Topological efficiency under graph operations

In this paper we present explicit formulas for computing the topological efficiency index of the most important graph operations such as the Cartesian product, composition, corona, join and hierarchical product of two graphs. We apply our results to compute this distance-related invariant for some important classes of molecular graphs and nano-structures by specializing components of these graph operations.     

A new molecularly imprinted polymer for selective extraction and pre‐concentration of guaifenesin in different samples: Adsorption studies and kinetic modeling

This paper describes the synthesis of a molecularly imprinted polymer by chemical oxidation of pyrrole as the functional monomer, and at the presence of guaifenesin as the template. The prepared polymer was used as adsorbent in molecularly imprinted solid‐phase extraction followed by spectrophotometric determination. Different parameters in the solid‐phase extraction including sample pH, adsorbent weight, washing solution, and elution solvent were studied to determine optimum conditions for isolation and enrichment of guaifenesin. The results showed guaifenesin was quantitatively adsorbed on the molecularly imprinted polymer at pH 6.0 and completely eluted with an ethanol–water solution (50% v/v). An enrichment factor of four with satisfactory recoveries (87.0–95.0%) was obtained. The solid‐phase extraction columns could be used for up to six consecutive elution‐loading cycles without significant decreases in the analyte recoveries. The method had a dynamic range of 3.0 × 10^?6–1.5 × 10^?4 mol/L with a limit of detection and limit of quantification of 1.4×10^?6 and 4.5×10^?6 mol/L, respectively. The proposed procedure was used for the extraction and determination of guaifenesin in different pharmaceutical formulations, with satisfying results being achieved.     

On ordinary generalized geometric–arithmetic index

The ordinary generalized geometric–arithmetic index of graphs is introduced and some properties especially lower and upper bounds in terms of other graph invariants and topological indices are obtained.     

Abelian coverings of finite general linear groups and an application to their non-commuting graphs

In this paper we introduce and study a family A_n(q)\mathcal{A}_{n}(q) of abelian subgroups of GL_n(q){\rm GL}_{n}(q) covering every element of GL_n(q){\rm GL}_{n}(q). We show that A_n(q)\mathcal{A}_{n}(q) contains all the centralizers of cyclic matrices and equality holds if q>n. For q>2, we obtain an infinite product expression for a probabilistic generating function for |A_n(q)||\mathcal{A}_{n}(q)|. This leads to upper and lower bounds which show in particular that

Computing the eccentric-distance sum for graph operations

In this paper, we present explicit formulas for computing the eccentric-distance sum of the most important graph operations such as the Cartesian product, join, composition, disjunction, symmetric difference, cluster and corona product of graphs. Also, we apply our results to compute this eccentricity-related invariant for some important classes of molecular graphs and nano-structures by specializing components of these graph operations.     

Sonochemical and solvothermal synthesis of methanol {2-[(2-hydroxy-1,1-dimethyl-ethylimino)-methyl]phenolato}-dioxidomolybdenum(VI) complex and its decomposition to MoO<Subscript>3</Subscript> nanoparticles

As a new precursor to prepare nano molybdenum trioxide, methanol {2-[(2-hydroxy-1,1-dimethylethylimino)-methyl]phenolato}dioxidomolybdenum(VI) complex (1) with the Schiff base ligand (H₂L) is synthesized by two different methods: solvothermal and sonochemical. Nanoparticles of 1 are obtained by one-pot solvothermal treatment of methanolic solutions of the ligand and di-oxomolybdenyl acetylacetonate at 150°C for 24 h and for improving the quality of nanostructures by sonochemical method with two types of solvents, different concentrations of initial reagents and also different sonication times. The thermal stability of nanosized compound 1 is studied by thermal gravimetric (TG) analysis and differential scanning calorimetry (DSC). Nanoparticles of orthorhombic α-MoO₃ are obtained by calcination of nanostructures of compound 1 at 700°C. All compounds and the obtained molybdenum trioxide nanostructures are characterized by elemental analysis, FT-IR, UV-Vis spectroscopy, X-ray powder diffraction (XRD), and scanning electron microscopy (SEM).     

On best simultaneous approximation in quotient spaces

We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.     

Dinuclear cadmium (II) Schiff base complex: synthesis,crystal structure,spectroscopic characterization and application as a new precursor for preparation of nano-cadmium oxide

A novel cadmium (II) nano-complex, [Cd(EtOH)(HL)(NO₃)]₂ (1), (H₂L = 2-[(2-hydroxy-propylimino) methyl] phenol) was synthesized by solvothermal and sonochemical methods. The new nanostructure was characterized by scanning electron microscopy (SEM), X-ray powder diffraction, Fourier transform infrared spectroscopy and UV–Vis spectroscopy. Single crystalline of compound 1 was obtained using a branch tube method. The determination of the structure by single-crystal X-ray crystallography shows that the complex is a centrosymmetric dimer in which deprotonated phenolates bridge the two seven-coordinate metal atoms and link the two halves of the dimer. The luminescent properties of the complex 1 were examined and compared with the free ligand. The thermal stability of nano-complex 1 was analyzed by thermal gravimetric analysis. Furthermore, the effect of the initial substrates concentration on size and morphology of compound 1 nanostructure was investigated in sonochemical method. After the solid-state transformation of compound 1 at 650 °C in air, pure-phase nano-sized cadmium (II) oxide was produced. The morphology and size of the prepared CdO samples were further observed using TEM and SEM. Investigation of the optical properties of the produced cadmium oxide, using UV–Vis spectroscopy, confirmed its semiconducting properties by revealing optical band gap at 2.93 eV. A blue shift is observed in the band gap when compared with bulk sample which is due to the quantum size effect.     

Groups whose non-linear irreducible characters are rational valued

A finite group G all of whose nonlinear irreducible characters are rational is called a \mathbbQ₁{\mathbb{Q}_1}-group. In this paper, we obtain some results concerning the structure of \mathbbQ₁{\mathbb{Q}_1}-groups.