A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula

Acta Mathematica Sinica, English Series - In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and...     

A New Trinuclear Zn(II) Complex {[Zn(μ-ONN)(μ<Subscript>2</Subscript>-O)(μ-OO)]<Subscript>2</Subscript>Zn}: Synthesis,Characterization, Thermal Decomposition and Antibacterial Activity

New centrosymmetric trinuclear zinc(II) complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} has been synthesized by the reaction of a potentially ONN tridentate Schiff base ligand, and N,N-dimethylethylendiamin, with Zn(OAc)₂·2H₂O in methanol, in the refluxed conditions and characterized by elemental analysis, FT-IR and UV–Vis spectroscopy. Single crystal X-ray structure analysis reveals a trinuclear complex {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} with zinc(II) ions connected by three different bridges, (μ-ONN) of the Schiff base ligand, μ₂-O and μ-OO of the acetate. The complex is centrosymmetric, with one of the Zn atoms located at the inversion center. While the central Zn(II) ion is six-coordinated, the coordination number of the other Zn(II) ions is five. Finally, the {[Zn(μ-ONN)(μ₂-O)(μ-OO)]₂Zn} complex was thermally decomposed in air at 700 °C resulted in ZnO nano crystalites with the average size of 42 nm. The antibacterial activity of ligand and its zinc(II) complex were tested against gram-positive and gram-negative bacteria. The ligand showed higher activity than its zinc(II) complex.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems

In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi e?ciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, su?cient conditions for local (weak) quasi e?cient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.     

Synthesis and application of a thermosensitive tri-block copolymer as an efficient sample treatment technique for preconcentration and ultra-trace detection of lead ions

We have designed and synthesized a thermosensitive tri-block copolymer for selective trace extraction of Pb(II) ions from biological and food samples. The polymer was characterized by Fourier transform IR and NMR spectroscopy, and by gel permeation chromatography. The critical aggregation concentration and lower critical solution temperature were determined via fluorescence and UV spectrophotometry, respectively. The effects of solution pH value, amount of copolymer, of the temperature on extraction and on phase separation, and of the matrix on the extraction of Pb(II) were optimized. Pb(II) ions were then quantified by FAAS. The use of this copolymer resulted in excellent figures of merit including a calibration plot extending from 0.5 to 160 μg L^?1 (with an R² of >0.99), a limit of detection (LOD) as low as 90 pg L^?1, an extraction efficiency of >98 %, and relative standard deviations of <4 % for eight separate extraction experiments.

Thermodynamics of aqueous solutions of poly ethylene glycol di-methyl ethers in the presence or absence of ammonium phosphate salts

Precise measurements of density and sound velocity at different temperatures ranging from 283.15 to 308.15 K for solutions of PEGDME250, PEGDME500 and PEGDME2000 in water and of PEGDME500 in aqueous solutions of 0.500 mol kg⁻¹ ammonium di-hydrogen phosphate ((NH₄)H₂PO₄) and di-ammonium hydrogen phosphate ((NH₄)₂HPO₄), binodal curves at temperature ranges 293.15-318.15 K for the aqueous PEGDME500 + (NH₄)₂HPO₄, PEGDME500 + (NH₄)₃PO₄, PEGDME2000 + (NH₄)H₂PO₄, PEGDME2000 + (NH₄)₂HPO₄, PEGDME2000 + (NH₄)₃PO₄ and PPG400 + (NH₄)₂HPO₄ two-phase systems, and liquid-liquid equilibrium data at temperature ranges 298.15-318.15 K for the aqueous PEGDME500 + (NH₄)₂HPO₄ and PEGDME2000 + (NH₄)₂HPO₄ two-phase systems have been taken. From the experimental density and sound velocity data, the apparent specific volume, excess specific volume, isentropic compressibility and isentropic compressibility deviation values have been determined and the effect of temperature, charge on the anion of electrolytes and molar mass of PEGDME on the volumetric and compressibility properties of the investigated polymer solutions as well as on the salting-out effect of PEGDMEs produced by ammonium phosphate salts has been studied.     

Direct electrochemistry of an [FeFe]-hydrogenase on a TiO2 electrode

[FeFe]-hydrogenases are efficient natural catalysts that can be exploited for hydrogen production. Immobilization of the recombinant [FeFe]-hydrogenase CaHydA was achieved for the first time on an anatase TiO(2) electrode. The enzyme is able to interact and exchange electrons with the electrode and to catalyze hydrogen production with an efficiency of 70%.     

A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs). First, we approximate all functions involved in the considerable problem via 2D‐OBPs. Then, by using the operational matrices of integration, differentiation, and product, the solution of Volterra singular PIDEs is transformed to the solution of a linear or nonlinear system of algebraic equations which can be solved via some suitable numerical methods. With a small number of bases, we can find a reasonable approximate solution. Moreover, we establish some useful theorems for discussing convergence analysis and obtaining an error estimate associated with the proposed method. Finally, we solve some illustrative examples by employing the presented method to show the validity, efficiency, high accuracy, and applicability of the proposed technique.     

Fractional‐order orthogonal Bernstein polynomials for numerical solution of nonlinear fractional partial Volterra integro‐differential equations

In this paper, a new two‐dimensional fractional polynomials based on the orthonormal Bernstein polynomials has been introduced to provide an approximate solution of nonlinear fractional partial Volterra integro‐differential equations. For this aim, the fractional‐order orthogonal Bernstein polynomials (FOBPs) are constructed, and its operational matrices of integration, fractional‐order integration, and derivative in the Caputo sense and product operational matrix are derived. These operational matrices are utilized to reduce the under study problem to a nonlinear system of algebraic equations. Using the approximation of FOBPs, the convergence analysis and error estimate associated to the proposed problem have been investigated. Finally, several examples are included to clarify the validity, efficiency, and applicability of the proposed technique via FOBPs approximation.