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Abstract  

The complexes of piperidine dithiocarbamate, 2-aminopyridine dithiocarbamate and organotin(IV) of the type R3Sn(L1), R2Sn(L1)2, R3Sn(L2), R2Sn(L2)2, [R=C6H5CH2 (benzyl), p-ClC6H4CH2 (p-chlorobenzyl), L 1=sodium piperidine dithiocarbamate and L 2=sodium 2-aminopyridine dithiocarbamate] have been synthesised and characterised by spectral studies (IR, UV, 1H NMR). Thermogravimetric (TG) and differential thermal analytical (DTA) studies have beeen carried out for these complexes and from the TG curves, the order and apparent activation energy for the thermal decomposition reactions have been elucidated. The various thermal studies have been correlated with some structural aspects of the complexes concerned. From DTA curves, the heat of reaction has been calculated.

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The paper is related to the lower and upper estimates of the norm for Mercer kernel matrices. We first give a presentation of the Lagrange interpolating operators from the view of reproducing kernel space. Then, we modify the Lagrange interpolating operators to make them bounded in the space of continuous function and be of the de la Vallée Poussin type. The order of approximation by the reproducing kernel spaces for the continuous functions is thus obtained, from which the lower and upper bounds of the Rayleigh entropy and the l 2-norm for some general Mercer kernel matrices are provided. As an example, we give the l 2-norm estimate for the Mercer kernel matrix presented by the Jacobi algebraic polynomials. The discussions indicate that the l 2-norm of the Mercer kernel matrices may be estimated with discrete orthogonal transforms.

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Abstract  

The thermodynamic and thermal properties of [Cu(L)2·Cl2], [Ni(L)2]·Cl2, [Co(L)2·Cl2]; L=1,2-bis(o-aminophenoxy)ethane (BAFE), complexes have been investigated. The thermal decomposition of the complexes took place in two distinct steps in endothermic reaction up to 700°C. The activation energy E, the entropy change S #, enthalpy H change and Gibbs free energy change G # were calculated from the results of thermogravimetry analysis (TG) and heat capacity from the results of differential scanning calorimetry (DSC). It was found that the thermal stabilities and activation energies of the complexes follow the order Ni(II)>Cu(II)>Co(II) and E Co<E Ni<E Cu, respectively.

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Abstract  

The reaction between [M(DMBG)2nH2O ((1) M:Ni, n = 0; (4) M:Cu, n = 1), ammonia/hydrazine and formaldehyde in methanol resulted in new complexes of type [ML]·nH2O ((2) M:Ni, L:L1, n = 0; (3) M:Ni, L:L2, n = 0, (5) M:Cu, L:L1, n = 0 and (6) M:Cu, L:L2, n = 3; HDMBG: N,N-dimethylbiguanide, L1 = ligand resulted from ammonia system and L2 = ligand resulted from hydrazine system). The features of complexes have been assigned from microanalytical, IR and UV–Vis data. The thermal transformations of compounds are complex processes according to TG and DTG curves including melting, phase transition, dehydration, oxidative condensation of –C=N– units as well as thermolysis processes. The final products of decomposition are the most stable metal oxides.

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Abstract  

The new mixed ligand complexes with formulae Co(4-bpy)2L2⋅2H2O (I), Cu(4-bpy)2L2⋅H2O (II) and Cd(4-bpy)L2⋅H2O (III) (4-bpy=4,4'-bipyridine, L=CCl3COO) were prepared. Analysis of the IR spectra indicate that 4-bpy is coordinated with metal ions and carboxylates groups bond as bidentate chelating ligands. The electronic spectra are in accordance with pseudo-octahedral environment around the central metal ion in the Co(II) and Cu(II) complexes. The thermal decomposition of the synthesized complexes was studied in air. A coupled TG-MS system was used to analyse the principal volatile thermal decomposition products of Co(II) and Cu(II) complexes. Corresponding metal oxides were identified as a final product of pyrolysis with intermediate formation of metal chlorides.

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Abstract  

The main aim of this paper is to prove that the maximal operator σ * α of the (C, α) means of the cubical partial sums of the two-dimensional Walsh-Fourier series is bounded from the Hardy space H 2/(2+α) to the space weak-L 2/(2+α).

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Abstract  

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L 2 norm.

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Abstract  

Thorium(IV) complexes of the type Th(NO3)4·3L·2C2H5OH, Th(SCN)4·L·C2H5OH and Th(SO4)2·2L·2C2H5OH (L=1-butyl-1-methylpiperazinium iodide(I) have been synthesised. From thermogravimetric (TG) curves, the decomposition pattern of the compounds has been analysed. The order, activation energy and apparent activation entropy of the thermal decomposition reaction have been elucidated. The heat of reaction has been calculated from differential thermal analysis (DTA) studies.

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Abstract

Müntz–Legendre polynomials L n(Λ;x) associated with a sequence Λ={λ k} are obtained by orthogonalizing the system in L 2[0,1] with respect to the Legendre weight. Under very mild conditions on Λ, we establish the endpoint asymptotics close to x=1. The main result is

ea
where and J 0 is the Bessel function of order 0.

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Abstract  

Four novel metal(II) complexes, Ni(L)2, Co(L)2, Cu(L)2, and Zn(L)2 (L = 5-(2-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrazol-4-yl)hydrazono)-1,3-diethyl-2-thioxo-dihydropyrimidine-4,6(1H,5H)-dione), were synthesized using the procedure of diazotization, coupling and metallization. Their structures were identified by elemental analyses, 1H NMR, ESI-MS and FT-IR spectra. The effect of different central metal(II) ions on absorption bands of the metal(II) complexes was researched. The thermal properties of the metal(II) complexes were investigated by thermogravimetry (TG) and differential scanning calorimetry (DSC). Furthermore, the thermodynamic parameters, such as activation energy (E*), enthalpy (∆H*), entropy (∆S*) and free energy of the decomposition (∆G*) are calculated from the TG curves applying Coats–Redfern method. The results show that the metal(II) complexes have suitable electronic absorption spectra with blue-violet light absorption at about 350–450 nm, high thermal stability with sharp thermal decomposition thresholds.

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