On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.     

Projection methods for computing Moore-Penrose inverses of unbounded operators

In this article we give a characterization of the convergence of projection methods which are useful for approximating the Moore-Penrose inverse of a closed densely defined operator between Hilbert spaces. We illustrate the main theorem with an example. Also a procedure for constructing the admissible sequence of projections is discussed.     

Local dependence functions for some families of bivariate distributions and total positivity

The purpose of this paper is to investigate a very useful application of a certain local dependence function γ_f(x,y), which was considered recently by Holland and Wang [20]. An interesting property of γ_f(x,y) is that the underlying joint density f(x,y) is TP₂ (that is, totally positive of order 2) if and only if . This gives an elegant way to investigate the TP₂ property of any bivariate distribution. For the Saramanov family, the Ali-Mikhail-Haq family of bivariate distributions and the family of bivariate elliptical distributions, we derive the local dependence function and obtain conditions for f(x,y) to be TP₂. These families are quite rich and include many other large classes of bivariate distributions as their special cases. Similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with Pareto conditionals.     

The biogenetic law

We develop one criterion for the selection of the content of a mathematics syllabus. We advocate the importance of the biogenetic law and stress the importance of a historical perspective in mathematical education.     

Spin state selective coherence transfer: a method for discrimination and complete analyses of the overlapped and unresolved 1H NMR spectra of enantiomers

In general, the proton NMR spectra of chiral molecules aligned in the chiral liquid crystalline media are broad and featureless. The analyses of such intricate NMR spectra and their routine use for spectral discrimination of R and S optical enantiomers are hindered. A method is developed in the present study which involves spin state selective two dimensional correlation of higher quantum coherence to its single quantum coherence of a chemically isolated group of coupled protons. This enables the spin state selective detection of proton single quantum transitions based on the spin states of the passive nuclei. The technique provides the relative signs and magnitudes of the couplings by overcoming the problems of enantiomer discrimination, spectral complexity and poor resolution, permitting the complete analyses of the otherwise broad and featureless spectra. A non-selective 180 degrees pulse in the middle of MQ dimension retains all the remote passive couplings. This accompanied by spin selective MQ-SQ conversion leads to spin state selective coherence transfer. The removal of field inhomogeneity contributes to dramatically enhanced resolution. The difference in the cumulative additive values of chemical shift anisotropies and the passive couplings, between the enantiomers, achieved by detecting Nth quantum coherence of N magnetically equivalent spins provides enhanced separation of enantiomer peaks. The developed methodology has been demonstrated on four different chiral molecules with varied number of interacting spins, each having a chiral centre.     

Microwave‐Assisted Synthesis and Antituberculosis Screening of Some 4‐((3‐(Trifluoromethyl)‐5,6‐dihydro‐[1,2,4]triazolo[4,3‐a]pyrazin‐7(8H)‐l)methyl)benzenamine Hybrids

In the present investigation, a series of 4‐((3‐(trifluoromethyl)‐5,6‐dihydro‐[1,2,4]triazolo[4,3‐a]pyrazin‐7(8H)‐yl)methyl)benzenamine analogs 6a–o were synthesized and characterized by IR, NMR (¹H and ¹³C), and mass spectra. All newly synthesized compounds 6a–o were prepared under conventional and microwave irradiation methods. These compounds obtained in higher yields and in shorter reaction times in the microwave irradiation method when compared with the conventional method. Synthesized compounds 6a–o were inspected for their in vitro antitubercular activity against Mycobacterium tuberculosis H₃₇Ra using an established XTT reduction menadione assay. Among the screened compounds, 6i (IC₅₀: 1.82 μg/mL), 6j (IC₅₀: 1.02 μg/mL), and 6k (IC₅₀: 1.59 μg/mL) showed excellent activity. Furthermore, compound 6i showed MIC₉₀ value of 16.02 μg/mL. In summary, the results indicate the identification of some novel, selective, and specific inhibitors against M. tuberculosis that can be explored further for the potential antitubercular drug.     

Microwave Synthesis of Fused Pyrans by Humic Acid Supported Ionic Liquid Catalyst and Their Antimicrobial,Antioxidant, Toxicity Assessment,and Molecular Docking Studies

A series of fused quinolinyl and quinolonyl pyrans were synthesized via a one‐pot reaction of quinolinyl and quinolonyl carbaldehydes, malononitrile, and a 1,3‐diketone. The reactions were catalyzed by a new humic acid supported 1‐butyl‐3‐methyl imidazolium thiocyanate ionic liquid under microwave irradiation conditions. Antimicrobial, antioxidant, and toxicity studies displayed various biological activities depending on structure of the pyrans.     

Nanohoop Rotaxanes from Active Metal Template Syntheses and Their Potential in Sensing Applications

The unique optoelectronic properties and smooth, rigid pores of macrocycles with radially oriented π systems render them fascinating candidates for the design of novel mechanically interlocked molecules with new properties. Two high‐yielding strategies are used to prepare nanohoop [2]rotaxanes, which owing to the π‐rich macrocycle are highly emissive. Then, metal coordination, an intrinsic property afforded by the resulting mechanical bond, can lead to molecular shuttling as well as modulate the observed fluorescence in both organic and aqueous conditions. Inspired by these findings, a self‐immolative [2]rotaxane was then designed that self‐destructs in the presence of an analyte, eliciting a strong fluorescent turn‐on response, serving as proof‐of‐concept for a new type of molecular sensing material. More broadly, this work highlights the conceptual advantages of combining compact π‐rich macrocyclic frameworks with mechanical bonds formed via active‐template syntheses.     

Investigation on the radiolytic stability of polybenzimidazole-based polymeric resins for the recovery of lanthanides,actinides, palladium from aqueous medium

Journal of Radioanalytical and Nuclear Chemistry - Radiolytic stability of polymeric resins is an important aspects in nuclear materials processing. The different dosage of gamma radiation was...     

Narrow band optical filter in fluorescein doped boric acid glass saturable absorber thin films

We demonstrate narrow band optical filter like frequency response with full width half maximum (FWHM) of nearly (1.75 ± 0.25) Hz in fluorescein doped boric acid glass films [10⁻⁴ M], using modulated optical phase conjugation and a nearly non-degenerate four wave mixing technique. Modulated optical phase conjugation signals are described in the limit of a weak probe and relatively strong pump beams. Both pump beams are of nearly equal intensity at a wavelength of 514.5 nm from a continuous-wave Ar⁺ laser. The probe beam frequency has been detuned with a ramp signal using a piezo electric mirror.