Use of singular value decomposition in system identification

Use of the singular value decomposition is suggested for problems of linear least-squares system identification rather than the usual method involving the normal equations.     

Transition metal catalysed Grignard-like allylic activation across tetragonal tin(II) oxide

The reaction of allyl halide and a carbonyl compound under the aegis of tetragonal tin(II) oxide and catalyticd ⁸,d¹⁰ metal complexes provides the corresponding homoallylic alcohol, via a novel allyl tin intermediate.     

Phase formation and crystallization in Bi-Sr-Ca-Cu-O thick films

Thick films of Bi₂Sr₂CaCu₂O_x superconducting at 84 K have been prepared on polycrystalline MgO substrates. The effect of heat treatment on phases formed at various stages of the film preparation is studied. Investigations show that a thin layer at the top is highly oriented while the bulk of the 212 phase material beneath it consists of randomly oriented grains. This appears to be the main reason for the low critical current densities obtained in practice.     

AC susceptibility measurements in some RTiFe11-xCox (R = Dy, Ho, Er) compounds: Spin-reorientation behavior

The DyTiFe_{11 - x}Co_x (x = 0, 1, 3), HoTiFe_{11 - x}Co_x (x = 0, 3) and ErTiFe₁₁ compounds, all exhibiting the T hMn₁₂-type structure, were studied for their ac susceptibility in the temperature range 20–300 K. The Dy- and Ho-containing compounds exhibited spin reorientation from axial to cone to planar, or from axial to cone in the temperature range 250-50 K, as expected. In this structure Dy and Ho with negative second-order Stevens' coefficients (_J < 0) favor planar rare earth sublattice anisotropy, while Fe and Co sublattices favor uniaxial and planar anisotropies, respectively and would be in competition as a function of temperature. A spin-reorientation type of behavior was also observed in the ErTiFe₁₁ compound near 50 K. This observation appears to imply that, in this compound, the higher-order crystal-field terms are important. The magnetization data revealed that in these systems the rare earth and transition metal sublattices coupled antiparallel, as is normally the case in the heavy rare-earth-transition-metal compounds.     

On Markuševič decompositions of Banach spaces

пРОВЕДЕНО сИстЕМАтИ ЧЕскОЕ ИсслЕДОВАНИЕ РАжлИЧНых тИпОВ РАжлОжЕНИИ, А ИМ ЕННО, пО МАРкУшЕВИЧУ, ОБОБЩЕН Ных И РАжлОжЕНИИ пО шА УДЕРУ. УкАжАНы пРИМЕРы, ИллУ стРИРУУЩИЕ ВжАИМООтНОшЕНИь ЁтИ х тИпОВ РАжлОжЕНИИ. Ос НОВНАь цЕль ДАННОИ РАБОты — ИжУЧЕ НИЕ РАжлОжЕНИИ пО МАРкУшЕВИЧУ (M-РАжл ОжЕНИИ). ОтМЕЧАЕтсь, Чт О пОслЕДОВАтЕльНОсть пРОЕкцИИ, сВьжАННАь с ОБОБЩЕНН ыМ РАжлОжЕНИЕМ, ьВльЕ тсь ЕДИНстВЕННОИ тОгДА И тОлькО тОгДА, кОгДА ЁтОM-РАжлОжЕНИЕ. пОлУ ЧЕНА хАРАктЕРИжАцИьM-РАжлОжЕНИИ В тЕРМИН Ах Их пОДпОслЕДОВАтЕ льНОстЕИ. пОлУЧЕНА тАкжЕ хАРАк тЕРИжАцИь пО шАУДЕРУ В тЕРМИНАхM-РАжлОжЕНИИ. НАкОНЕц, пОлУЧЕНы ОтНОшЕНИь Д ВОИстВЕННОстИ МЕжДУM-РАжлОжЕНИьМИ НЕкОтО РОгО пРОстРАНстВА И НЕкОтОРыМИ РАжлОжЕ НИьМИ сОпРьжЕННОгО п РОстРАНстВА.     

Analysis of periodic-quasiperiodic nonlinear systems via Lyapunov-Floquet transformation and normal forms

In this paper a general technique for the analysis of nonlinear dynamical systems with periodic-quasiperiodic coefficients is developed. For such systems the coefficients of the linear terms are periodic with frequency ω while the coefficients of the nonlinear terms contain frequencies that are incommensurate with ω. No restrictions are placed on the size of the periodic terms appearing in the linear part of system equation. Application of Lyapunov-Floquet transformation produces a dynamically equivalent system in which the linear part is time-invariant and the time varying coefficients of the nonlinear terms are quasiperiodic. Then a series of quasiperiodic near-identity transformations are applied to reduce the system equation to a normal form. In the process a quasiperiodic homological equation and the corresponding ‘solvability condition’ are obtained. Various resonance conditions are discussed and examples are included to show practical significance of the method. Results obtained from the quasiperiodic time-dependent normal form theory are compared with the numerical solutions. A close agreement is found.     

Enhancing the dissolution of hydrophobic guests using solid state inclusion complexation: characterization and in vitro evaluation

The objectives of the present investigation were to prepare and characterize solid inclusion complexes of Etodolac (ETD) with β-cyclodextrin (β-CD) in order to study the effect of complexation on the dissolution rate of ETD, a hydrophobic guest molecule. Phase solubility curve was classified as a typical A_L-type for the cyclodextrins (CD’s), showing that soluble complex was formed. The inclusion complexes in the molar ratio of 1:1 and 1:2 (β-CD–ETD) were prepared by various methods such as kneading, co-evaporation and in molar ratio of 1:1 by spray dried technique respectively. The molecular behaviors of ETD in all samples were characterized by nuclear magnetic resonance (NMR) spectroscopy, fourier-transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC) and powder X-ray diffraction (PXRD) studies and Scanning Electron microscopy (SEM) analysis. The results of these studies indicated that complexes prepared by kneading, co-evaporation and spray drying techniques showed inclusion of the ETD molecule into the CD’s cavities. The highest improvement in in vitro dissolution profiles was observed in complexes prepared with spray dried technique. Mean in vitro dissolution time indicated significant difference between the release profiles of ETD from complexes and physical mixtures and from pure ETD.     

Copper(II) complexes of thioarylazo-pentanedione: Structures,magnetism, redox properties and correlation with DFT calculations

Copper(II) complexes of 3-((2-(alkylthio)phenylazo)-2,4-pentanedione, tridentate O, N, S donor ligands, are described in this work. Chloride bridged copper(II) polymers (1) and thiocyanato bridged copper(II) dimmers (2) are characterized by a single crystal X-ray diffraction study. The complexes show antiferromagnetic interactions, with J = −0.5 ± 0.1 cm⁻¹ (1a) and −25.8 ± 0.5 cm⁻¹ (2b), which implies stronger coupling in the –SCN-bridging compound. The spectra, redox and magnetism are explained by DFT studies.     

Dielectric properties of rare earth double perovskite oxide Sr2CeSbO6

A polycrystalline rare earth double perovskite oxide, strontium cerium antimonate, Sr₂CeSbO₆ (SCS), is synthesized by solid-state reaction technique. The X-ray diffraction pattern at room temperature of SCS shows orthorhombic phase with the lattice parameters, a = 8.84 Å, b = 6.22 Å, and c = 5.83 Å. Fourier transform infrared spectrum shows two phonon modes of the sample at around 550 cm^?1 and 670 cm^?1 due to the antisymmetric SbO₆ stretching vibration. The compound shows significant frequency dispersion in its dielectric properties. The complex impedance plane plots show that the relaxation (conduction) mechanism in SCS is purely a bulk effect arising from the semiconductive grains having the grain resistance = 3.8 × 10⁶ Ω and the grain capacitance = 1.03 × 10^?10 F at 603 K. The frequency-dependent conductivity spectra follow the universal power law. The conductivity at 100 Hz varies from 2 × 10^?7 Sm^?1 to 1.97 × 10^?5 Sm^?1 with the increase of temperature from 303 K to 703 K, respectively. The relaxation mechanism of the sample in the framework of electric modulus formalism is modelled by Davidson–Cole equation. The activation energy of the sample, calculated from both conductivity and modulus spectra is found to be ～0.15 eV. Such a value of activation energy indicates that the conduction mechanism for SCS is due to electron hopping. The scaling behaviour of imaginary electric modulus suggests that the relaxation describes the same mechanism at various temperatures.