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.     

An eco-safe approach to benzopyranopyrimidines and 4H-chromenes in ionic liquid at room temperature

An environmentally benign, ionic liquid promoted multicomponent protocol to benzopyrano(2,3-d)pyrimidines and 4H-chromenes has been developed at room temperature. Results of the reaction depend on the nature of the nucleophile used in the reaction. Secondary amines result in the formation of benzopyrano(2,3-d)pyrimidines, whereas thiols give rise to 4H-chromenes under the same set of reaction conditions.     

A mathematical model to characterise effects of liquid hold-up on bosh silicon transport in the dripping zone of a blast furnace

A first principle based mathematical model has been developed to characterise the effect of total liquid hold-up on the bosh silicon distribution behaviour in the dripping zone of a blast furnace. Two specific cases of hold-up behaviour have been investigated, namely, hold-up in the absence and in the presence of counter current gas flow conditions. The model exemplifies coupled phenomenon of chemical kinetics, transport processes and liquid hold-up to characterise the silicon behaviour in the dripping zone. The present modelling investigation shows that the bosh silicon level diminishes with the enhanced liquid hold-up in the dripping zone. Further, the influence of counter current gas flow on the hold-up is not significant. However, it has been observed that the liquid phase temperature reduces with increased liquid hold-up in dripping zone under steady state operating conditions. The model predictions of bosh silicon distribution have been validated with the published literatures (bulk values) and found to be in good agreement.     

Rhodium(I) carbonyl complexes of ether‐phosphine ligands and their reactivity

The reactions of dimeric complex [Rh(CO)₂Cl]₂ with hemilabile ether‐phosphine ligands Ph₂P(CH₂) _nOR [n = 1, R = CH₃ (a); n = 2, R = C₂H₅ (b)] yield cis‐[Rh(CO)₂Cl(P ～ O)] (1) [P ～ O = η ¹‐(P) coordinated]. Halide abstraction reactions of 1 with AgClO₄ produce cis‐[Rh(CO)₂(P ∩ O)]ClO₄ (2) [P ∩ O = η ²‐(P,O)chelated]. Oxidative addition reactions of 1 with CH₃I and I₂ give rhodium(III) complexes [Rh(CO)(COCH₃)ClI(P ∩ O)] (3) and [Rh(CO)ClI₂(P ∩ O)] (4) respectively. The complexes have been characterized by elemental analyses, IR, ¹H, ¹³C and ³¹P NMR spectroscopy. The catalytic activity of 1 for carbonylation of methanol is higher than that of the well‐known [Rh(CO)₂I₂]^? species. Copyright © 2002 John Wiley & Sons, Ltd.     

Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer.Untersucht wurden kombinierte Effekte der Permeabilität des Mediums, des magnetischen Feldes, der Auftriebskräfte und der Dissipation auf die instationäre Mischkonvektions-Strömung über einen horizontalen Zylinder und eine Kugel, die in einem porösen Medium eingebettet sind. Die nichtlinearen gekoppelten partiellen Differentialgleichungen mit drei unabhängigen Variablen wurden numerisch unter Benutzung eines impliziten Finite-Differenzen-Verfahrens in Verbindung mit der Quasi-Linearisierungstechnik gelöst. Die Oberflächenreibung und die Wärme- und Stoffübertragung steigen mit der Permeabilität des Mediums, dem magnetischen Feld und dem Auftriebsparameter an. Die Wärme- und Stoffübertragung fällt stetig in Strömungsrichtung ab, wohingegen die Oberflächenreibung von Null ansteigt, ein Maximum erreicht und wieder auf Null abfällt. Die Oberflächenreibung und die Wärme- und Stoffübertragung werden signifikant von der Verteilung der Freistromgeschwindigkeit beeinflut. Es wurde festgestellt, das der Dissipations-Parameter stärker die Wärmeübertragung als die Oberflächenreibung und die Stoffübertragung beeinflut.     

Understanding guest and pressure‐induced porosity through structural transition in flexible interpenetrated MOF by Raman spectroscopy

Interpenetrating metal organic frameworks are interesting functional materials exhibiting exceptional framework properties. Uptake or exclusion of guest molecules can induce sliding in the framework making it porous or non‐porous. To understand this dynamic nature and how framework interaction changes during sliding, metal organic framework (MOF) 508 {Zn(BDC)( 4,4′‐Bipy)_0.5 · DMF(H₂O)_0.5} was selected for study. We have investigated structural transformation in MOF‐508 under variable conditions of temperature, pressure and gas loading using Raman spectroscopy and substantiated it with IR studies and density functional theory (DFT) calculations. Conformational changes in the organic linkers leading to the sliding of the framework result in changes in Raman spectra. These changes in the organic linkers are measured as a function of high pressure and low temperature, suggesting that the dynamism in MOF‐508 framework is driven by ligand conformation change and inter‐linker interactions. The presence of Raman signatures of adsorbed CO₂ and its librational mode at 149 cm⁻¹ suggests cooperative adsorption of CO₂ in the MOF‐508 framework, which is also confirmed from DFT calculations that give a binding energy of 34 kJ/mol. Copyright © 2015 John Wiley & Sons, Ltd.     

One pot three component synthesis of spiro [indolo-3,10’-indeno[1,2-b]quinolin]-2,4,11’-triones as a new class of antifungal and antimicrobial agents

A simple and efficient three component procedure has been developed for the synthesis of highly substituted spiro[indolo-3,10'-indeno[1,2-b]quinolin]-2,4,11'-triones by one pot three component condensation of enaminones, isatin and indane-1,3-dione in ethanol:water (1:1) in presence of ceric ammonium nitrate (CAN) as catalyst. This method provides several advantages such as lesser reaction time, high yield of products and operational simplicity. The antimicrobial activity of some of the compounds has been investigated against six microbial strains, some of the tested compounds showed good antimicrobial activity.     

Integrated quality by design (QbD) and design of experiments (DoE) approach for UFLC determination of telaprevir in rat serum

An ultrafast liquid chromatographic bioanalytical method was developed and validated for the determination of telaprevir in Wistar albino rat serum. Principles of quality by design (QbD) were implemented for enhancing the bioanalytical liquid–liquid extraction of telaprevir from rat serum. A Box–Behnken design was utilized in the studies by selecting extraction time, centrifugation speed, and vortex time as the critical method variables for evaluating their effect on the critical analytical attribute, i.e., %recovery of telaprevir. Chromatographic separation was achieved within a run time of 10?min using a C-18 column and mobile phase comprising of methanol:borate buffer of pH 9 (90:10 v/v) flowing at 1.2?mL/min. Photodiode array detection was performed at 270?nm. Results of validation studies were satisfactory. The method was linear over a concentration of 25–10,000?ng/mL. Limit of detection for the developed method was 10?ng/mL. Further, design of experiments (DoE) used for inter-day accuracy and precision study suggested superior method reliability. This integrated QbD- and DoE-based approach ensured the development of a validated and reliable analytical method for optimum bioanalysis of telaprevir in biological matrix.     

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.     

Solid-supported palladium nano and microparticles: an efficient heterogeneous catalyst for ligand-free Suzuki-Miyaura cross coupling reaction

Solid-supported nano and microparticles of Pd(0) (SS-Pd) were prepared and used as heterogeneous catalysts for Suzuki-Miyaura cross coupling reactions of aryl halides (chloro, bromo and iodo) and phenyl boronic acid under mild and ligand-free conditions. Scanning electron microscope (SEM) and UV-vis based studies were performed to observe the distribution of nano and microparticles of palladium over solid surface and their oxidation states. In addition, the catalyst could be reused up to seven runs without significant loss of activity and stable enough under moist conditions.