Sinc-Galerkin method for solving linear sixth-order boundary-value problems

There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is made. It is shown that the Sinc-Galerkin method yields better results.

     

Mössbauer and infrared spectroscopic studies of novel mixed valence states in cobaltous ferrocyanides and ferricyanides

Novel mixed valence states have been obtained by the treatment of cobaltous ferrocyanides (Co⁺²Fe^II) and ferricyanides (Co⁺²Fe^III) in an ozone flow. The CN stretching bands occur at 2085 cm^–1 for Co⁺²Fe^II and at 2160 cm^–1 for Co⁺²Fe^III. After the ozonization process of Co⁺²Fe^II, an intense band approximately at 2125 cm^–1 is detected. This intermediate band must correspond to a mixed valence state of the type: Fe^II–CN–Co²⁺–NC–Fe^III Mössbauer spectra recorded in situ during the ozonization of Co⁺²Fe^II show the presence of two components: a doublet with isomer shift and quadrupole splitting values close to the cobalti ferricyanide and a very broad line for the mixed valence state. From the Mössbauer and infrared spectra of the aged samples of the Co⁺²Fe^II after ozonization, a relaxation process to the initial state of the samples is observed but the mixed valence state is stable.     

The synthesis and structure of potassium cyanotrimethylaluminate

The reaction of KCN with Al(CH₃)₃ to form K[Al(CH₃)₃CN] is greatly facilitated by the presence of an aromatic solvent: for p-xylene a solid complex, K[Al(CH₃)₃CN]·C₆H₄(CH₃)₂, has been isolated. The crystal structure of potassium cyanotrimethylaluminate has been determined from three-dimensional X-ray data measured by counter methods. K[Al(CH₃)₃CN] crystallizes in the monoclinic space group C2/c with cell dimensions a = 19.902(7), b = 9.211(4), c = 9.615(4) Å, β = 107.74(5)°, and p_calcd. = 1.09 g cm^?1 for Z = 8. Least squares refinement gave a conventional weighted R factor of 4.9% for 807 independent reflections. The monomeric [Al(CH₃)₃CN]^? units possess no crystallographic symmetry, and the packing in the unit cell is such that the nitrogen atoms on three such units approach the potassium atom to within 3.11 Å. The average aluminum-methyl carbon bond distance is 1.971 (7) Å, while the aluminum-cyano carbon distance is 2.047 (7) Å. This significant lengthening is attributed to partial electron deficiency in the aluminum-cyano carbon bond.     

The classical solution of the one-dimensional two-phase stefan problem with energy specification

Summary Existence and unicity for the solution of the one-dimensional two-phase Stefan problem with energy specification in the liquid phase is established via potential theoretic arguments employing the Schauder fixed point theorem and a contracting map.This work was supported in part by NSF Grant MCS-7801687.This work was carried out at UT-Austin while on sabbatical from the University of Adelaide.     

Six‐coordinate Co2+ with imidazole,NH3, and H2O ligands: Approaching spin crossover

Octahedral, six‐coordinate Co²⁺ can exist in two spin states: S = 3/2 and S = 1/2. The difference in energy between high spin (S = 3/2) and low spin (S = 1/2) is dependent on both the ligand mix and coordination stereochemistry. B3LYP calculations on combinations of neutral imidazole, NH₃, and H₂O ligands show that low‐spin isomers are stabilized by axial H₂O ligands and in structures that also include trans pairs of equatorial NH₃ and protonated imidazole ligands, spin crossover structures are predicted from spin state energy differences. Occupied Co d orbitals from the DFT calculations provide a means of estimating effective ligand strength for homoleptic and mixed ligand combinations. These calculations suggest that in a labile biological system, a spin crossover environment can be created. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007