Some fixed point results on a metric space with a graph

Combining some branches is a typical activity in different fields of science, especially in mathematics. Naturally, it is notable in fixed point theory. Over the past few decades, there have been a lot of activity in fixed point theory and another branches in mathematics such differential equations, geometry and algebraic topology. In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using main idea of their work and the idea of combining fixed point theory and graph theory, we present some iterative scheme results for G-contractive and G-nonexpansive mappings on graphs.     

Comparison of the site occupancies determined by combined Rietveld refinement and density functional theory calculations: example of the ternary Mo-Ni-Re σ phase

The site occupancies of the Mo-Ni-Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3(5) = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg-Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo-Ni-Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results.     

Heavy ion interactions of (14.0 MeV/u) Pb with U

The interactions of ²⁰⁸Pb projectiles with ^natU target have been studied at 14.0 MeV/u beam energy using two different threshold detectors; mica and lexan. The elastic scattering data have been separated from the binary events and used for the determination of quarter-point angle θ_1/4 (≡ grazing angle θ_gr). The values of maximum angular momentum , radius of interaction R_int and reaction cross-section σ_R^exp(el.) were then deduced by making use of the value of θ_1/4. The data of inelastic events of different multiplicities have been used to determine partial reaction cross-sections. The sum of the partial cross-sections, therefore, yielded another independent value of reaction cross-section σ_R^exp(inel.) that in turn was used to derive the alternative values of , θ_gr, and R_int independently. The average of these quantities provided the experimental values of the reaction parameters that are comparable to the theoretical predictions.     

Double sequential fission in the reaction (16.7 MeV/u) U + Au observed with mica detectors

One of the main advantages of using dielectric track detectors in the study of heavy ion interactions is the possibility of observing each multi-prong event individually with complete kinematical details. It is thus possible to analyze even those reaction channels that have very low branching ratios. In the study of reactions induced by 16.7 MeV/u uranium ions incident on natural gold targets, we have observed 18 four-pronged events in a total detector area of 24 cm². Using a polynomial range-energy relationship, empirically fitted to the observed data of binary and ternary events, it was possible to perform kinematical analysis of 10 out of 18 events. The masses and relative velocities of the reaction products, determined in this analysis were compared with theoretical prediction based on double sequential fission process. An agreement within one standard deviation with respect to theoretical values has been found for eight analysed events.     

Biological Potentials and Phytochemical Constituents of Raw and Roasted Nigella arvensis and Nigella sativa

Nigella species are widely used to cure various ailments. Their health benefits, particularly from the seed oils, could be attributed to the presence of a variety of bioactive components. Roasting is a critical process that has historically been used to facilitate oil extraction and enhance flavor; it may also alter the chemical composition and biological properties of the Nigella seed. The aim of this study was to investigate the effect of the roasting process on the composition of the bioactive components and the biological activities of Nigella arvensis and Nigella sativa seed extracts. Our preliminary study showed that seeds roasted at 50 °C exhibited potent antimicrobial activities; therefore, this temperature was selected for roasting Nigella seeds. For extraction, raw and roasted seed samples were macerated in methanol. The antimicrobial activities against Streptococcus agalactiae, Streptococcus epidermidis, Streptococcus pyogenes, Candida albicans, Escherichia coli, Enterobacter aerogenes, Klebsiella pneumoniae, and Klebsiella oxytoca were determined by measuring the diameter of the zone of inhibition. The cell viability of extracts was tested in a colon carcinoma cell line, HCT-116, by using a microculture tetrazolium technique (MTT) assay. Amino acids were extracted and quantified using an automatic amino acid analyzer. Then, gas chromatography–mass spectrometry (GC–MS) analysis was performed to identify the chemical constituents and fatty acids. As a result, the extracts of raw and roasted seeds in both Nigella species showed strong inhibition against Klebsiella oxytoca, and the raw seed extract of N. arvensis demonstrated moderate inhibition against S. pyogenes. The findings of the MTT assay indicated that all the extracts significantly decreased cancer cell viability. Moreover, N. sativa species possessed higher contents of the measured amino acids, except tyrosine, cystine, and methionine. The GC–MS analysis of extracts showed the presence of 22 and 13 compounds in raw and roasted N. arvensis, respectively, and 9 and 11 compounds in raw and roasted N. sativa, respectively. However, heat treatment decreased the detectable components to 13 compounds in roasted N. arvensis and increased them in roasted N. sativa. These findings indicate that N. arvensis and N. sativa could be potential sources of anticancer and antimicrobials, where the bioactive compounds play a pivotal role as functional components.     

Comparative Analysis of Microbial Consortiums and Nanoparticles for Rehabilitating Petroleum Waste Contaminated Soils

Nano-bioremediation application is an ecologically and environmentally friendly technique to overcome the catastrophic situation in soil because of petroleum waste contamination. We evaluated the efficiency of oil-degrading bacterial consortium and silver nanoparticles (AgNPs) with or without fertilizer to remediate soils collected from petroleum waste contaminated oil fields. Physicochemical characteristics of control soil and petroleum contaminated soils were assessed. Four oil-degrading strains, namely Bacillus pumilus ({"type":"entrez-nucleotide","attrs":{"text":"KY010576","term_id":"1248281175"}}KY010576), Exiguobacteriaum aurantiacum ({"type":"entrez-nucleotide","attrs":{"text":"KY010578","term_id":"1248281177"}}KY010578), Lysinibacillus fusiformis ({"type":"entrez-nucleotide","attrs":{"text":"KY010586","term_id":"1248281185"}}KY010586), and Pseudomonas putida ({"type":"entrez-nucleotide","attrs":{"text":"KX580766","term_id":"1159332275"}}KX580766), were selected based on their in vitrohydrocarbon-degrading efficiency. In a lab experiment, contaminated soils were treated alone and with combined amendments of the bacterial consortium, AgNPs, and fertilizers (ammonium nitrate and diammonium phosphate). We detected the degradation rate of total petroleum hydrocarbons (TPHs) of the soil samples with GC-FID at different intervals of the incubation period (0, 5, 20, 60, 240 days). The bacterial population (CFU/g) was also monitored during the entire period of incubation. The results showed that 70% more TPH was degraded with a consortium with their sole application in 20 days of incubation. There was a positive correlation between TPH degradation and the 100-fold increase in bacterial population in contaminated soils. This study revealed that bacterial consortiums alone showed the maximum increase in the degradation of TPHs at 20 days. The application of nanoparticles and fertilizer has non-significant effects on the consortium degradation potential. Moreover, fertilizer alone or in combination with AgNPs and consortium slows the rate of degradation of TPHs over a short period. Still, it subsequently accelerates the rate of degradation of TPHs, and a negligible amount remains at the end of the incubation period.     

A note on: Quasi-linear quotients and shellability of pure simplicial complexes

The purpose of this note is to point out a careless error in the algebraic criterion of shellability of a pure simplicial complex Δ given in [1 Anwar, I., Raza, Z. (2015). Quasi-linear quotients and shellability of pure simplicial complexes. Commun. Algebra 43:4698–4704.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].