Pentadiagonal Oscillatory Matrices with Two Spectrum in Common

We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σ_i(A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ₁ and σ₂. The pairs σ, σ₁ and σ₁, σ₂ must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ₁ in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ₁ and σ₂ in common.     

Spectrophotometric and AAS determination of trace amounts of cobalt after preconcentration by using alpha-benzilmonoxime-microcrystalline naphthalene.

The formed cobalt-a-benzilmonoxime complex was adsorbed onto microcrystalline naphthalene. Then it was determined by zero and first derivative spectrophotometry and by atomic absorption spectrophotometry (AAS) after dissolving into chloroform and methylisobutylketone (MIBK), respectively. Under optimum conditions, cobalt in the range of 1.0 - 20.0, 0.4 - 30.0 and 2.5 - 50.0 microg could be determined by spectrophotometry, first derivative spectrophotometry and AAS method, respectively. By the method, a preconcentration factor equal to approximately 30 for cobalt was obtained. The effect of diverse ions on the determination of 5.0 microg cobalt was also studied. The method was successfully applied to some pharmaceuticals and synthetic alloy samples.     

A Symmetric-Impulse Approximation Applied to the Faddeev Theory on the Charge Transfer Amplitude

Off-the-shell anomalous factors of the two-body Coulomb transition matrices appear in the integral form of the Faddeev second-order nuclear-electronic amplitude, for proton-hydrogen charge transfer scattering in a typical nlm → n′l′m′ transition. A symmetric-impulse approximation (SIA) is applied to eliminate these factors and an induction method is proposed to analytically calculate the remaining integrals. The nuclear-electronic amplitude is derived for the general case, and for totally symmetric collisions, in terms of generalized hypergeometric functions of two variables, F ₄, and of one variable, ₃ F ₂, respectively. The angular distribution of the second-order nuclear-electronic charge transfer amplitude shows the Thomas mechanism as a peak or a hump for symmetric and asymmetric collisions. There also exists a peak in the forward angular distribution of the second-order nuclear-electronic amplitude, which partly cancels the kinematic peak in the angular distribution of the charge transfer differential cross sections.     

Spectrophotometric study of interaction of 2,3-dichloro-5,6-dicyano-1,4-benzoquinone with diaza-18-crown-6 and diaza-15-crown-5 in acetonitrile and chloroform solutions

Interactions of diaza-18-crown-6 and diaza-15-crown-5, as electron donors, with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ), as an electron acceptor, have been investigated spectrophotometrically in acetonitrile and chloroform solutions. The results indicated immediate formation of an electron donor-electron acceptor complex DA: [reaction in text] which is followed by two relatively slow consecutive reactions: [reaction in text]. The pseudo-first-order rate constants for the formation of the ionic intermediate and the final product have been evaluated at various temperatures by computer fitting of the absorbance time data to appropriate equations. The formation constants of the resulting DA complexes have also been determined. The influences of both the azacrown's structure and the solvent properties on the formation of DA complexes and the rates of subsequent reactions are discussed.     

Conductance study of ammonium complexes with several crown ethers and cryptands in nitrobenzene,acetonitrile and dimethylformamide solutions

The formation of ammonium complexes with several crown ethers and cryptands in nitrobenzene, acetonitrile and dimethylformamide solutions was investigated by conductometry at 25°C. Stability constants of the resulting 1:1 complexes sere determined from the molar conductance-mole ratio data and found to vary in the order DC18C6>18C6>DB30C10>DB21C7>DB24C8>DB18C6>15C5>B15C5>12C4, in the case of crown complexes, and in the order C222>C221>C211>C22>C21 for the ammonium cryptates. The stabilities of the complexes varied inversely with the Gutmann donicity of the solvents. Influences of the number of members in the macrocycle, nature of the substituents in the polyether ring, cavity size and dimensionality, conformations of the free and complexed ligands and number of N⁺–H bonds available for hydrogen bonding are discussed.     

Conductance study of the thermodynamics of ammonium ion complexes with several crown ethers in acetonitrile solution

A conductance study concerning the interaction between ammonium ion and several crown ethers in acetonitrile solution has been carried out at different temperatures. The stability constants of the resulting 11 complexes at various temperatures were determined from the molar conductance-mole ratio data and found to vary in the order DC18C6>18C6>DB30C10>DB21C7>DB24C8>DB18C6>15C5>B15C5. The enthalpy and entropy of complexation were determined from the temperature dependence of the formation constants. The influence on the thermodynamic data of different parameters such as cavity size and dimensionality of crown ethers, nature of substituents in the polyether ring, conformations of the free and complexed ligands, solvent-ligand interaction and number of N–H bonds available for hydrogen bonding are discussed.     

Zn(II)-selective membrane electrode based on tetra(2-aminophenyl) porphyrin

A new PVC membrane electrode for Zn²⁺ ions based on tetra(2-aminophenyl) porphyrin (TAPP) as membrane carrier is prepared. The sensor exhibits a linear stable response over a wide concentration range (5.0×10⁻⁵ to 1.0×10⁻¹ M) with a slope of 26.5 mV/decade and a limit of detection 3.0×10⁻⁵ M (1.96 ppm). It has a response time of about l0 s and can be used for at least 8 months without any divergence in potential. The propose membrane sensor revealed good selectivities for Zn²⁺ over a wide variety of other metal ions and can be used in pH range of 3.0–6.0. It was successfully applied to the direct determination of zinc in a pharmaceutical sample and also as an indicator electrode in potentiometric titration of Zn²⁺ ions.     

Design and characterization of [(Et)3 N-H]FeCl4 as a nanomagnetic ionic liquid catalyst for the synthesis of xanthene derivatives under solvent-free conditions

The triethylamine-based nanomagnetic ionic liquid, [(Et)₃ N-H]FeCl₄, was synthesized, and its structural and chemical characteristics were detected. The thermogravimetric analysis indicated its high thermal stability with a decomposition temperature higher than 300 °C. Additionally, [(Et)₃ N-H]FeCl₄ was used to efficiently catalyze the synthesis of xanthene derivatives under solvent-free conditions at 120 °C. [(Et)₃ N-H]FeCl₄ was recycled and reused at least five times.

Graphical abstract