In this article, we consider the conformal change of the Matsumoto-Randers transformation of the m(th)-root metric. We establish the conditions for projective flatness and projective dual flatness under homothetic change, and we also derive the explicit form of the projective factor for the considered metric. Moreover, some useful applications of the flatness properties of this metric are discussed.
In the present study, we have examined the effect of velocity and thermal slip-on Williamson hybrid ferrofluid, which incorporates copper and magnetite nanoparticles flowing over a shrinking sheet under combined convective conditions. The governing partial differential equations are made convenient for solution by applying suitable similarity transformations. A numerical solution is obtained by using MATLAB bvp4c software. The investigation focuses on analyzing the impact of the Williamson parameter, the combined convective parameter and the suction parameter on velocity and temperature profiles. It is observed that with increasing Williamson parameter, temperature rises and velocity decreases. Conversely, velocity increases and temperature decrease with an increase in the combined convective parameter. Additionally, the behavior of the Nusselt and skin friction coefficients under slip conditions is presented graphically. It can be concluded from the study that the velocity slip parameter increases the velocity, while the thermal slip parameter reduces the temperature. This indicates that the interplay between velocity and thermal slip parameters significantly influences the fluid dynamics and thermal characteristics of the system. Overall, understanding of these effects is crucial for optimizing performance in applications involving fluid flow and heat transfer in micro as well as macro scale level situations.
In this paper, we extend the concept of the Elzaki transform to define the Katugampola Elzaki transform, which is based on the Katugampola fractional derivative. We establish a relationship between the Katugampola Elzaki transform and the usual Elzaki transform, and we derive the Katugampola Elzaki transforms for both derivatives and integrals. We present several results for selected functions under the Katugampola Elzaki transform. Furthermore, we establish fundamental properties of the proposed transform, including linearity, change of scale, shifting, and convolution theorem.
In this article, a novel probability distribution called the Alpha Power Logarithmic Transformed Exponential (APLTE) distribution is introduced. This new model generalizes the logarithmic transformed exponential distribution by incorporating an additional shape parameter through the alpha power transformation method. Various distributional properties of the proposed model are explored, such as reliability characteristics, moment generating function, quantile, order statistics and entropy. Estimation of parameters of proposed distribution has been approached by maximum likelihood estimation and maximum product spacing estimation methods. Asymptotic confidence interval of the parameters in terms of average length of confidence limit is also obtained for both the methods. A simulation study is conducted to examine the performance of these estimators. To demonstrate the applicability of the suggested model, two real data sets have been taken into consideration, and the results have been compared with selected competing distributions.
The purpose of the present article is to obtain some sufficient conditions for hypergeometric functions belonging to certain classes of univalent functions. We also obtain some inclusion relations between some classes of univalent functions. Finally, we discuss an integral operator associated with hypergeometric functions.
The object of the present paper is to study the generalized Tanaka-Webster connection in Lorentzian para-Sasakian manifold. We begin by reviewing key preliminaries and fundamental results necessary for our development. The curvature tensors and Ricci tensor with respect to the generalized Tanaka-Webster connection are then examined in detail. We investigate conditions under which the manifold satisfies certain curvature constraints, including R.S = 0, R.R = 0, R.C = 0, and R.P = 0. Several geometric properties and implications of these conditions are derived and discussed.
In this article, we introduce the fractional bicomplex calculus in the Caputo sense, based on the alteration of the Cauchy-Riemann operator using the one-dimensional Caputo derivative in each direction of the bicomplex basis. We derive the fractional Leibniz's rule over the bicomplex numbers in the Caputo sense. Also, we discuss properties of some elementary functions viz. analytic polynomials, exponential function, and trigonometric function. Further, we define the fractional bicomplex Laplace operator and the fractional harmonic bicomplex functions connected with the fractional Cauchy-Riemann operator.
The object of the present paper is to characterize *-Conformal eta-Ricci solitonon a three-dimensional trans-Sasakian manifold. First, the natureof *-Conformal eta -Ricci soliton on three-dimensional trans-Sasakian manifoldhas been studied. Then, some results on 3-dimensional trans-Sasakianmanifold acknowledging *-Conformal eta -Riccisoliton where the Ricci tensor iscyclic parallel and of Codazzi type are found. Some certain curvature conditionson 3-dimensional trans-Sasakian manifold acknowledging *-Conformal eta -Ricci soliton has also been considered here. Finally, an example has beenconstructed to verify the results obtained.
Bianchi type-VI0 inflationary cosmological models for barotropic fluid distribution with flat potential in general relativity are investigated. To get the deterministic solution of these models, we assume that expansion theta is proportional to shear sigma which leads to A = B-n where n is constant and also assumed barotropic fluid condition i.e. p = y rho, 0 <= y <= 1 where p is pressure, and rho is the matter density. The behaviour of these models from physical and geometrical aspects is discussed in detail.
Detailed nano-structural characterization of nanomaterials is an important issue since it enables precise understanding of the chemical, optical, electronic, magnetic and other physical properties for their possible utilization/integration into modern multifunctional devices and technology. Accurate determination of the crystallographical parameters, crystallite shape & size, micro strain, dislocation density of nanoparticles is the first step of characterization of nanomaterials. In this article, we have refined the X-ray diffraction (XRD) data of ultrafine ZrO2 nanoparticles (NPs) using least square technique based PowderX and Rietveld profile analysis for the precise extraction of the crystallographic parameters. PowderX analysis suggested both cubic and tetragonal crystal structure of ZrO(2 )NPs due to too much similarity in the two phases. Notably, best fitted Rietveld refinement affirmed tetragonal structure (Space group P 42/nmc (No. 137), Z=2) of ultrafine ZrO(2 )NPs. Size and strain parameters of ultrafine ZrO(2 )NPs were precisely estimated using eight different models and well compared with the HRTEM micrograph analysis. The analysis yielded 6 (+/- 2) nm size and lattice strain of 3.14 x 10(-3) the ultrafine ZrO(2 )NPs. It is concluded that Rietveld, WHF analysis and lognormal size distribution of ultrafine NPs are most appropriate techniques for estimating the crystal structure and size-strain parameters ZrO(2 )NPs.
In this paper E-Bayesian and Hierarchical Bayesian estimation methods are used to estimate the scale parameter of Power Hazard Distribution under 4 different loss functions-Squared Error Loss Function (SELF), Entropy Loss Function, Weighted Balance Loss function (WBLF), Minimum Expected Loss Function (MELF). The definition and properties of E-Bayesian and Hierarchical Bayesian estimation are provided. Relations among E-Bayesian estimators along with relations between E-Bayesian and Hierarchical Bayesian estimators are derived. A simulation study is carried out to compare these estimators using Mean Square Error (MSE) with the help of tool of R language on simulated data. To demonstrate the applicability of derived estimators, a real dataset is analyzed.
When conducting a sample survey, it is important to have a complete list of all units to be sampled, known as a sampling frame. However, sometimes this list may be incomplete, making it challenging to estimate the population's characteristics. This paper presents a new weighted PPS Ratio estimator for the population mean, which works for both complete and incomplete frame using Probability Proportional to Size with replacement (PPSWR) method. The paper calculates the bias and mean square error (MSE) of the estimator and discusses how to determine the best sample size and retainment factor with a cost-effective method. Using simulated data, the paper shows that this new estimator is more accurate and efficient as compared to the existing ones.
In this work, we utilize the C-Class function to derive several fixed point results within the framework of parametric metric spaces. Our findings extend and refine the contributions of Heera Ahirwar and Kavita Shrivastava [1], particularly under new rational contractive conditions. To emphasize the significance of our results, we provide examples for better illustration. This development enriches the understanding of fixed point theory and paves the way for its application in more intricate and varied mathematical contexts. As a result, our research propels the field forward, offering a strong basis for future studies and broad applications in mathematical science and engineering.
In this paper, we study a spatially homogeneous and anisotropic Bianchi type-V dark energy cosmological model in modified scale covariant theory of gravitation. Exact solution of generated Einstein's field equations are obtained by assuming (i) a special form of average scale factor of the model corresponding to the constant negative value of deceleration parameter and (ii) the interaction term between dark energy and other different part of matter in the universe. The physical and dynamical behaviours of the model are discussed. The model describes the accelerated phase of expanding universe.
In this paper we have investigated a spatially homogeneous locally rotationally symmetric (LRS) Bianchi type-I space-time in the presence of perfect fluid source in scale-covariant theory of gravitation formulated by Canuto et al. [7]. The field equations are solved by considering bilinear form of the DP (Deceleration Parameter) q as a function of cosmic time t as: (i) q = m(1-t)/1+t, m >= 0, which renders early decelerating and late time accelerating cosmological model and (ii) q = - mt/1+t, m >= 0, which renders accelerated expansion model of the universe. The physical and geometrical properties of the derived models are also discussed.
The Bianchi type VIh=_1 Universe with a variable cosmological parameter has been studied in the framework of f ( R, T) theory of gravity, where R is Ricci sclar and T is trace of the stress energy momentum tensor. The general solution of the models is derived by adopting the functional form f( R, T) = f1( R) + f2 ( T) along with polytropic equation of state and a power law approach. By considering these components, a comprehensive analysis of dynamical parameters of the Bianchi type VIh=_1 Universe has been performed.
The purpose of this paper is not only to construct a mathematical model for the steady-state dispersion of non-buoyant air pollutants emitted from a continuous point source but also to find the analytical solution to it and then to explain graphically the effect of various parameters on the concentration of air pollutants. The wind velocity and removal rate are both assumed to be variable and are assumed to follow the power law profile. The concentration profile of non-buoyant air pollutants is analyzed for different parametric values in relation to the downwind, crosswind, and vertical distances. The results are analyzed graphically and conclusions are drawn from the various graphs.
In the present paper, the effect of internal heat source on the onset of double-diffusive convection in a rotating nanofluid layer saturating a sparsely distributed porous medium has been investigated using Darcy-Brinkman model. A linear stability analysis has been carried out for the case of free boundaries. Expressions for thermal Darcy-Rayleigh numbers for stationary and oscillatory convection are determined numerically and valid approximations are also made in the complex equations for oscillatory convection to get useful results. The dual impact of the Darcy number on the fluid system for stationary convection is analyzed numerically and predicted graphically. It is also shown that the parameters such as Rotation, Dufour and Soret have stabilizing influence, whereas the nanoparticle concentration Rayleigh number has a destabilizing effect on the onset of stationary convection.
In this paper, we introduce a new generalised p-k multi-index Mittag Leffler function and derive the integral representation of "p-k multi-index Mittag Leffler function". We also establish its relation with other functions, obtain Laplace, k-Laplace and Mellin transforms of the function and explain its basic properties.
The current work deals with locally rotationally symmetric (LRS) Bianchi type II string cosmological models for bulk viscous fluid and barotropic equation of state with dark energy( Lambda). To achieve a deterministic solution, we have assumed that the coefficient of shear viscosity(sigma)is proportional to expansion(0) and xi 0= K(constant), as considered by Zimdahl [26], where is coefficient of bulk viscosity. Also (Lambda) is taken proportional to R (-3). Some geometrical and physical characteristics are also discussed for these models.
