The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating Taylor expansion with explicit remainder term

In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit remainder term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration method. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term and errors are analyzed.     

Chloroacetonylation of CC double bonds promoted by manganese(III) acetate

The addition of acetylacetone to alkenes was performed using Mn(OAc)₃·2H₂O in the presence of HCl. The intermediate formed was trapped by chloride. Removal of one of the acetyl groups with ammonia under very mild conditions provided compounds derived from chloroacetonylation of the double bonds.     

Some topological and geometric properties of generalized Euler sequence space

In this paper, we introduce the Euler sequence space e ^r (p) of nonabsolute type and prove that the spaces e ^r (p) and l(p) are linearly isomorphic. Besides this, we compute the α-, β- and γ-duals of the space e ^r (p). The results proved herein are analogous to those in [ALTAY, B.—BASŠAR, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002), 701–715] for the Riesz sequence space r ^q (p). Finally, we define a modular on the Euler sequence space e ^r (p) and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space e ^r (p) has property (H) but it is not rotund (R).     

Theoretical calculations on structural and electronic properties of BGaAsBi alloys

The structural and electronic properties of cubic B _x Ga_1?x As_1?y Bi _y alloys with bismuth (Bi) concentration of 0.0625, 0.125, 0.1875 and 0.25 are studied with various boron (B) compositions by means of density functional theory (DFT) within the Wu-Cohen (WC) exchange correlation potential based on generalized gradient approximation (GGA). For all studied alloy structures, we have implemented geometric optimization before the volume optimization calculations. The obtained equilibrium lattice constants and band gap of studied quaternary alloys are investigated for the first time in literature. While the lattice constant behavior changes linearly with boron concentration, increasing small amount of bismuth concentration alter the lattice constant nonlinearly. The present calculation shows that the band gap decreases with increasing bismuth concentration and direct band gap semiconductor alloy became an indirect band gap with increasing boron concentration. From the band offset calculation we have shown that increasing B and Bi concentration in host GaAs reduced the valance band offset in a heterostructure formed by GaAs and studied alloys.     

Gödel type metrics in three dimensions

We show that the Gödel type metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. We also show that there exists only one first order partial differential equation satisfied by the components of fluid’s velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the Gödel type metrics to solve the Ricci and Cotton flow equations. When the vector field u ^μ is a Killing vector field, we came to the conclusion that the stationary Gödel type metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors.     

Experimental and DFT studies of ethyl N′-3-(1H-imidazol-1-yl) propylcarbamoyl benzohydrazonate monohydrate

The Imidazole compound, Ethyl N′-3-(1H-imidazol-1-yl) propylcarbamoyl benzohydrazonate monohydrate, has been synthesized and characterized by IR, NMR, electronic spectroscopy, and X-ray single-crystal determination. Molecular geometry from X-ray experiment of the title compound in the ground state has been compared using the density functional method (B3LYP) with 6-31G+(d) basis set. To determine conformational flexibility, molecular energy profile of the title compound was obtained by DFT calculations with respect to two selected degrees of torsional freedom, which were varied from −180° to +180° in steps of 10°. Besides, molecular electrostatic potential (MEP), natural bond orbitals (NBO), frontier molecular orbitals (FMO), and thermodynamic properties were performed at B3LYP/6-31G+(d) level of theory.     

A new rational approximation technique based on transformational high dimensional model representation

In this work, a new rational approximation scheme, based on the recently developed Transformational High Dimensional Model Representation (THDMR) approximation method is developed. As an initial step to the construction of a rational approximation for multivariate functions via THDMR, this paper focuses on the general theoretical background of the method and gives explicit formulae for the computation of such approximants. The performance of the technique is shown by several examples both in univariate and bivariate cases.     

Synthesis,complexation and antifungal,antibacterial activity studies of a new macrocyclic schiff base

A new macrocyclic ligand, L was synthesized using the high dilution condition with condensation of triethylene glycol diamine and terephtalaldehyde in ethanol. The obtained product, L was identified by FT‐IR, ¹H‐NMR, ¹³C‐NMR and Mass spectroscopy. The extraction equilibrium constants were estimated using dichloromethane/water membranes transfer with ICP‐AES and AES spectroscopy. Biological studies of this compound was determinated with disc diffusion method. The biological activity results showed that the synthesized ligand L has high activity against the studied microorganisms and high complexation ability against the Fe²⁺ cation.     

No fluctuation approximation in any desired precision for univariate function matrix representations

The operator involving problems are mostly handled by using the matrix representations of the operators over a finite set of appropriately chosen basis functions in a Hilbert space as long as the related problem permits. The algebraic operator which multiplies its operand by a function is the focus of this work. We deal with the univariate case for simplicity. We show that a rapidly converging scheme can be constructed by defining an appropriate fluctuation operator which projects, in fact, to the complement of the space spanned by appropriately chosen finite number of basis functions. What we obtain here can be used in efficient numerical integration also.     

Antimicrobial activity studies of mononuclear and binuclear mixed-ligand copper(II) complexes derived from Schiff base ligands and 1,10-phenanthroline

Mixed-ligand complexes of copper(II) with 1,10-phenanthroline and various Schiff bases have been prepared and characterized by elemental analysis, electronic and i.r. spectra, magnetic moment and molar conductance data. The Schiff base behave as bidentate ligands, and the mixed-ligand copper(II) complexes of the ligands HL1, HL2 and HL4 are binuclear. The conductivity data for all the complexes are consistent with those expected for an electrolyte. Antimicrobial activities of some of the ligands and complexes have been tested against Bacillus megaterium and Candida tropicalis. 1H and 13C n.m.r. spectra have been recorded in order to solve the solution structure of the ligands. Thermal properties of all complexes have been studied by the d.t.a. and t.g.a. techniques.