The incorporation of fractional calculus into nanofluid models has proven effective in capturing the complex dynamics of nanofluid flow and heat transfer, thereby enhancing the precision of predictions in this intricate field. In this study, the dynamics of a viscoelastic second-grade nanofluid model are examined through the application of the Laplace transform technique on a vertical plate. Initially, the model is formulated as coupled partial differential equations to describe the second-grade nanofluid system. The governing equations are then rendered dimensionless using appropriate dimensionless parameters. The non-dimensional model is subsequently generalized by introducing a modified Caputo fractional derivative operator. To model a homogenous nanofluid, nanoparticles of $\mathrm{Al}_2 \mathrm{O}_3$ in nanometer-sized form are suspended in mineral transformer oil. The Laplace transform is employed to solve the momentum, energy, and mass diffusion equations, providing analytical solutions. Graphical and tabular analyses are conducted to assess the influence of various physical parameters—including the fractional order, nanoparticle volume fraction, and time parameter—on the velocity, thermal, and concentration profiles. The results indicate that increasing the nanoparticle volume fraction, fractional order, and time parameter significantly enhances the rate of heat transfer. Additionally, it is observed that the velocity, temperature, and concentration profiles are notably affected by increasing the volume fraction of nanoparticles. The accuracy and reliability of the obtained solutions are validated through comparisons with existing literature. This work advances the understanding of nanofluid dynamics and presents valuable insights for industrial applications, particularly in enhancing heat transfer performance.
This work aims to apply the spherical fuzzy set (SFS), a flexible framework for handling ambiguous human opinions, to improve decision-making processes in recycled water. It specifically looks at the application of Sugeno-Weber (SW) triangular norms in the spherical fuzzy (SF) information domain, providing reliable approximations that are necessary for decision-making. A new class of aggregation operators is presented in this paper. These operators are specifically made for spherical fuzzy information systems and include the interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPA), interval value spherical fuzzy Sugeno–Weber power geometric (IVSFSWPWG), and interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPWA). The realistic features and special cases of these operators are demonstrated, highlighting how well they fit into practical scenarios. A new method for multi-attribute decision-making (MADM) is used for a range of real-world applications with different requirements or characteristics. The efficacy of the recommended methodologies is demonstrated with an example of a recycled water selection process. Additionally, a thorough comparison method is provided to show how the suggested aggregation strategies work and are relevant by contrasting their results with those of the current methods. The study's conclusion highlights the potential contribution of the recommended research to the advancement of decision-making techniques in dynamic and complex environments. It also summarizes its findings and discusses its prospects moving forward.
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.
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