On the commutativity degree of compact groups

In any finite group G, the commutativity degree of G (denoted by d(G)) is the probability that two randomly chosen elements of G commute. More generally, for every n ≥ 2 the nth commutativity degree (denoted by d _n (G)) is the probability that a randomly chosen ordered (n + 1)-tuple of the group elements is mutually commuting. The aim of this paper is to generalize the definition of d(G) and d _n (G) to every compact group G (infinite and even uncountable). We shall state some results concerning compact groups and we will extend some results in Erfanian et al. (Comm. Algebra 35 (2007), 4183–4197) and Lescot (J. Algebra 177 (1995), 847–869).     

A one‐pot efficient four‐component reaction for the synthesis of 2‐(arylamino)‐2‐(5‐aryl‐1,3,4‐oxadiazol‐2‐yl)propyl benzoate (or acetate) derivatives

Reactions of (N‐isocyanimino) triphenylphosphorane with 2‐oxopropylbenzoate (or acetate) in the presence of aromatic carboxylic acids and primary amines proceed smoothly at room temperature and in neutral conditions to afford sterically congested 1,3,4‐oxadiazole derivatives in high yields. The reaction proceeds smoothly and cleanly under mild conditions, and no side reactions were observed. © 2011 Wiley Periodicals, Inc. Heteroatom Chem 22:692–698, 2011; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20735     

Screening Anti-Cancer Drugs against Tubulin using Catch-and-Release Electrospray Ionization Mass Spectrometry

Tubulin, which is the building block of microtubules, plays an important role in cell division. This critical role makes tubulin an attractive target for the development of chemotherapeutic drugs to treat cancer. Currently, there is no general binding assay for tubulin–drug interactions. The present work describes the application of the catch-and-release electrospray ionization mass spectrometry (CaR-ESI-MS) assay to investigate the binding of colchicinoid drugs to αβ-tubulin dimers extracted from porcine brain. Proof-of-concept experiments using positive (ligands with known affinities) and negative (non-binders) controls were performed to establish the reliability of the assay. The assay was then used to screen a library of seven colchicinoid analogues to test their binding to tubulin and to rank their affinities.

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N-isocyaniminotriphenylphosphorane (Ph3PNNC) as an efficient reagent for the synthesis of ferrocene-containing 1,3,4-oxadiazole derivatives

Reaction of N-isocyaniminotriphenylphosphorane (Ph₃PNNC) with an aromatic aldehyde in the presence of ferrocene carboxylic acid and a secondary amine proceeds smoothly at room temperature under neutral conditions to afford sterically congested ferrocene-containing 1,3,4-oxadiazole derivatives in high yields. The reaction progresses smoothly and clearly under mild conditions and no side reactions were observed.     

CO2 reforming of methane over nickel catalysts supported on nanocrystalline MgAl2O4 with high surface area

In this paper dry reforming of methane (DRM) was carried out over nanocrystalline MgAl2O4-supported Ni catalysts with various Ni loadings. Nanocrystalline MgAl2O4 spinel with high specific surface area was synthesized by a co-precipitation method with the addition of pluronic P123 triblock copolymer as surfactant, and employed as catalyst support. The prepared samples were characterized by X-ray diffraction (XRD), N2 adsorption, H2 chemisorption, temperature-programmed reduction (TPR), temperature-programmed oxidation (TPO), temperature- programmed desorption (TPD) and transmission and scanning electron microscopies (TEM, SEM) techniques. The obtained results showed that the catalyst support has a nanocrystalline structure (crystal size: about 5 nm) with a high specific surface area (175 m2 g-1) and a mesoporous structure. Increasing in nickel content decreased the specific surface area and nickel dispersion. The prepared catalysts showed high catalytic activity and stability during the reaction. SEM analysis revealed that whisker type carbon deposited over the spent catalysts and increasing in nickel loading increased the amount of deposited carbon. The nickel catalyst with 7 wt% of nickel showed the highest catalytic activity.     

The ratio of the charm structure functions F k c (k = 2, L) at low x in deep inelastic scattering with respect to the expansion method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio R ^c = F _L ^c /F ₂ ^c , which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function F ₂ ^c in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.     

External electric field, hydrostatic pressure and conduction band non-parabolicity effects on the binding energy and the diamagnetic susceptibility of a hydrogenic impurity quantum dot

Electric field, hydrostatic pressure and conduction band non-parabolicity effects on the binding energies of the lower-lying states and the diamagnetic susceptibility of an on-center hydrogenic impurity confined in a typical GaAs/Al_xGa_1−xAs spherical quantum dot is theoretically investigated, by direct diagonalization of the Hamiltonian. To this end, the effect of band non-parabolicity has been performed, by means of the Luttinger-Kohn effective mass equation. Binding energies and diamagnetic susceptibility of the hydrogenic impurity are computed as a function of the dot size, external electric field strength and hydrostatic pressure, with considering the edge-band non-parabolicity. Results show that the external electric field and the hydrostatic pressure have an obvious influence on the binding energies and the diamagnetic susceptibility of the impurity.     

Study of physical chemistry on biosorption of zinc by using Chlorella pyrenoidosa

Discharge of heavy metals from metal processing industries is known to have adverse effects on the environment. Biosorption of heavy metals by metabolically inactive biomass of microbial organisms is an innovative and alternative technology for removal of these pollutants from aqueous solution. Presence of heavy metals in the aquatic system is posing serious problems. Zinc has been used in many industries and removal of Zn ions from waste water is significant. Biosorption is one of the economic methods used for removal of heavy metals. In the present study, the biomass obtained from the dried Chlorella pyrenoidosa was used for evaluating the biosorption characteristics of Zn ions in aqueous solutions. Batch adsorption experiments were performed with this material and it was found that the amount of metal ions adsorbed increased with the increase in the initial metal ion concentration. In this study effect of agitation time, initial metal ion concentration, temperature, pH and biomass dosage were studied. Maximum metal uptake (q _max) observed at pH 5 was 101.11 mg/g. The biosorption followed both Langmuir and Freundlich isotherm model. The adsorption equilibrium was reached in about 1 h. The kinetic of biosorption followed the second-border rate. The biomass could be regenerated using 0.1 M HNO₃. A positive value of ΔH° indicated the endothermic nature of the process. A negative value of the free energy (ΔG°) indicated the spontaneous nature of the adsorption process. A positive value of ΔS° showed increased randomness at solid-liquid interface during the adsorption of heavy metals, it also suggests some structural changes in the adsorbate and the adsorbent. FTIR Spectrums of Chlorella pyrenoidosa revealed the presence of hydroxyl, amino, carboxylic and carbonyl groups. The scanning electron micrograph clearly revealed the surface texture and morphology of the biosorbent.     

Selenium heterocycles XLIV. Syntheses of 8,9‐dihydro‐1,2,3‐thiadiazolo[4,5‐a]‐4,7‐dihydroxynaphthalene and 1,2,3‐selenadiazolo[4,5‐a]‐4,7‐dimethoxynaphthalene

The reaction of thionyl chloride with the semicarbazone 2 gave 4,5‐dihydro‐6,9‐dihydroxynaphtho‐[1,2‐d][1,2,3]thiadiazole ( 3 ) instead of 4,5‐dihydro‐6,9‐dimethyoxynaphtho[1,2‐d][1,2,3]thiadiazole ( 4 ). Selenium dioxide oxidation of compound 2 gave 4,5‐dihydro‐6,9‐dimethyoxynaphtho[1,2‐d][1,2,3]selenadiazole ( 5 ). Oxidation of compound 5 with 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone afforded 6,9‐dimethyoxynaphtho[1,2‐d][1,2,3]selenadiazole ( 6 ).