239 resultados para Legendre Formula


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Solid solutions of the formula La2−xLnxCuO4 (Ln = Pr, Nd) possess the orthorhombic structure of La2CuO4 for small values of x and transform to the tetragonal Nd2CuO4 structure at a critical value of x. At the critical composition, there is an abrupt change in specific volume as well as the Image ratio. The material exhibits temperature-independent electrical resistivity below the critical value x and semiconducting behaviour above it. The specific volume and Image ratio smoothly decrease with increase in x in the La2Cu1−xNixO4 system, although the solid solution possess the tetragonal K2NiF4 structure when x>0.1. Compositions with x>0.1 exhibit a gradual semiconductor metal transition similar to that of La2NiO4, the transition temperature decreasing with increasing

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Heterometallic {3d-4f-5d} aggregates with formula [{LMe2Ni(H2O)Ln(H2O)4.5}2{W(CN)8}2]·15H2O, (LMe2 stands for N,N-2,2-dimethylpropylenedi(3-methoxysalicylideneiminato) Schiff-base ligand) with Ln = Gd, Tb, Dy, have been obtained by reacting bimetallic [LMe2Ni(H2O)2Ln(NO3)3] and Cs3{W(CN)8} in H2O. The hexanuclear complexes are organized in 1-D arrays by means of hydrogen bonds established between the solvent molecules coordinated to Ln and the CN ligands of an octacyanometallate moiety. The X-ray structure was solved for the Tb derivative. Magnetic behavior indicates ferromagnetic {W–Ni} and {Ni–Ln} interactions (JNiW = 18.5 cm-1, JNiGd = 1.85 cm-1) as well as ferromagnetic intermolecular interactions mediated by the H-bonds. Dynamic magnetic susceptibility studies reveal slow magnetic relaxation processes for the Tb and Dy derivatives, suggesting SMM type behavior for these compounds.

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Scheelite-related -Ln2Mo3O12(Ln = La, Pr, Nd, Sm, Gd, Tb, or Dy) oxides are reduced by hydrogen at 780–870 K yielding molybdenum (IV) oxides of formula Ln2Mo3O9. The latter crystallize in a tetragonal scheelite (ABO4) type structure where one third of the A sites and a quarter of the anion sites are vacant: Ln2/3(cat)1/3MoO3(an). The reaction Ln2Mo3O12+ 3H2 Ln2Mo3O9(an)3+ 3H2O may be regarded as topochemically controlled, since both the parent and the product phases have scheelite-related structures. Infrared spectra and electrical and magnetic properties of these metastable defect scheelite phases are reported.

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Reaction of Bi2O3 with MgO, NiO, Co3O4 and Al2O3 gives rise to the corresponding ternary bismuth oxides, Bi18Mg8O36, Bi18Ni8O36, Bi20Co6O39 and Bi24Al2O39. These oxides have the general formula Bi26�xMxO40�y and exhibit BCC structures related to α - Bi2O3. In the first three solids, the metal ions, M, replace bismuth randomly at the octahedral 24r sites (space group 123); in the last case, aluminium ions occupy the tetrahedral 2a sites, the phase being isostructural with Bi24Ge2O40. Starting from Bi2O3 and NiO, orthorhombic Bi2Ni2O5 has also been obtained.

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Complexes of lanthanide iodides with 3-methylpyridine-1-oxide of the formula Ln(3-MePyO)8I3.xH2O where x = 0 for Ln = La and Tb, x = 1 for Ln = Pr, and x = 2 for Ln = Nd, Sm, Dy, Yb, and Y have been prepared and characterized by chemical analyses, conductance, infrared, proton nmr, and DTA data. Infrared and proton nmr data have been interpreted in terms of the coordination of the ligand to the metal ion through the oxygen of the N—O group. Proton nmr spectrum of the Yb(III) complex is indicative of a restricted rotation of the pyridine ring about the N—O bond.

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The complex crystallizes in the space group P21/c with four formula units in a unit cell of dimensions a= 12.747, b= 7.416, c= 17.894 A and/3= 90.2 °. The structure has been solved by the symbolic addition procedure using three-dimensional photographic data and refined to an R value of 0.079 for 2019 observed reflexions. The pyramidal nature of the two hetero nitrogen atoms in the antipyrine molecule is inter:nediate between that observed in free antipyrine and in some of its metal complexes. The molecule is more polar than that in crystals of free antipyrine but less so compared with that in metal complexes. In the salicylic acid molecule, the hydroxyl group forms an internal hydrogen bond with one of the oxygen atoms in the carboxyl group. The association between the salicylic acid and the antipyrine molecules is achieved through an intermolecular hydrogen bond with the other carboxyl oxygen atom in the salicylic acid molecule as the proton donor and the carboxyl oxygen atom of the antipyrine molecule as the acceptor.

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The spectrum of short-closed chains up to N=12 are studied by exact diagonalization to obtain the spin-wave spectrum of the Hamiltonian H=2J Sigma i=1Nsi.si+1+2J alpha Sigma i=1Nsi.si+2, -1.0formula obtained by the Anderson approximation (1952). The results of short chains indicate that S=0 bound magnon states lie partly below the spin-wave states with S=1 only for alpha >or=0.3 and alpha

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The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

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A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

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A ternary metal complex involving Vitamin B6 with the formula [Cu(bipy)(pn) (OH)]H2O (bipy = 2,2'²-bipyridine, PN = anionic pyridoxine) has been synthesized and studied in the solid state by means of spectroscopy and X-ray crystallography. The geometry around copper(II) is distorted square pyramidal, two oxygens from phenolic and 4-(hydroxymethyl) groups of pn, two nitrogens from bipy and an axial OH- ion forming the coordination sphere. In this structure pn exists in a new anionic form with deprotonation of the phenolic group. The structure also provides a rare example of monodentate hydroxyl coordination to copper.

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The spin degree of freedom is largely disregarded in existing theories of the density-dependent optical properties of an interacting electron-hole plasma in quasiequilibrium. Here, we extended the pair equation, which is applicable to a bulk semiconductor at elevated temperatures, to calculate optical nonlinearities due to a spin-polarized plasma. We obtained agreement with recent circular dichroism data in laser-excited GaAs by using the plasma density alone as the fitting parameter. The simplicity of our theory, based on the analytical pair-equation formula, makes it ideal for conveniently modelling absorption in a carrier spin-polarized semiconductor.

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Nanoparticles of trivalent Eu3+-doped Nd2O3 phosphors have been prepared using a low-temperature solution combustion method with metal nitrate as precursor and oxalyldihydrazide as a fuel at a fairly low temperature (<500 degrees C) and in a very short time (<5 min). A powder X-ray diffraction pattern reveals that cubic Nd2O3 : Eu3+ crystallites are directly obtained without the requirement of further calcinations. The crystallite size, evaluated from Scherer's formula, was found to be in the range of 20-30 nm. The microstructure and morphology were studied by scanning electron microscopy, which showed the phosphor to be foamy and fluffy in nature. Thermoluminescence characteristics of the Nd2O3 : Eu3+ have been studied using gamma irradiation. These demonstrate that the phosphor is suitable for use as a dosimeter.

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X-ray powder diffraction along with differential thermal analysis carried out on the as-quenched samples in the 3BaO-3TiO(2)-B2O3 system confirmed their amorphous and glassy nature, respectively. The dielectric constants in the 1 kHz-1 MHz frequency range were measured as a function of temperature (323-748 K). The dielectric constant and loss were found to be frequency independent in the 323-473 K temperature range. The temperature coefficient of dielectric constant was estimated using Havinga's formula and found to be 16 ppm K-1. The electrical relaxation was rationalized using the electric modulus formalism. The dielectric constant and loss were 17 +/- 0.5 and 0.005 +/- 0.001, respectively at 323 K in the 1 kHz-1 MHz frequency range which may be of considerable interest to capacitor industry.

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Surfactant anion intercalated hydroxy salts of copper and cobalt of the formula M(OH)(2-x)(surf)(x)center dot mH(2)O [M = Cu, Co; surf = dodecyl sulfate. dodecyl benzene sulfonate. and x = 0.5 for Cu and 0.67 for Co] delaminate readily in 1-butanol to give translucent colloidal dispersions that are stable for months. The extent of delamination and the colloidal dispersion observed in these solids is higher than what had been observed for layered double hydroxides. The dispersions yield the corresponding nanoparticulate oxides on solvothermal decomposition. While the copper hydroxy salt forms similar to 300 nm dendrimer-like CuO nanostructures comprising nanorods of similar to 10 nm diameter, the cobalt analogue forms similar to 20 nm superparamagnetic particles of Co3O4.

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By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.