Fixed and periodic point theory in certain spaces

This paper proves the existence of periodic and fixed points for contractive conditions in metric (symmetric) space.     

A facile single-step approach to achieve in situ expanded g-C3N4 for improved photodegradation performance

Improved graphitic carbon nitride (g-C₃N₄) was synthesized through a unique one-step cost-effective technique involving a dynamic gas bubbling phenomenon using ammonium chloride (NH₄Cl) as a bubbling agent. An extensive investigation was carried out to optimize the weight ratio of NH₄Cl and melamine during the thermal pyrolysis process. Here, we report an improved form of g-C₃N₄ namely “expanded g-C₃N₄” with increased interlayer distance and remarkable volume expansion. The surface area of this improved version has notably increased leading to higher photocatalytic efficiency as compared with its counterpart, an synthesized without adding NH₄Cl. Synthesized photocatalyst materials were further used to study the Rhodamine B photodegradation under visible light. It was observed that the expanded g-C₃N₄ showed a 2.4 times higher photodegradation rate than its counterpart and degraded 94% of the dye in just 30 min.     

Synthesis,Spectroscopic Studies,and Biological Activity of Organosilicon(iv) Complexes of Ligands Derived from 2-Aminobenzothiazole Derivatives and 2-Hydroxy-3-Methoxy Benzaldehyde

Abstract

The Schiff bases derived from the condensation of 2-aminobenzothiazole derivatives and 2-hydroxy-3-methoxybenzaldehyde and their silicon(IV) complexes with the general formula R₂Si(L)Cl (R = Et, Bu, Ph, L = 2-(2-hydroxy-3-methoxy) benzylideneaminobenzo-thiazole) have been synthesized. These complexes have been characterized by elemental analysis, molar conductance, and spectroscopic studies including IR and NMR (¹H, ¹³C, and ²⁹Si) spectroscopy. The analytical data suggest trigonal bipyramidal geometry around the silicon atom in the resulting complexes. The ligands and their organosilicon complexes have also been evaluated for in vitro antimicrobial activity against bacteria (Staphylococcus aureus, Bacillus subtilis, and Escherichia coli) and fungi (Aspergillus niger and Candida albicans). The complexes were found to be more potent as compared to the ligands.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Structural,optical and electrical properties of sulfur-incorporated amorphous carbon films

Amorphous carbon–sulfur (a-C:S) composite films were prepared by vapor phase pyrolysis technique. The structural changes in the a-C:S films were investigated by electron microscopy. A powder X-ray diffraction (XRD) study depicts the two-phase nature of a sulfur-incorporated a-C system. The optical bandgap energy shows a decreasing trend with an increase in the sulfur content and preparation temperature. This infers a sulfur incorporation and pyrolysis temperature induced reduction in structural disorder or increase in sp ² or π-sites. The presence of sulfur (S 2p) in the a-C:S sample is analyzed by the X-ray photoelectron spectroscopy (XPS). The sp ³/sp ² hybridization ratio is determined by using the XPS C 1s peak fitting, and the results confirm an increase in sp ² hybrids with sulfur addition to a-C. The electrical resistivity variation in the films depends on both the sulfur concentration and the pyrolysis temperature.     

Preparation of Chitosan Based Scaffolds Using Supercritical Carbon Dioxide

A novel chitosan-formaldehyde porous derivative (scaffolds) was prepared by reaction of 85% deacetylated chitosan with 37% aq. formaldehyde using supercritical carbon dioxide (sc. CO₂). Prior to reaction, the chitosan hydrogel was prepared in 1% aq. acetic acid (AcOH) and formaldehyde. The prepared hydrogel was subjected to solvent exchange. The identity of the Schiff base was confirmed by Fourier transform infrared spectroscopy (FTIR). The chitosan-derivative was evaluated by thermal analysis, scanning electron microscopy, and porosimetry analysis. Overall, the sc. CO₂ assisted chitosan derivative opens new perspectives as biomedical material.     

Unsteady flow with heat and mass transfer due to impingement of slot jet on an inclined plate

The unsteady laminar incompressible boundary layer flow due to a two-dimensional slot jet on a flat plate at an angle of attack has been studied. The unsteadiness in the flow field is due to the free stream velocity distribution or wall temperature (concentration) which varies with time. The governing partial differential equations in primitive variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The effect of the variation of the free stream velocity distribution with time is found to be more pronounced on the skin friction than on the heat or mass transfer. The Prandtl number and the variation of the wall temperature with time strongly affect the heat transfer. Similarly, the Schmidt number and the variation of the concentration at the wall with time strongly affect the mass transfer. Beyond a certain critical value of the viscous dissipation parameter, the plate gets heated instead of being cooled.     

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear coupled differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.     

Positive solutions and pattern formation in a diffusive tritrophic system with Crowley–Martin functional response

Nonlinear Dynamics - In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin...