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Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

This paper is related to the dynamics of stellar structure under the influence of modified gravity (in particular f (T) gravity, where T is associated with a torsion scalar). We contemplate non-static plane geometry equipped with fluid dissipation in the form of diffusion limit. The suitable variables to handle the analysis are explored. To comprehend the dynamics of the system, we acquire the dynamical equations with the aid of Bianchi identities. We calculate the Taub mass for our structure and develop the relations of mass in the form of collapsing velocity, derivative of proper radial, and time. The scalars to comprehend the evolution and structure are explored for non-static plane geometry. These scalars have a novel existence for this structure. We find that the homogeneous expansion and homologous ways of evolution interrelate with each other. We perform the investigation for two cases that is dissipative and non-dissipative. The nature of the fluid in the dissipative case is shear and geodesic. We calculate the variety of solutions in this case. The analysis is concluded by analyzing the stability of the vanishing Y TF constraint. [ABSTRACT FROM AUTHOR]

In this paper, we discuss various analytical solutions of the planner geometry with anisotropic fluid as well as vanishing complexity factor condition in the framework of f(픾) theory. The matching conditions are employed at the interior and exterior hypersurfaces. The connection between the matter parameters and the Weyl tensor has been constructed. For dissipative and non-dissipative structures, we examine four different conformal Killing vector possibilities, while some possibilities adhere to the 풴TF = 0 condition along with the matching conditions, where 풴TF indicates the trace free part of the electric component of the Riemann tensor. Several theoretical models are provided to show how a non-static system evolves. [ABSTRACT FROM AUTHOR]

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use f (T ,) modified gravity, which is characterized by the trace of an energy–momentum tensor as and torsion scalar T , Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics. [ABSTRACT FROM AUTHOR]

This work explores the effect of activation energy on bioconvection flow of oxytactic microorganisms with nano-encapsulated phase change materials in complex shaped enclosure. The inner wavy wall is partially fixed at the constant high temperature. The proposed problem has been modeled first using the conservation laws and then simulated by utilizing finite element method. The discretized system of nonlinear algebraic equation is computed using the Newtons method. The obtained results have been analyzed for the several important controlling parameters. It has been observed that the vortex centers have been established near the adiabatic walls for lower values of Lewis number. The average Sherwood number and density of motile microorganism are the increasing functions of chemical reaction parameter. Moreover, the average Nusselt number declines with rising values of Peclet number. [ABSTRACT FROM AUTHOR]

We investigate spherically symmetric classes of anisotropic solutions within the realm of a schematic gravitational decoupling scheme, primarily decoupling through minimal geometric deformation, applied to non-rotating, ultra-compact, self-gravitational fluid distributions. In this respect, we employ the minimal complexity factor scheme to generate physically realistic models for anisotropic matter distributions, using a well-behaved model. The zero-complexity factor condition enables us to determine the deformation function for solving the decoupled system. We explore all the structure-defining scalar variables, such as density inhomogeneity, strong energy condition, density homogeneity, and the complexity factor (an alloy of density inhomogeneity and pressure anisotropy) for the decoupling constant ranging between 0 and 1. We observe that the anisotropy vanishes when the coupling constant is set to unity. This finding holds significance as it implies that, in the context of a zero-complexity factor approach, an anisotropic matter distribution becomes perfect without requiring any isotropy requirements. This work effectively explored the impact of complexity on the composition of self-gravitational stellar distributions. This effective approach enables the development of new, physically realistic isotropic stellar models for anisotropic matter distributions. Additionally, our findings indicate that the complexity factor in static, spherically symmetric self-gravitational objects can significantly affect the nature of the matter distribution within these systems. It is concluded that the minimally deformed Durgapal-IV model features an increasing pressure profile, and the local anisotropy of pressure vanishes throughout the model under complexity-free conditions. [ABSTRACT FROM AUTHOR]

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes. [ABSTRACT FROM AUTHOR]

The focus of our work is the analysis of a specific celestial structure known as a gravastar in the background of f (G , T 2) gravity. To derive the field equations and conservation laws related to this modified theory, we examine the spherically static symmetric geometry consisting of isotropic pressure. The Schwarzschild solution represents the layer of the outside vacuum. The equation of state (EoS), which defines the equality for pressure of ultra-relativistic matter and energy density, portrays the central layer. However, the inner layer shows that the repulsive pressure is equivalent to the energy density and exhibits a repulsive constraint on the core of the intermediate shell. We examine the spherical gravastar model using several suitable realistic properties. We deduce different parameters corresponding to the self-gravitating structure. [ABSTRACT FROM AUTHOR]

In this paper, the natural convective flow of hybrid nanofluid over the vertical plate has been examined. Cattaneo law of thermal flux is used to characterize thermal transport. The novel model for fractional constitutive equation is expressed by the time fractional Caputo–Fabrizio integral. The analytical solution of the generalized convective flow of viscous fluid over the vertical plate along generalized conditions is obtained by using the Laplace transform. Mathcad is used to determine numerically the influence of the physical and fractional parameters on the temperature and velocity field to depict the results graphically. [ABSTRACT FROM AUTHOR]