Vol. 11, No. 2 (2022): Regular Issue

We apply the method of domain structured chaos for a dynamics with orbits whirling among infinitely many modules. Thus, the conservative conditions of chaos existence are weakened to model irregular dynamics. The research proves that the Poincar\'{e} chaos is of exceptional use for analysis of stochastic processes. Examples, illustrating the results are provided.

The variance theorem from the field of statistical analysis is used to evaluate the experimental data set of a classical heat diffusion experiment measuring temperatures as a function of time on a thermocouples prepared aluminium bar. The experimental data set during heating of the bar shows a nonlinear behavior. Known mathematical concepts to describe anomalous diffusion are shortly quoted and subsequent a novel approach of evaluating the data is presented. On the basis of the fundamental solution of the homogenous diffusion equation using finite boundaries defined by the discrete positions of the thermocouples, three different linearly independent momenta: expectation value, variance, and asymmetry are determined. For each momentum the parameter: thermal diffusivity $a$ of the solution equation is calculated. The three values are in the same range and coincide well to the known technical diffusivity of aluminium.

The interest behind this article is to examine the electrohydrodynamic number, and heat transfer impacts on two dimensional, laminar, incompressible nanofluid boundary layer flow over a wedge. The well-known nanoparticle volume fraction model was applied to approximate the viscosity, thermal diffusivity, heat capacitance, and thermal conductivity of the nanofluid. The nanoparticles itemized here are Nickel, $Ni$, and Nickel Zinc Ferrite $Ni(Zn)O.Fe_2O_3$ with base liquid as water (Liquid $H_2O$). The governing system of equations is reduced in the system of nonlinear differential equations and solved numerically using MATLAB. The impact of the electrohydrodynamic parameter $k_1$, nanoparticle volume fraction $\phi$, electric field functions $g_1$ on the velocity profile, the influence of the Prandtl number $Pr$, joule heating energy parameter $s_2$, and ion kinetic work parameter $s_3$ on temperature profile has examined. Further surface drag forces and the rate of heat transfer are inspected. A comparison is made with the available outcomes in the literature and present outcomes is a satisfactory concurrence with the findings in the literature for particular values. The velocity profile increases with an increase in electrohydrodynamic number, and also increases more in the case of Nickel than Nickel Zinc Ferrite. A decreasing trend in the velocity profile is observed for increasing values of electric field functions in both types of nanofluids. The temperature rises more in Nickel Zinc Ferrite than Nickel for an increase in the ion kinetic parameter. The cumulative effect of nanoparticle volume fraction and electric field function leads to decreases the heat transfer rate.

The concept of interval metric is defined in 2010. In the general interval metric, the domain is any set of points and range is one -dimensional interval space $ IR $. The tool used here to prove its metric properties is the Moore interval module. In this paper, we extend the concept of interval metric to the function space $ C[a,b] $. We are giving a detailed extension of the concept of metric from a single value to an interval by taking all the possible values from the minimum-maximum interval, and the range of all such possible values is considered as the diameter distance. We also prove the completeness property and Banach fixed point theorem for the new metric in $ C[a,b] $.

A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which there are no rainbow triangles. For two given graphs $H, G$ and two positive integers $k,s$ with $s\leq k$, the $k$-colored Gallai-Ramsey number $gr_{k}(K_{3}: s\cdot H,~ (k-s)\cdot G)$ is the minimum integer $n$ such that every Gallai $k$-colored $K_{n}$ contains a monochromatic copy of $H$ colored by one of the first $s$ colors or a monochromatic copy of $G$ colored by one of the remaining $k-s$ colors. In this paper, we determine the value of Gallai-Ramsey number in the case that $H=K_{4}^{+}$ and $G=K_{3}$. Thus the Gallai-Ramsey number $gr_{k}(K_{3}: K_{4}^{+})$ is obtained.

We obtain local and global rate of approximation by two new variants, $D_n^{M,1}(f,x)$ and $D_n^{M,2}(f,x)$ of Bernstein Durrmeyer operators, recently introduced by Acu et al. By utilizing a suitable Ditzian-Totik modulus of smoothness, we prove that the approximation process $D_n^{M,2}(f,x)$ is quadratic convergent. An error estimate for the functions of bounded variation by the B\'{e}zier variant of the operators $D_n^{M,1}(f,x)$ is obtained.

A new class of nonlinear viscoelastic wave equation is studied. Under appropriate conditions imposed on h, the global existence of solutions with any initial data is proved when $m\geq p$, and a finite time blow-up with negative initial energy is obtained when $p>m$.

An analysis is executed to study the MHD flow of Jeffrey nanofluid over a nonlinear radial stretching sheet with the influence of thermal radiation and heat generation/absorption. Two more realistic conditions namely convective conditions and zero nanoparticles mass flux condition are applied on the boundary. By applying suitable similarity transformations, the constitutive equation along with energy and concentration equations changed to set of ordinary differential equations. The ODE's(ordinary differential equation) are solved numerically by bvpc4 method. The outcomes are then displayed for numerous values of the physical parameter and discussed. It is obvious that heat transfer rate is noticeably higher for augment Deboray number and friction factor declines with higher values of inertia Coefficient. To validate our obtained outcomes, a comparison in a limiting case is also given and found in excellent agreement.

This is paper reports an investigation of oxytacic-bioconvective flow in a porous square cavity under the influence of viscous dissipation. Darcy model of Boussinesq approximation is employed to formulate the bioconvective flow in the porous medium. The governing nonlinear partial differential equations are nondimensionalised using suitable dimensionless parameters then solved by Galerkin finite element method. The computational numerical results are described by the surface plots of stream function, temperature, concentrations of oxygen and microorganisms, average Nusselt number, average Sherwood numbers of concentrations of oxygen and microorganisms. The effects of key parameters such as Peclet number (Pe), Rayleigh number of bioconvection (Rb), Eckert number (Ec), Lewis number (Le) and Rayleigh number (Ra) are presented and inspected. Eckert number (Ec) and Peclet number (Pe) improve the bioconvection flow and rate of heat transfer. It is also observed that the isoconcentration patterns of oxygen and microorganism density are controlled by Ec and Pe.

Anisotropic Bianchi type-III metric is studied with cloud strings and electromagnetic field in General Relativity. To get determinate solutions of field equations we have taken the help of (i) shear scalar proportional to scalar expansion proposed by Collins [1] and (ii) Hybrid expansion law proposed by Akarsu et al. [2]. We have obtained all the cosmological parameters corresponding to the model, also we have provided a physical discussion of our model using a graphical representation of these parameters. The physical and kinematical properties found in this model exhibit an accelerating expansion of the universe, which are compatible with current cosmological observations.

In this paper we introduce a Gaussian-like function, as a solution of a Conformable Differential Equation (CDE) of order $0<\alpha\le 1$, able to describe the nearest-neighbor energy-level spacing distribution of quantum systems; where $\alpha$ can be identified as the level-repulsion parameter. In addition, we study some properties of conformable operators and the stability of the solutions of the CDE.

Several degree based topologcal indices are usually used to characterize chemical compounds. Such as Randi\'{c} index, the sum-connectivity index, the harmonic index, $ABC$ index, and the geometric-arithmetic index etc. In the paper, we compute the values about the topological indices of subdivision graph.

In this paper, we prove the existence and uniqueness of solutions for a class of nonlinear fractional Volterra-Fredholm integro differential equations with nonlocal conditions. In addition, the Ulam-Hyers and Ulam-Hyers-Rassias stability for solutions of the given problem are also discussed. The desired results are proved by using Pachpatte's integral inequality, aid of fixed point theorems due to Banach and Schaefer's fixed point theorems.

The outbreak of novel coronavirus disease, namely COVID-19, has become an international public health problem in a very short period. To control the dispersal of the disease from its source, mostly all countries have restricted transportation activities as well as lockdown is implemented. This study intended to explore the effects of travel restrictions due to the outbreak of COVID-19 on air pollution. In the present work, a mathematical model has been created using two compartments lockdown and pollution. Equilibrium point and its boundedness is shown with detailed computations. The main output is computed through basic reproduction number called threshold value. With sufficient conditions, local and global stability of equilibrium points convey attention to dynamical behaviour of model. Backward bifurcation has been conducted with reference of basic reproduction number. The main objective of paper is to reduce pollution by applying optimal control strategy on lockdown. Numerical simulation and sensitivity analysis lead more light on obtained analytically results.

The present article mainly focuses on effect of thermal radiation on magneto hydrodynamic squeezing flow of Casson fluid between two equidistant plates. Non-linear partial differential equations of motion which are governing the flow are made non-dimensional by imposing similarity transformations. Runge-Kutta-Fehlberg scheme used here to solve these non-linear equations, by converting them into a set of initial value problem with single order. The velocity and temperature profile analysis has been carried out by taking into consideration of different parameters involved in it such as, squeeze number, magnetic number, Eckert number, radiation parameter, Prandtl number and Casson fluid parameter etc., and discussed them graphically in suitable manner such that interesting aspects of the solution can be adopted. And also, numerical results of nusselt number and skin friction co-efficient have been shown in this presentation. Velocity profile increases for increasing magnetic parameter near upper plate but it decreases near lower plate. Further same behavior observed for increasing squeeze number. Temperature profile increases with increasing magnetic parameter, radiation parameter and Casson fluid parameter but decreases with Eckert number.