Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces

In this paper, we introduce the new iterative sequences with errors approximating the common fixed point for a couple of quasi-contractive mappings and show the stability of the iterative procedures with errors in q-uniformly smooth Banach spaces. Our results extend, improve and unify the corresponding results of Chidume, Osilike, Liu, and others.     

Model of a microwave beam coupling to CO2 laser plasma

We have designed a transmission line model of the microwave coupling mechanism for a microwave pumped CO₂ laser. The model is a total loss ridge waveguide transmission line having nonuniform impedance. The laser plasma is modeled as a frequency-dependent lossy dielectric and acts as a distributed resistance in the length of the microwave cavity. The coupling structure of the microwaves is designed not to be resonant at the microwave source frequency of 2.45 GHz at 1 kW and propagating the total microwave field energy to be absorbed without internal reflection. An exact solution to this general transmission line propagation constant for a shunt resistance along length of the guide is found. The measurements and predictions of the parameters of the plasma conductivity as a function of the attenuation constant agree closely.     

Ferrate(VI) and ferrate(V) oxidation of cyanide,thiocyanate, and copper(I) cyanide

Cyanide (CN⁻), thiocyanate (SCN⁻), and copper(I) cyanide (Cu(CN)₄³⁻) are common constituents in the wastes of many industrial processes such as metal finishing and gold mining, and their treatment is required before the safe discharge of effluent. The oxidation of CN⁻, SCN⁻, and Cu(CN)₄³⁻ by ferrate(VI) (Fe^VIO₄²⁻; Fe(VI)) and ferrate(V) (Fe^VO₄³⁻; Fe(V)) has been studied using stopped-flow and premix pulse radiolysis techniques. The rate laws for the oxidation of cyanides were found to be first-order with respect to each reactant. The second-order rate constants decreased with increasing pH because the deprotonated species, FeO₄²⁻, is less reactive than the protonated Fe(VI) species, HFeO₄⁻. Cyanides react 10³–10⁵ times faster with Fe(V) than with Fe(VI). The Fe(V) reaction with CN⁻ proceeds by sequential one-electron reductions from Fe(V) to Fe(IV) to Fe(III). However, a two-electron transfer process from Fe(V) to Fe(III) occurs in the reaction of Fe(V) with SCN⁻ and Cu(CN)₄³⁻. The toxic CN⁻ species of cyanide wastes is converted into relatively non-toxic cyanate (NCO⁻). Results indicate that Fe(VI) is highly efficient in removing cyanides from electroplating rinse water and gold mill effluent.     

Effect of low intensity laser interaction with human skin fibroblast cells using fiber-optic nano-probes

Over the past forty years, many efforts have been devoted to study low power laser light interactions with biological systems. Some of the investigations were performed in-vitro, on bulk cell populations. Our present work was undertaken to apply specially engineered fiber-optic based nano-probes for the precise delivery of laser light on to a single cell and to observe production of low power laser light induced reactive oxygen species (ROS). A normal human skin fibroblast (NHF) cell line was utilized in this investigation and the cells were irradiated under two different schemes of exposure: (1) an entire NHF cell population within a Petri dish using a fan beam methodology, and (2) through the precise delivery of laser energy on to a single NHF cell using fiber-optic nano-probe. Photobiostimulative studies were conducted through variation of laser intensity, exposure time, and the energy dose of exposure. Laser irradiation induced enhancement in the rate of cell proliferation was observed to be dependent on laser exposure parameters and the method of laser delivery. The total energy dose (fluence) had a greater influence on the enhancement in the rate of cellular proliferation than compared to laser intensity. The enhancement in the growth rate was observed to have a finite life-time of several days after the initial laser exposure. Fluorescent life-time imaging of ROS was performed during the nano-based single cell exposure method. The kinetics of ROS generation was found to depend strongly on the laser fluence and not on the laser intensity.     

Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

This paper studies the existence of solutions to the singular boundary value problem

Optimal conditions of solvability of nonlocal problems for second-order ordinary differential equations

For the differential equation

u^″=f(t,u)     

Deoxygenative reduction of carbon dioxide to methane, toluene, and diphenylmethane with [Et2Al]+ as catalyst

The strong Lewis acid [Et(2)Al](+) catalyzes the reduction of carbon dioxide with hydrosilanes under mild conditions to methane. In benzene solution, the side products toluene and diphenylmethane are also obtained through Lewis acid catalyzed benzene alkylation by reaction intermediates.     

Common fixed point theorems and minimax inequalities in locally convex Hausdorff topological vector spaces

In this article, we introduce the concept of a family of set-valued mappings generalized Knaster–Kuratowski–Mazurkiewicz (KKM) w.r.t. other family of set-valued mappings. We then prove that if X is a nonempty compact convex subset of a locally convex Hausdorff topological vector space and 𝒯 and 𝒮 are two families of self set-valued mappings of X such that 𝒮 is generalized KKM w.r.t. 𝒯, under some natural conditions, the set-valued mappings S ∈ 𝒮 have a fixed point. Other common fixed point theorems and minimax inequalities of Ky Fan type are obtained as applications.