The composition of the copolymers was calculated from nitrogen analysis and the structure was analyzed by IR, ¹H and ¹³C-NMR. The order of relative reactivity (1/r₁) and the tendency toward alternation of monomer units in the copolymer for these two monomers, is 4-fluorostyrene (1.96) > pentafluorostyrene (0.51). Higher glass transition temperature of the copolymers in comparison with that of homopolymers indicates a decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit.     

Influence of the Metal Ion on the Two‐Photon Absorption Properties of Lanthanide Complexes Including Near‐IR Emitters

The synthesis of tris(2‐thenoyltrifluoroacetonate)lanthanide(III) complexes featuring a diethylaminostyryl‐2,2′‐bipyridine coligand was achieved for lanthanum; the near‐infrared (NIR) emitters neodymium, erbium, and ytterbium; and the transition‐metal yttrium. The photophysical properties were thoroughly studied, and it was demonstrated that the conjugated bipyridine ligand acts as a good antenna for the sensitization of the NIR emitters. The two‐photon absorption (TPA) properties of all five complexes were investigated by using both two‐photon excited fluorescence and the Z‐scan method. We demonstrate that the nature of the rare earth ion has almost no influence on the TPA properties centered on the conjugated bipyridyl ligand. Finally, we show that Yb^III is sensitized by a two‐photon antenna effect, and that Nd^III is mostly sensitized by a one‐photon process involving direct excitation of forbidden f–f transitions.