Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

Structural adaptability in the system Bi2O3 - WO3 : Higher members of the homologous series Bi2WnO3n+3

The ultramicrostructure of phases with n = 1, 2 and 3 in the hypothetical series Bi2WnO3n+3 has been investigated by high resolution electron microscopy and energy dispersive X-ray emission spectroscopy. For n = 1 and 2, well ordered phases with the predicted compositions have been obtained, but for n = 3, a severely disordered assemblage containing intergrowths of the two known structures and strips of the n = 3 member is produced. No evidence for ordered structures with n > 2 has yet been obtained.

Structural adaptability in the system Bi2O3 --- WO3 : Higher members of the homologous series Bi2WnO3n+3

The ultramicrostructure of phases with n = 1, 2 and 3 in the hypothetical series Bi2WnO3n+3 has been investigated by high resolution electron microscopy and energy dispersive X-ray emission spectroscopy. For n = 1 and 2, well ordered phases with the predicted compositions have been obtained, but for n = 3, a severely disordered assemblage containing intergrowths of the two known structures and strips of the n = 3 member is produced. No evidence for ordered structures with n > 2 has yet been obtained.

Dielectric anisotropy and relaxation studies of the homologous series of N-(4-n-alkyloxy-2-hydroxy-benzylidene)-4-carbethoxyaniline

Dielectric properties of the homologous series of newly synthesized nonchiral compounds N-(4-n-alkyloxy-2-hydroxy-benzylidene)-4-carbethoxyaniline, (n = 6, 8, 10, 12) having wide temperature range (∼60°C) smectic A (SmA) phase, have been studied by the impedance spectroscopy in the frequency range of 100 Hz to 1 MHz. Measurements have been carried out for two principal alignments (planar as well as homeotropic) of the SmA phase. Dielectric anisotropy (Δε' = ε'∥ - ε'⊥) for all the members of the series has been found to be negative for the whole temperature range of SmA phase. Magnitude of the dielectric anisotropy (|Δε'|) has been found to decrease with the number of alkyl chains. Relaxation frequencies corresponding to the rotation of the individual molecules about their short axes, lie below 1 MHz and obey the Arrhenius law by which activation energies have been determined. However, the relaxation frequencies corresponding to the rotation of the molecules about their short axes apparently lie above 10 MHz.

Kernels for large margin time-series classification

In this paper we propose a novel family of kernels for multivariate time-series classification problems. Each time-series is approximated by a linear combination of piecewise polynomial functions in a Reproducing Kernel Hilbert Space by a novel kernel interpolation technique. Using the associated kernel function a large margin classification formulation is proposed which can discriminate between two classes. The formulation leads to kernels, between two multivariate time-series, which can be efficiently computed. The kernels have been successfully applied to writer independent handwritten character recognition.

Effect of substitution on molecular conformation and packing features in a series of aryl substituted ethyl-6-methyl-4-phenyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylates

The supramolecular structures of eight aryl protected ethyl-6-methyl-4-phenyl-2-thioxo-1,2,3,4 tetrahydropyrimidine-5-carboxyl ates were analyzed in order to understand the effect of variations in functional groups on molecular geometry, conformation and packing of molecules in the crystalline lattice. It is observed that the existence of a short intra-molecular C-H center dot center dot center dot pi interaction between the aromatic hydrogen of the aryl ring with the isolated double bond of the six-membered tetrahydropyrimidine ring is a key feature which imparts additional stability to the molecular conformation in the solid state. The compounds pack via the cooperative involvement of both N-H center dot center dot center dot S=C and N-H center dot center dot center dot O=C intermolecular dimers forming a sheet like structure. In addition, weak C-H center dot center dot center dot O and C-H center dot center dot center dot pi intermolecular interactions provide additional stability to the crystal packing.

Local structure in LaMnO3 and CaMnO3 perovskites: A quantitative structural refinement of mn K-edge XANES data

Hole-doped perovskites such as La1-xCaxMnO3 present special magnetic and magnetotransport properties, and it is commonly accepted that the local atomic structure around Mn ions plays a crucial role in determining these peculiar features. Therefore experimental techniques directly probing the local atomic structure, like x-ray absorption spectroscopy (XAS), have been widely exploited to deeply understand the physics of these compounds. Quantitative XAS analysis usually concerns the extended region [extended x-ray absorption fine structure (EXAFS)] of the absorption spectra. The near-edge region [x-ray absorption near-edge spectroscopy (XANES)] of XAS spectra can provide detailed complementary information on the electronic structure and local atomic topology around the absorber. However, the complexity of the XANES analysis usually prevents a quantitative understanding of the data. This work exploits the recently developed MXAN code to achieve a quantitative structural refinement of the Mn K-edge XANES of LaMnO3 and CaMnO3 compounds; they are the end compounds of the doped manganite series LaxCa1-xMnO3. The results derived from the EXAFS and XANES analyses are in good agreement, demonstrating that a quantitative picture of the local structure can be obtained from XANES in these crystalline compounds. Moreover, the quantitative XANES analysis provides topological information not directly achievable from EXAFS data analysis. This work demonstrates that combining the analysis of extended and near-edge regions of Mn K-edge XAS spectra could provide a complete and accurate description of Mn local atomic environment in these compounds.

Ligand series from V = O stretching frequency of oxovanadium(IV) complexes*1

A ligand series obtained from V = O stretching frequencies for different monomeric complexes of oxovanadium(IV) is shown to parallel the nephelauxetic series. The ligand series obtained from streching frequencies of other systems are also shown to compare well with the nephelauxetic series rather than the spectrochemical series.

Molecular model for U centres in caesium iodide

A molecular model has been developed to study the vibrations of U centres in caesium iodide. Employing the rigid ion model with nearest-neighbour short-range forces, the dynamical matrix of order 27 × 27 was solved to obtain the frequencies of the localized modes and the perturbed lattice modes. The results are compared with those obtained from the Green function method.

Studies in sesquiterpenes-XX. Acetoxymethylation of longifolene

Longifolene in Prins reaction with formaldehyde yielded the expected ω-acetoxymethyl longifolene, which was transformed into a number of interesting derivatives. Configuration of the Prins product has been arrived at by NMR measurements. The UV absorption of these derivatives show a considerable bathochromic shift with respect to those in the camphene series and this could be attributed to the slight twisting of the ethylenic linkage in longifolene and its derivatives.

Studies in the Sandalwood Oil Series. III. Chain Effect on Terpene Transformations

The carboxyl chain of some molecules has been found to be responsible for causing rearrangements and controlling their course. This chain effect, which operates during reactions involving carbonium ions, is illustrated with examples from Sandalwood oil chemistry.

Studies in the sandalwood-oil series. I. The structure, synthesis, and configuration of the lactone of tricycloekasantalic acid

The structure, synthesis, and configuration of the lactone of tricycloekasantalic acid have been described. It has been shown that in the formation of this lactone (XII) from the acids (I) or (II) a rearrangement is involved.