Unique Solution of Integral Equations via Intuitionistic Extended Fuzzy b-Metric-Like Spaces

In this manuscript,our goal is to introduce the notion of intuitionistic extended fuzzy b-metric-like spaces.We establish some fixed point theorems in this setting.Also,we plot some graphs of an example of obtained result for better understanding.We use the concepts of continuous triangular norms and continuous triangular conorms in an intuitionistic fuzzy metric-like space.Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions.Triangular conorms are known as dual operations of triangular norms.The obtained results boost the approaches of existing ones in the literature and are supported by some examples and applications.

Spectrokinetics study of probable effects of diverse inorganic ions on bleaching of dye

Toluidine blue(TB)is an important anticoagulant metachromasia molecule showing a pronounced variation in the visible spectrum due to the aggregation phenomenon and electrostatic interaction with the charged synthetic and biologic polymers.The current study describes the interactive role of diverse inorganic material ions on the bleaching of toluidine blue(tolonium chloride)(TB^(+))with urea in acidic and basic media using the spectrophotometric technique.The spectra of TB and urea with different cations and anions were monitored and their characteristic features are presented here.The negative effect of added cations on reduction may be the result of altered electron pathways which led to suppression of the reduction/bleaching of TB,while a slight decrease in dye reduction by added anions may be due to the scavenging of the OH*radical.It has been observed in the case of Co^(2+)that in addition to the electron-transfer reaction,other processes like layer and precipitate formation also appear to be taking place.The dye bleaching process followed pseudo first order kinetics with respect to TB,urea,and H^(+)ion,whereas significant decoloration in the presence of urea proved that reductants control the redox reaction.No decoloration in acidic medium with diverse ions was seen compared to alkaline media,showing that water pH played an important role in the bleaching of dye.The reduction/bleaching of dye was investigated at different temperatures,and energy parameters were evaluated for a TB^(+)-Urea reaction,including the energy of activation(Ea=39.60 kJ·mol^(–1)),enthalpy of activation(ΔH#=34 kJ$mol^(–1)),entropy of activation(ΔS#=146.5 kJ mol^(–1)·K^(–1)),and free energy of activation(ΔG*=–52.35 kJ·mol^(–1)).A mechanism of interaction of diverse ions in dye bleaching and a mechanism of reduction based on the above findings is proposed.

Effects of CuCl_(2)·6H_(2)O and ZnCl_(2)·6H_(2)O on the viscosity of aqueous ethanol mixtures

The effects of CuCl_(2) and ZnCl_(2) on the viscosity in aqueous ethanol mixtures(10%–50%v/v)were studied in the concentration range 1.0×10^(–2)–8.0×10^(–2) mol·dm^(–3) at different temperatures.It was found that the viscosities increased with an increase in the concentration of the salts and percent composition of ethanol content,whereas it decreased with an increase in temperature.Ion-ion and ion-solvent interactions are determined with the help of A-and B-coefficients of Jones-Dole equation.The values of A-and B-coefficients are irregular and increase with a rise in temperature and also with an increase in ethanol contents for both salts.Negative values of B-coefficients show that ion solvent interactions is comparatively small and suggest that CuCl_(2) and ZnCl_(2) behave as structure breakers in aqueous ethanol mixtures.Thermodynamic parameters like the energy of activation(Eη)and change in entropy of activation(ΔS*)were also evaluated which confirm the structure breaker behavior of salts in aqueous ethanol mixtures.