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The paper studies axial gravitational perturbations of the Hayward black hole, a regular geometry that also arises as an effective solution in asymptotically safe gravity. By computing grey-body factors with the 6th-order WKB method and comparing them to predictions based on the quasinormal modes, the correspondence between transmission coefficients and quasinormal spectra is verified. Quantum corrections, parametrized by $γ$, are shown to suppress both the grey-body factors and the absorption cross-section, while the correspondence remains accurate at the percent level for low multipoles and essentially exact for higher ones.

Using the fact that, for a broad class of Morris-Thorne wormholes, the maximum of the effective potential is located at the throat, we derive accurate analytic WKB expressions for the quasinormal modes and grey-body factors of various traversable wormholes. In the eikonal limit, these analytic expressions acquire a compact form and satisfy the correspondence between the quasinormal modes and the radii of the wormhole shadows.

An adaptive control approach for a three-phase grid-interfaced solar photovoltaic system based on the new Neuro-Fuzzy Inference System with Rain Optimization Algorithm (ANROA) methodology is proposed and discussed in this manuscript. This method incorporates an Adaptive Neuro-fuzzy Inference System (ANFIS) with a Rain Optimization Algorithm (ROA). The ANFIS controller has excellent maximum tracking capability because it includes features of both neural and fuzzy techniques. The ROA technique is in charge of controlling the voltage source converter switching. Avoiding power quality problems including voltage fluctuations, harmonics, and flickers as well as unbalanced loads and reactive power usage is the major goal. Besides, the proposed method performs at zero voltage regulation and unity power factor modes. The suggested control approach has been modeled and simulated, and its performance has been assessed using existing alternative methods. A statistical analysis of proposed and existing techniques has been also presented and discussed. The results of the simulations demonstrate that, when compared to alternative approaches, the suggested strategy may properly and effectively ide

In this research manuscript, we explore cylindrically symmetric solutions within the framework of modified $f(R)$ theories of gravity, where $R$ representing the Ricci scalar. The study focuses on analyzing the cylindrical solutions within realistic space-time regions and investigates three distinct cases of exact solutions derived from the field equations of $f(R)$ theory of gravity. Moreover, we examine well-known Levi-Civita and cosmic string solutions for the said modify gravity. Furthermore, the manuscript delves into the implications of the obtained results by exploring energy conditions for each case. Notably, a violation of null energy conditions is observed, suggesting the potential existence of cylindrical wormholes. The findings contribute to the understanding of modified $f(R)$ theories of gravity, providing valuable insights into the nature of cylindrically symmetric solutions and their implications in theoretical physics.

In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions

In this paper we introduce the notion of I-convergence of sequences of k-dimensional subspaces of an inner product space, where I is an ideal of subsets of N, the set of all natural numbers and k in N. We also study some basic properties of this notion.

In this paper we introduce and study the notion of I-convergence of sequences in a metric-like space, where I is an ideal of subsets of the set N of all natural numbers. Further introducing the notion of I*-convergence of sequences in a metric-like space we study its relationship with I-convergence.

We have derived precise analytic expressions for the quasinormal modes of test scalar, and Dirac fields in the background of the dilaton black hole. To achieve this, we employ the higher-order WKB expansion in terms of $1/\ell$. A comparison between the analytic formulas and time-domain integration reveals that the analytic approach generally yields more accurate results than the numerical results previously published using the lower-order WKB approach. We demonstrate that in the eikonal regime, test fields adhere to the correspondence between null geodesics and eikonal quasinormal modes.

By employing an expansion in terms of the inverse multipole number, we derive analytic expressions for the quasinormal modes (QNMs) of scalar, Dirac, and Maxwell perturbations in the Hayward black hole (BH) background. The metric has three interpretations: as a model for a radiating BH, as a quantum-corrected BH owing to the running gravitational coupling in the Asymptotically Safe Gravity, and as a BH solution in the Effective Field Theory. We show that the obtained compact analytical formulas approximate QNMs with remarkable accuracy for $\ell > 0$.

In this manuscript, we study the behavior of charged isotropic compact stellar objects within the framework of the modified Gauss-Bonnety theory of gravity by considering the Tolman Kuchowicz spacetime. We use some matching conditions of spherically symmetric space-time with Bardeen model as an exterior geometry and examine the physical behavior of stellar structures. In the current analysis, we discuss the energy conditions to check the viability of our model. Many physical aspects have been examined, such as energy density, pressure evolution, equation of state parameter, and causality condition. Furthermore, an equilibrium condition can be visualized through the modified Tolman-Oppenheimer-Volkov equation. Further, we study mass-radius function, compactness and redshift function, which are some essential features of the charged compact star model. It is worthwhile to mention here for the current study that our stellar structure in the background of Bardeen's model is more viable and stable.

Recently, two models of quantum-corrected Schwarzschild-like black holes were developed within Effective Quantum Gravity, and the spectra of bosonic perturbations have been analyzed in several recent studies. In this work, we investigate the quasinormal modes of a massless Dirac field perturbations around these black holes. By employing the higher-order WKB method and time-domain integration, we achieved consistency between the two approaches within their common range of validity. This concordance enables us to distinguish the two quantum-corrected black hole models from each other and from their Schwarzschild limit through their quasinormal spectra. In addition, we find approximate analytic expressions for quasinormal modes and grey-body factors in the form of expansion beyond the eikonal limit.

Recently, a correspondence between quasinormal modes and grey-body factors of black holes has been established. This correspondence is known to be exact in the eikonal regime for a large class of asymptotically flat black holes and approximate when the multipole number \( \ell \) is small. In this work, we demonstrate that there exists a regime where the correspondence holds with unprecedented accuracy even for the lowest multipole numbers: specifically, for perturbations of massive fields in the background of asymptotically de Sitter black holes, provided the field mass is not very small. We also fill the gap in the existing literature via finding the grey-body factors of a massive scalar field in the Schwarzschild- de Sitter background, when $μM/m_{P}$ is not small.

Dynamic response evaluation in structural engineering is the process of determining the response of a structure, such as member forces, node displacements, etc when subjected to dynamic loads such as earthquakes, wind, or impact. This is an important aspect of structural analysis, as it enables engineers to assess structural performance under extreme loading conditions and make informed decisions about the design and safety of the structure. Conventional methods for dynamic response evaluation involve numerical simulations using finite element analysis (FEA), where the structure is modeled using finite elements, and the equations of motion are solved numerically. Although effective, this approach can be computationally intensive and may not be suitable for real-time applications. To address these limitations, recent advancements in machine learning, specifically artificial neural networks, have been applied to dynamic response evaluation in structural engineering. These techniques leverage large data sets and sophisticated algorithms to learn the complex relationship between inputs and outputs, making them ideal for such problems. In this paper, a novel approach is proposed for eva

Language Models have ushered a new age of AI gaining traction within the NLP community as well as amongst the general population. AI's ability to make predictions, generations and its applications in sensitive decision-making scenarios, makes it even more important to study these models for possible biases that may exist and that can be exaggerated. We conduct a quality comparative study and establish a framework to evaluate language models under the premise of two kinds of biases: gender and race, in a professional setting. We find out that while gender bias has reduced immensely in newer models, as compared to older ones, racial bias still exists.

We compute quasinormal modes of test fields around spherically symmetric black holes with a global monopole in bumblebee gravity. The frequency of oscillation and the damping rate exhibit significant decreasing as the global monopole parameter is increased. An intriguing observation arises in the extreme limit, where the quasinormal modes manifest a form of universal behavior: the actual oscillation frequency remains unaltered despite variations in the Lorentz symmetry breaking (LSB) parameter. Our calculations are conducted through two distinct methods, both of which yield results that align remarkably well. Furthermore, we derive an analytical formula for quasinormal modes within the eikonal approximation and beyond it. In the limits of either vanishing deficit angle or bumblebee parameters, the compact and sufficiently accurate analytic expressions for quasinormal modes are obtained.