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A new approach is adopted to completely classify the Lagrangian associated with the static cylindrically symmetric spacetime metric via Noether symmetries. The determining equations representing Noether symmetries are analyzed using a Maple algorithm that imposes different conditions on metric coefficients under which static cylindrically symmetric spacetimes admit Noether symmetries of different dimensions. These conditions are used to solve the determining equations, giving the explicit form of vector fields representing Noether symmetries. The obtained Noether symmetry generators are used in Noether's theorem to find the expressions for corresponding conservation laws. The singularity of the obtained metrics is discussed by finding their Kretschmann scalar. [ABSTRACT FROM AUTHOR]

The growing interest in satellite imagery has triggered the need for efficient mechanisms to extract valuable information from these vast data sources, providing deeper insights. Even though deep learning has shown significant progress in satellite image classification. Nevertheless, in the literature, only a few results can be found on weight initialization techniques. These techniques traditionally involve initializing the networks' weights before training on extensive datasets, distinct from fine-tuning the weights of pre-trained networks. In this study, a novel weight initialization method is proposed in the context of satellite image classification. The proposed weight initialization method is mathematically detailed during the forward and backward passes of the convolutional neural network (CNN) model. Extensive experiments are carried out using six real-world datasets. Comparative analyses with existing weight initialization techniques made on various well-known CNN models reveal that the proposed weight initialization technique outperforms the previous competitive techniques in classification accuracy. The complete code of the proposed technique, along with the obtained results, is available at https://github.com/WadiiBoulila/Weight-Initialization. • A novel weight initialization strategy for DL is proposed. • A step-by-step mathematical proof are provided to detail the proposed method. • Several experiments have been conducted on multiple public datasets. • Results show excellent performances of the proposed method. • The code is shared at https://github.com/WadiiBoulila/Weight-Initialization. [ABSTRACT FROM AUTHOR]

We show that many of the recent proved fixed point results in partial b-metric spaces can be obtained by the corresponding ones in b-metric spaces by introducing a simple method. On the other hand, we prove point out that, in general, our method is not applicable for certain partial b-metric fixed point theorems. [ABSTRACT FROM AUTHOR]

The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numerical examples that support our main results and illustrate the convergence behavior of the proposed process. Further, we present a data-dependence result that is also supported by a nontrivial numerical example. Finally, we discuss the solution of a nonlinear fractional differential equation by utilizing our results. [ABSTRACT FROM AUTHOR]

This study involves the generalization of partial metric spaces and strong controlled metric type spaces through the introduction of the notion of strong controlled partial metric type spaces. This research pursues a dual objective: firstly, to scrutinize fixed points related to contractions of the Kannan type within the framework of strong controlled partial metric type spaces, encompassing both linear and nonlinear contractions; secondly, to furnish illustrative examples and applications that underscore the consequential implications of our theoretical contributions., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

Neutrosophic sets provide greater versatility in dealing with a variety of uncertainties, including independent, partially independent, and entirely dependent scenarios, which q-ROF soft sets cannot handle. Indeterminacy, on the other hand, is ignored completely or partially by q-ROF soft sets. To address this issue, this study offers a unique novel concept as known as q-RONSS, which combines neutrosophic set with q-ROF soft set. This technique addresses vagueness using a set of truth, indeterminacy, and false membership degrees associated with the parametrization tool, with the condition that the sum of the qth power of the truth, indeterminacy, and false membership degrees be less than or equal to one. In addition, this study outlines operational laws for the suggested structure. The main purpose this article is to define some averaging and geometric operators based on the q-rung orthopair neutrosophic soft set. Furthermore, this article provides a step-by-step method and a mathematical model for the suggested techniques. To solve a MADM issue, this research article proposes a numerical example of people selection for a specific position in a real estate business based on a variety of criteria. Finally, to demonstrate the proposed model's superiority and authenticity, this article performs several analyses, including sensitivity analysis, to address the reliability and influence of various parameter "q" values on the alternatives and the ultimate ranking outcomes using the averaging and geometric operators. A comparison of the proposed operators to current operators demonstrates the validity of the proposed structure. Furthermore, a comparison of the proposed structure to current theories demonstrates its superiority by overcoming their limits and offering a more flexible and adaptable framework. Finally, this study reviews the findings and consequences of our research., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution., Competing Interests: The authors declare that they have no conflict of interests., (© 2024 The Author(s).)

We discuss the existence of a fixed point for a self mapping and its uniqueness satisfying ( ϕ ˙ , η ˙ ) -generalized contractive condition including altering distance functions of rational terms in an ordered b -metric space. It is also discussed whether the two self-maps under the same contraction condition can be coincident and coupled coincident. The results are backed up by a dearth of numerical examples and application to nonlinear quadratic integral equation., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

In this work, a family of hybrid contractions, termed Jaggi-type hybrid (ℵ- τ )-contractive mapping is proposed in metric space equipped with a graph and new conditions under which the mapping is a Picard operator are studied. The novel ideas proposed in this manuscript are exemplified to display the validity of the presented results and to show how they differ from the existing ones. Additionally, some corollaries which reduce our proposed notion to some recently announced concepts in the existing findings are indicated and examined. Finally, we study Ulam-type stability for the fixed point equations with hybrid contractions., Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Nabil Mlaiki reports financial support was provided by 10.13039/501100012639Prince Sultan University, Riyadh 11586, Saudi Arabia. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

The research article in hand provides a new mechanism that deals with the investigation of the triangular analytical fuzzy solutions (TAFS) of the two-dimensional fuzzy fractional order wave equation (2-D FFWE) through the Hukuhara conformable fractional derivative (HCFD) along with the concept of [ g H ] and [ g H - p ] differentiability. The mechanism consists of a fuzzy traveling wave method coupled with additive operating splitting (AOS). The procedure for the aforesaid mechanism starts with the extension of the HCFD to the fuzzy conformable fractional derivative (FCFD). Furthermore, some properties of FCFD that play a vital role in this study like, ( [ i - g H ] , [ i i - g H ] , [ i - p ] , [ i i - p ] ) -differentiability, switching point, fuzzy chain rule, and traveling wave method are discussed in detail. Further, fuzzy traveling wave method coupled with the procedure of the additive operating splitting (AOS) method is adopted to investigate the triangular analytical fuzzy solution of the Two-dimensional fuzzy wave equation (2-D FWE). Finally, some examples are provided that support our arguments., Competing Interests: There does not exist conflict of interest, (© 2024 The Author(s).)