Similarity of hybrid numbers

The set of hybrid numbers $𝕂$ is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =− hi =ε+ i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x ⁻¹ qx = p . And, it is denoted by p ∼ q . In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for $\text{◂,▸}\mathbf{p},\mathbf{q},\mathbf{c}\in 𝕂\mathbf{.}$     

Cobalt(II), nickel(II) and copper(II) complexes of a Schiff base ligand: synthesis,structural characterization and luminescence properties

A Schiff base ligand (HL), 2,4-dimethoxy-N-(5-chloro-2-hydroxybenzylidene)-benzenamine, derived from 5-chloro-2-hydroxybenzaldehyde and 2,4-dimethoxyaniline, and its metal complexes [Co(L)₂]·CH₃OH (1), [Ni(L)₂] (2), [Cu(L)₂] (3) have been synthesized. The compounds were characterized by analytical and spectroscopic methods. In addition, the structures of the Schiff base HL and its Co(II) complex were determined by single-crystal X-ray analysis. The Co(II) center is six-coordinate, being coordinated to two imine nitrogen, two phenolate oxygen and two methoxy oxygen atoms of two crystallographically independent Schiff base ligands. Luminescence properties of HL and its complexes were investigated both in solution and in the solid state.     

Palladium(II)-N-heterocyclic carbene-catalyzed direct C2- or C5-arylation of thiazoles with aryl bromides

Herein we report, a series of new benzimidazolium chlorides as N-heterocyclic carbene (NHC) ligand and their corresponding palladium(II)-NHC complexes with the general formula [PdCl₂(NHC)₂] were synthesized. All new compounds were characterized by ¹H NMR, ¹³C NMR, IR spectroscopy and elemental analysis techniques. The catalytic activity of palladium(II)-NHC complexes was investigated in the direct C2- or C5-arylation of thiazoles with aryl bromides in presence of palladium(II)-NHC at 150?°C for 1?h. These complexes exhibited the good catalytic performance for the direct arylation of thiazoles. The arylation of thiazoles regioselectively produced C2- or C5-arylated thiazoles in moderate to high yields.     

Surfactant-assisted polyol preparation of nickel powders with different morphologies

Sub-micrometer nickel powders of controlled size and morphology were produced by a surfactant-assisted polyol method, using ethylene glycol (EG) as solvent and reductant in the presence of sodium dodecyl sulfate (SDS) surfactant and NaOH. The resultant Ni powders were characterized by XRD, SEM, EDS, and FTIR. Spherical, hexagonal, and triangular fcc Ni powders from 0.30 to 0.60 μm were obtained in the presence of SDS; irregular spherical fcc Ni powders were obtained in its absence. The concentrations of SDS, NaOH and Ni(CH₃COO)₂·4H₂O greatly influence the product morphology and size.      

Syntheses, characterization, antimicrobial and genotoxic activities of new Schiff bases and their complexes

Two new Schiff base ligands (L¹, L²) have been prepared from the reaction of 2,6-diacetylpyridine and 2-pyridinecarboxyaldehyde with 4-amino-2,3-dimethyl-1-phenyl-3-pyrozolin-5-on, and their Co(II), Cu(II), Ni(II), Mn(II), and Cr(III) metal complexes have also been prepared. The complexes are formed by coordination of N and O atoms of the ligands. Their structures were characterized by physico-chemical and spectroscopic methods. The analytical data shows that the metal to ligand ratio in the Schiff base complexes is 1:2. The Schiff base ligands and all complexes were evaluated for their in vitro antibacterial and antifungal activities by the disc diffusion method. In addition, the genotoxic properties of the ligands were studied.     

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

Degree of Approximation for Bivariate Chlodowsky–Szasz–Charlier Type Operators

We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky–Szasz–Charlier type and estimate the order of approximation in terms of mixed modulus of continuity.     

On {\left(1,3 \right) }-Cartan null Bertrand curves in semi-Euclidean 4-space with index 2

In this paper, we study generalized Cartan null Bertrand curves in semi-Euclidean 4-space \({\mathbb{E}_{2}^{4}}\) with index 2.     

Palladium‐catalyzed Suzuki reaction using 1,3‐dialkylbenzimidazol‐2‐ylidene ligands in aqueous media

From readily available starting compounds, six functionalized 1,3‐dialkylbenzimidazolium salts ( 2a–c and 4a–c ) have been prepared and characterized by conventional spectroscopic methods and elemental analyses. A highly effective, easy to handle, and environmentally benign process for palladium‐mediated Suzuki cross‐coupling was developed. The in situ prepared three‐component systems Pd(OAc)₂/1,3‐dialkylbenzimidazolium chlorides and Cs₂CO₃ catalyze quantitatively the Suzuki cross‐coupling of deactivated aryl chlorides. © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:419–423, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20034