Anisotropic cosmological models in f (R, T) theory of gravitation

A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of f(R,T) gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.     

The cohomology of orbit spaces of certain free circle group actions

Suppose that \(G =\mathbb{S}^1\) acts freely on a finitistic space X whose (mod p) cohomology ring is isomorphic to that of a lens space \(L^{2m-1}(p;q_1,\ldots,q_m)\) or \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). The mod p index of the action is defined to be the largest integer n such that α ⁿ ?≠?0, where \(\alpha \,\epsilon\, H^2(X/G;\mathbb{Z}_p)\) is the nonzero characteristic class of the \(\mathbb{S}^1\)-bundle \(\mathbb{S}^1\hookrightarrow X\rightarrow X/G\). We show that the mod p index of a free action of G on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\) is p???1, when it is defined. Using this, we obtain a Borsuk–Ulam type theorem for a free G-action on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). It is note worthy that the mod p index for free G-actions on the cohomology lens space is not defined.     

Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients

Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with time-dependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic, double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.     

Kinetics of the Oxidation of D‐Glucose and Cellobiose by Acidic Solution of N‐Bromoacetamide Using Transition Metal Complex Species, [RuCl3(H2O)2OH] −, as Catalyst

The kinetics of Ru(III)‐catalyzed and Hg(II)‐co‐catalyzed oxidation of D‐glucose (Glc) and cellobiose (Cel) by N‐bromoacetamide (NBA) in the presence of perchloric acid at 40 °C have been investigated. The reactions exhibit the first order kinetics with respect to NBA, but tend towards the zeroth order to higher NBA. The reactions are the first order with respect to Ru(III) and are fractional positive order with respect to [reducing sugar]. Positive effect of Cl^? and Hg(OAc)₂ on the rate of reaction is also evident in the oxidation of both reducing sugars. A negative effect of variation of H⁺ and acetamide was observed whereas the ionic strength (µ) of the medium had no influence on the oxidation rate. The rate of reaction decreased with the increase in dielectric constant and this enabled the computation of d_AB, the size of the activated complex. Various activation parameters have been evaluated and suitable explanation for the formation of the most reactive activated complex has been given. The main products of the oxidation are the corresponding arabinonic acid and formic acid. HOBr and [RuCl₃(H₂O)₂OH]^? were postulated as the reactive species of oxidant and catalyst respectively. A common mechanism, consistent with the kinetic data and supported by the observed effect of ionic strength, dielectric constant and multiple regression analysis, has been proposed. Formation of complex species such as [RuCl₃·S·(H₂O)OH]^? and RuCl₃·S·OHgBr·OH during the course of reaction was fully supported by kinetic and spectral evidences.     

THE CHARACTERIZATION OF EFFICIENCY AND SADDLE POINT CRITERIA FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM WITH VANISHING CONSTRAINTS

In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results.     

A study of nanosized zinc oxide and its nanofluid

The synthesis and characterization of nanosized zinc oxide and its nanofluid in a polyvinyl alcohol (PVA) matrix have been done in the present investigation. Crystalline zinc oxide nanoparticles are synthesized using single-step chemical method while the nanofluids are prepared by the dispersion of nanoparticles in PVA solution using an ultrasonicator. The prepared nanoparticles are characterized using X-ray diffraction, SEM?CEDX and UV?Cvisible spectrum. The particle size distribution measurement is carried out by acoustic particle sizer. The ultrasonic velocities are measured in the synthesized nanofluid under different physical conditions using an ultrasonic interferometer. It is found that the degree of crystallinity of nanoparticles depends on the evaporation rate during its synthesis and ultrasonic velocity has non-linear relation with temperature for the present nanofluid.     

Coupled Higgs field equation and Hamiltonian amplitude equation: Lie classical approach and (G′/G)-expansion method

In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G??/G)-expansion method, where G?=?G(??) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.     

Target dependence of clan model parameter in 84 Kr 36 – Emulsion interactions at 1 GeV per nucleon

This article focusses on the study of clan model parameters and their target dependence in light of void probability scaling for heavy (Ag and Br) and light (C, N and O) groups of targets present in nuclear emulsion detector using ⁸⁴Kr₃₆ at ～1 A GeV. The variation of scaled rapidity-gap (rap–gap) probability with single moment combination has been studied. We found that experimental points lie approximately on the negative binomial distribution (NBD) curve, indicating a scaling behaviour. The increase in average clan multiplicities ( \(\bar {N}\) ) for interactions with the pseudorapidity interval (Δη) was also observed. The values of \(\bar {N}\) for AgBr targets are larger than those for C/N/O target and also average number of particles per clan ( \(\bar {n}_{\mathrm {c}}\) ) increases with increase in pseudorapidity interval. We further observed that for a particular target, the average number of particles per clan ( \(\bar {n}_{\mathrm {c}}\) ) increases with an increase in the size of projectile nucleus.