In the present work we investigate the collapsing and expanding solutions of the Einstein's field equation of anisotropic fluid in spherically symmetric space-time and with charge within the framework of ${f(R, T)}$ theory, where $R$ denotes the Ricci scalar and $T$ denotes the trace of the energy$-$momentum tensor. We also evaluate the expansion scalar, whose negative values result in collapse and positive values yield expansion. We analyzed the impacts of charge in ${f(R, T)}$ theory on the density and pressure distribution of the collapsing and expanding fluid and noticed the involvement of anisotropic fluid in the process of collapsing and expanding with charge in $ {f(R, T)}$. Furthermore, the definition of mass function has been used to analyse the condition for the trapped surface, and it has been found that in this case there is only one horizon. In all scenarios, the effects of coupling parameters $\lambda$ and $q$ have been thoroughly examined. Additionally, we have created graphs representing pressures, anisotropy, and energy density in ${f(R, T)}$ theory and check the effect of charge on these quantities.
Food inflation presents a significant challenge in Nigeria. This study examines the volatility of four primary food items—tomatoes, yam, yellow garri, and imported rice—in Cross River State, Nigeria, utilizing data on monthly retail prices per kilogram from January 1997 to November 2023, sourced from the National Bureau of Statistics (NBS). Three asymmetric volatility models were employed: Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH), Threshold Autoregressive Conditional Heteroscedasticity (TARCH), and Power Autoregressive Conditional Heteroscedasticity (PARCH). The parameters of these models were estimated using three distributions of error innovations: Normal, Student's t-distribution, and Generalized Error Distribution (GED). The performance of the models was assessed based on log-likelihood for fitness and Root Mean Square Error (RMSE) for forecasting accuracy. The results indicated that non-Gaussian error innovations outperformed the normal distribution. Notably, higher persistence in volatility was observed for yam and tomatoes compared to yellow garri and imported rice. Tomatoes exhibited the highest volatility persistence among the food items analyzed. Significant Generalized Autoregressive Conditional Heteroscedasticity (GARCH) terms for tomatoes and yam suggested that past volatility has a significant positive impact on their current volatility, whereas this effect was not significant for yellow garri and imported rice (p$<$0.05). The leverage effect was found to be insignificant, indicating that positive and negative shocks in volatility exert similar effects on the volatility of these food items. These findings underscore the urgent need for incentives and adequate security measures to ensure food sufficiency in Cross River State and Nigeria at large.
This investigation was conducted to assess the impact of effort, interest, and cognitive competence on statistics achievement, mediated by self-concept among students. The study engaged 453 students enrolled in a statistics course at Yarmouk University, Jordan, who completed a self-report questionnaire. Path analysis facilitated the examination of both direct and indirect influences exerted by effort, interest, and cognitive competence on statistics achievement, with self-concept serving as a mediator. It was found that effort, interest, and cognitive competence significantly directly affected statistics achievement. Furthermore, self-concept was observed to partially mediate the relationships between each of effort, interest, cognitive competence, and statistics achievement. These results underscore the critical roles of effort, interest, and cognitive competence as predictors of success in statistics. The partial mediation by self-concept suggests its important but not exclusive role in enhancing academic outcomes. This study contributes to educational strategies by highlighting the potential of interventions focused on self-concept enhancement to improve academic performance in statistical education. Implications for educators and policy-makers are discussed in terms of designing effective educational interventions.
In this study, an extensive examination of topological parameters derived from molecular structures is conducted, with a specific focus on the Randic index, Geometric Arithmetic (GA) index, and Atom Bond Connectivity (ABC) index. These indices are applied to concealed non-Kekulean benzenoids and subdivided networks within line graphs. The investigation reveals patterns and relationships that were previously unexplored, shedding light on the structural intricacies of chemical compounds. The utility of graph theory as an effective tool for modeling and designing interconnection devices within the realm of chemical research is underscored. Such an approach not only advances the field of mathematical chemistry but also enriches understanding of the manipulation of chemical structures for extensive scientific applications. This analysis contributes to the body of knowledge by highlighting the relevance of these indices in unveiling complex molecular topologies and their potential implications for theoretical and applied chemistry.
In the pursuit of advancing multi-attribute group decision-making (MAGDM) methodologies, this study introduces two novel aggregation operators: the Induced Confidence Complex Pythagorean Fuzzy Ordered Weighted Geometric Aggregation (ICCPyFOWGA) operator and the Induced Confidence Complex Pythagorean Fuzzy Hybrid Geometric Aggregation (ICCPyFHGA) operator. These operators are characterized by their capacity to integrate various decision criteria based on complex Pythagorean fuzzy sets (CPyFSs), with an emphasis on the influence of confidence levels. Key structural properties of these operators, such as idempotency, boundedness, and monotonicity, are rigorously established. Furthermore, the practical applicability of these models in real-world decision-making scenarios is demonstrated through a descriptive example that underscores their efficiency and effectiveness. The analytical results affirm that the proposed operators not only enhance decision-making precision but also offer a flexible framework for addressing diverse decision-making environments. This contribution marks a significant advancement in the field of decision science, providing a robust tool for experts and practitioners involved in complex decision-making processes.
In the field of graph theory, the exploration of connectivity patterns within various graph families is paramount. This study is dedicated to the examination of the neighbourhood degree-based topological index, a quantitative measure devised to elucidate the structural complexities inherent in diverse graph families. An initial overview of existing topological indices sets the stage for the introduction of the mathematical formulation and theoretical underpinnings of the neighbourhood degree-based index. Through meticulous analysis, the efficacy of this index in delineating unique connectivity patterns and structural characteristics across graph families is demonstrated. The utility of the neighbourhood degree-based index extends beyond theoretical graph theory, finding applicability in network science, chemistry, and social network analysis, thereby underscoring its interdisciplinary relevance. By offering a novel perspective on topological indices and their role in deciphering complex network structures, this research makes a significant contribution to the advancement of graph theory. The findings not only underscore the versatility of the neighbourhood degree-based topological index but also highlight its potential as a tool for understanding connectivity patterns in a wide array of contexts. This comprehensive analysis not only enriches the theoretical landscape of graph descriptors but also paves the way for practical applications in various scientific domains, illustrating the profound impact of graph theoretical studies on understanding the intricacies of networked systems.
Inducing variables are the parameters or conditions that influence the membership value of an element in a fuzzy set. These variables are often linguistic in nature and represent qualitative aspects of the problem. Thus, the objective of this paper is introduce some aggregation operators based on inducing variable, such as induced complex Polytopic fuzzy ordered weighted averaging aggregation operator (I-CPoFOWAAO) and induced complex Polytopic fuzzy hybrid averaging aggregation operator (I-CPoFHAAO). Induced aggregation operators in decision-making process are indispensable tools for managing uncertainty, integrating multiple criteria, facilitating consensus, and providing a formal and flexible framework for modeling and solving complex decision problems. At the end of the paper, we make an illustrative example to prove the ability and efficiency of the novel proposed aggregation operators.
In this investigation, the exact formulas for geometric-harmonic (GH), neighborhood geometric-harmonic (NGH), harmonic-geometric (HG), and neighborhood harmonic-geometric (NHG) indices were systematically evaluated for hyaluronic acid-curcumin (HAC) and hyaluronic acid-paclitaxel (HAP) conjugates. Through this evaluation, a comprehensive quantitative assessment was conducted to elucidate the structural characteristics of these conjugates, highlighting the intricate geometric and harmonic relationships present within their molecular graphs. The study leveraged these indices to illuminate the complex interplay between geometric and harmonic properties, providing a novel perspective on the molecular architecture of HAC and HAP conjugates. This analytical approach not only sheds light on the structural nuances of these compounds but also offers a unique lens through which their potential in drug delivery applications can be assessed. Graphical analyses of the results further enhance the understanding of these molecular properties, presenting a detailed visualization that complements the quantitative findings. The integration of these topological descriptors into the study of HAC and HAP conjugates represents a significant advance in the field of medicinal chemistry, offering valuable insights for researchers engaged in the development of innovative drug delivery systems. The findings underscore the utility of these descriptors in characterizing the molecular topology of complex conjugates, setting the stage for further exploration of their applications in therapeutic contexts.
This study introduces an advanced framework for picture fuzzy linear programming problems (PFLPP), deploying picture fuzzy numbers (PFNs) to articulate diverse parameters. Integral to this approach are the three cardinal membership functions: membership, neutral, and non-membership, each contributing distinctly to the formation of the PFLPP. Emphasis is placed on employing these degrees to formulate the PFLPP in its most unadulterated form. Furthermore, the research delineates a novel optimization model, tailored specifically for the resolution of the PFLPP. A meticulous case study, accompanied by a numerical example, is presented, demonstrating the efficacy and robustness of the proposed methodology. The study culminates in a comprehensive discussion of the findings, highlighting pivotal insights and delineating potential avenues for future inquiry. This exploration not only advances the theoretical underpinnings of picture fuzzy sets but also offers practical implications for the application of linear programming in complex decision-making scenarios.
In the realm of decision-making, the delineation of uncertainty and ambiguity within data is a pivotal challenge. This study introduces a novel approach through complex intuitive hesitant fuzzy sets (CIHFS), which offers a unique multidimensional perspective for data analysis. The CIHFS framework is predicated on the concept that membership degrees reside within the unit disc of the complex plane, thereby providing a more nuanced representation of data. This method stands apart in its ability to simultaneously process and analyze data in a two-dimensional format, incorporating additional descriptive elements known as phase terms into the membership degrees. The study is bifurcated into two primary phases. Initially, a possibility degree measure is proposed, facilitating the ranking of numerical values within the CIHFS context. Subsequently, the development of innovative operational rules and aggregation operators (AOs) is undertaken. These AOs are instrumental in amalgamating diverse options within a CIHFS framework. The research dissects and deliberates on various AOs, including weighted average (WA), ordered weighted average (OWA), weighted geometric (WG), ordered weighted geometric (OWG), hybrid average (HA), and hybrid geometric (HG). Furthermore, the study extends to the realm of multi-criteria decision making (MCDM), where it proposes a methodology utilizing intricate intuitive and fuzzy information. This methodology emphasizes the objective management of weights, thereby enhancing the decision-making process. The study's findings hold significant implications for the optimization of resources and decision-making strategies, providing a robust framework for the application of CIHFS in practical scenarios.
In the realm of epidemiological modeling, the intricacies of epidemic dynamics are elucidated through the lens of compartmental models, with the SIR (Susceptible-Infectious-Recovered) and its variant, the SIS (Susceptible-Infectious-Susceptible) model, being pivotal. This investigation delves into both deterministic and stochastic frameworks, casting the SIR model as a continuous-time Markov chain (CTMC) in stochastic settings. Such an approach facilitates simulations via Gillespie's algorithm and integration of stochastic differential equations. The latter are formulated through a bivariate Fokker-Planck equation, originating from the continuous limit of the master equation. A focal point of this study is the distribution of extinction time, specifically, the duration until recovery in a population with an initial count of infected individuals. This distribution adheres to a Gumbel distribution, viewed through the prism of a birth and death process. The stochastic analysis reveals several insights: firstly, the SIR model as a CTMC encapsulates random fluctuations in epidemic dynamics. Secondly, stochastic simulation methods, either through Gillespie's algorithm or stochastic differential equations, offer a robust exploration of disease spread variability. Thirdly, the precision of modeling is enhanced by the incorporation of a bivariate Fokker-Planck equation. Fourthly, understanding the Gumbel distribution of extinction time is crucial for gauging recovery periods. Lastly, the non-linear nature of the SIR model, when analyzed stochastically, enriches the comprehension of epidemic dynamics. These findings bear significant implications for epidemic mitigation and recovery strategies, informing healthcare resource planning, vaccine deployment optimization, implementation of social distancing measures, public communication strategies, and swift responses to epidemic resurgences.
In the realm of emergency response, where time and information constraints are paramount, and scenarios often involve high levels of toxicity and uncertainty, the effective management of industrial control systems (ICS) is critical. This study introduces novel methodologies for enhancing decision-making processes in emergency situations, specifically focusing on ICS-security. Central to this research is the employment of spherical hesitant fuzzy soft set (SHFSS), a concept that thrives in the presence of ambiguity and incomplete information. The research adopts and extends the parametric families of t-norms and t-conorms, as introduced by Yager, to analyze these sets. This approach is instrumental in addressing multi-attribute decision-making (MADM) problems within the ICS-security domain. To this end, four distinct aggregation operators (AOs) are proposed: spherical hesitant fuzzy soft yager weighted averaging aggregation, spherical hesitant fuzzy soft yager ordered weighted averaging aggregation, spherical hesitant fuzzy soft yager weighted geometric aggregation, and spherical hesitant fuzzy soft yager ordered weighted geometric aggregation. These operators are tailored to harness the operational benefits of Yager's parametric families, thereby offering a robust framework for dealing with decision-making problems under uncertainty. Further, an algorithm specifically designed for MADM is presented, which integrates these AOs. The efficacy and precision of the proposed methodology are demonstrated through a numerical example, applied in the context of an ICS security supplier. This example serves as a testament to the superiority of the approach in handling complex decision-making scenarios inherent in ICS-security management.
In contemporary military contexts, the determination of an optimal course of action (COA) in combat operations emerges as a critical challenge. This study delineates a decision support methodology for military applications, employing sophisticated decision analysis techniques. The initial phase entails the identification of pivotal criteria for assessing and ranking COAs, followed by the assignment of weight coefficients to each criterion via the full consistency method (FUCOM). Subsequently, the Einstein weighted arithmetic average operator (EWAA) was utilized for the aggregation of expert opinions, ensuring a consensual evaluation of these criteria and culminating in the final values of their weight coefficients. The ensuing phase focuses on the selection of an optimal COA, incorporating the grey complex proportional assessment (COPRAS-G) method. This method addresses uncertainties and varying criterion values. Expert ratings were again aggregated using the EWAA operator. The findings from this phase are designed to provide military commanders with precise, data-driven guidance for decision-making. To validate and verify the stability of the proposed model, a series of tests were conducted, including a rank reversal test, sensitivity analysis regarding changes in weight coefficients, and a comparative analysis with alternative methods. These assessments uniformly indicated the model's consistency, stability, and validity as a military decision support tool. Emphasizing a high degree of confidence in COA selection, the methodology advocated herein is applicable to decision-making processes in the planning and execution of military operations. The uniform application of professional terms, consistent with the broader context of this research, ensures clarity and coherence in its presentation. The approach outlined in this study stands as a testament to rigorous analytical methodologies in the realm of military strategic planning, offering a robust framework for decision-making under conditions of uncertainty and complexity.
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