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This paper focuses on obtaining exact solutions of nonlinear Akbota equation through the application of the modified Khater method and Sardar sub-equation method. Renowned as one of the latest and precise analytical schemes for nonlinear evolution equations, this method has proven its efficacy by generating diverse solutions for the model under consideration. The equation is crucial in the study of optical solitons, which are stable pulses of light that maintain their shape over long distances. The Akbota equation helps in understanding the behavior and stability of these solitons. The governing equation undergoes transformation into an ordinary differential equation through a well-suited wave transformation. This analytical simplification paves the way for the derivation of trigonometric, hyperbolic, and rational solutions through the proposed methods. To illuminate the physical behavior of the model, the study presents graphical plots of the selected solutions of Khater and Sardar sub-equation method. This visual representation, achieved by selecting appropriate values for arbitrary parameters, enhances the understanding of the system’s dynamics. All calculations in this study are meticulously conducted using the Mathematica and Maple software, ensuring accuracy and reliability in the analysis of the obtained solution. Furthermore we investigate the sensitivity analysis of the dynamical system. [ABSTRACT FROM AUTHOR]

The intended research aims to explore the convection phenomena of a hybrid nanofluid composed of gold and silver nanoparticles. This research is novel and significant because there is a lack of existing studies on the flow behavior of hybrid nanoparticles with important physical properties of blood base fluids, especially in the case of sidewall ruptured dilated arteries. The implementation of combined nanoparticles rather than unadulterated nanoparticles is one of the most crucial elements in boosting the thermal conduction of fluids. The research methodology encompasses the utilization of advanced bio-fluid dynamics software for simulating the flow of the nanofluid. The physical context elucidates the governing equations of momentum, mass, momentum, and energy in terms of partial differential equations. The results are displayed in both tabular and graphical forms to demonstrate the numerical and graphical solutions. The effect of physical parameters on velocity distribution is illustrated through graphs. Furthermore, the study's findings are unique and original, and these computational discoveries have not been published by any researcher before. The finding implies that utilizing hybrid nanoparticles as drug carriers holds great promise in mitigating the effects of blood flow, potentially enhancing drug delivery, and minimizing its impact on the body. [ABSTRACT FROM AUTHOR]

This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V–L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures. [ABSTRACT FROM AUTHOR]

The current study focuses on investigating the solutions of the mathematical model in the form of special functions. The phenomenon is described by a set of partial differential equations, which are then transformed into non-dimensional form. In order to improve the rheology of the Casson fluid, a fractional model is developed by using a new fractional operator Constant Proportional Caputo (CPC) approach to investigate and formulate the dynamics of Casson fluid flow and heat transfer phenomena subjected to ramped wall temperature. The fluid flow is elaborated near an infinitely vertical plate with characteristics velocity u 0 . We began by introducing appropriate variables to transform the mathematical model into non-dimensional form. Laplace transformation operator applied to gain the solution from fractional model, then obtained results expressed in the form of well-known special functions. The influence of various pertinent parameters involving in the solution was carefully examined to unveil intriguing findings. Upon comparison, we observed that the CPC approach yielded better results, after comparison with classical models documented in the literature, with graphical representations provided to illustrate these outcomes. To comprehensively analyze the dynamics of the proposed problem, physical influence of various parameters is studied and repercussions are graphically highlighted and discussed. Additionally, we derived results in a limiting sense, including Casson and viscous fluid models transitioning from the classical form to the fractionalized fluid model. [ABSTRACT FROM AUTHOR]

Halide perovskite materials belong to a fascinating novel class, and recently captured incredible attention as a leading aspirant for next-generation photovoltaic technology, because of their flexible chemistry and extraordinary optoelectronic properties, they also deliver a pattern for designing new materials for energy conversion and energy storage applications. In this study, we thoroughly explore the structural, electronic, optical and mechanical properties of the inorganic halide cubic perovskites (CsInX3; X = Br, Cl) for solar cell (SC) application, simulated under density functional theory (DFT) based WIEN2k code with PBE-GGA approximation. The optimized lattice parameters were found to be 11.67 Ǻ for CsInBr3 and 11.16 Ǻ for CsInCl3, respectively. The variation in the structural parameters with changing the halogen atom from Br to Cl was observed. The electronic and optical properties were computed by TB-mBJ method. These halide perovskites reveal an indirect energy bandgap quantified as 1.22 and 2.2 eV, high absorption coefficient and low reflectivity. The elastic constants (C11, C12 and C44) followed the Born stability condition, and confirmed the mechanical stability. According to the Poisson ratio (ν) and Pugh's ratio (B/G), materials endorsed ductile behaviour as well exhibit anisotropic nature. Moreover, our theoretical findings suggested that the investigated materials have high absorption coefficients, high conductivity and low reflectivity, which makes them promising contender for SC applications. [ABSTRACT FROM AUTHOR]

Development of efficient electrodes for supercapacitor remains a key challenge. Besides energy conversion, halide perovskites gained substantial focus for energy storage applications, thanks to their excellent redox properties and flexible chemistry. Here, PANI and fullerene (C60) successfully incorporated with halide perovskite materials (CsInCl3) by employing facile sol-gel auto-combustion method. The physico-chemical properties were thoroughly examined using XRD, FE-SEM, EDX, CV, GCD, and EIS techniques. XRD confirmed the tetragonal phase, while FE-SEM coupled with EDX revealed porous type morphology and confirmed the presence of the elements Cs, In, Cl, and C. From electrochemical analysis, cyclic voltammetry (CV) confirmed the pseudo-capacitive character of the PANI-based electrode. Galvanostatic charge-discharge (GCD) exhibited outstanding specific capacitance (1835.3 F/g), power density (1470.8 W/Kg), and energy density (68.7 Wh/Kg) at current density of 0.5 A/g in 1 M KOH. Electrochemical impedance spectroscopy (EIS) revealed small semi-circle of PANI-based electrode showing low charge transfer resistance (Rct) and solution resistance (Rs) at the electrode-electrolyte interface. Moreover, the PANI-based electrode demonstrated exemplary cyclic stability, retains approximately 91.2% of its original capacitance after 4000th charge-discharge cycles. Above findings proposed the synergy impact of PANI-based (CsInCl3/PANI) composite electrodes are highly efficient for supercapacitor electrodes because of large porosity and efficient/smooth transportation of ions at the electrode-electrolyte interface. [ABSTRACT FROM AUTHOR]

Nowadays, manufacturers face intense pressure to maintain a high standard of quality. Due to the damage to machine components, manufacturing processes degrade over time, resulting in substandard products. Generally, statistical process control tools such as control charts aid in identifying patterns and trends indicative of process changes. This investigation delves into the effectiveness of cumulative sum control charts using the sample mean and median as plotting statistics. Run-length measurements assess performance after the charts experience linear and quadratic drifts in non-normal setups under zero- and steady-state conditions. The findings reveal that Cumulative Sum (CUSUM) charts outperform zero-state monitoring compared to steady-state monitoring. Notably, the CUSUM chart for the mean is suitable for normal and Gamma distributions, exhibiting a greater ability for drift detection under biased and unbiased Average Run Lengths. This study offers valuable insights into enhancing manufacturing quality through effectively implementing and comparing Shewhart, Exponentially Weighted Moving Average, and CUSUM charts. By evaluating their performance under various conditions and comparing them with other control chart methods, this research provides valuable guidance for industries seeking to improve process monitoring and product quality. It is essential to acknowledge that the findings are based on specific experimental conditions and may not fully capture the complexity of real-world manufacturing environments. For practical purposes, the suggested charts are also applied to real-world case studies, including air quality (focusing on five metal oxide chemistry sensors: carbon monoxide concentration, non-metonic hydrocarbons, benzene, total nitrogen oxides, and nitrogen dioxide) and maintenance data (including air temperature, rotating speed, and equipment failure). [ABSTRACT FROM AUTHOR]

A massive landslide occurred in Domeshi area, District Muzaffarabad, Pakistan, in two distinct phases: an initial movement on August 1, followed by complete failure on August 4, 2023. The landslide movement persisted for 96 h, with a runout distance of 500 m. The event destroyed numerous residential structures, impacting multiple families, and causing extensive damage to cultivated land and road infrastructure. To comprehensively understand the failure mechanisms, a detailed study was undertaken, encompassing site investigations, unmanned aerial vehicle (UAV) photography, geotechnical and geophysical investigations, petrographic analysis, kinematics, and numerical simulations. The field evidence indicates that the active deformation along the Jhelum Fault (JF) within the landslide’s main body weakened the surrounding rock formations. Intense rainfall saturated pre-existing fractures, creating critical zones of weakness. Highly plastic clays along fault plane contributed significantly to volume changes, especially during and after rainfall events. Kinematic analysis identified bedding joints as prevalent failure planes for planar sliding. Geophysical survey revealed a layer of unconsolidated material extending 25–30 m below the landslide’s scarp, accompanied by various fractures, including a deep fracture (i.e., JF) up to 300 m depth. Petrographic investigations showed microfractures, micro faults, and intragranular mineral breakage, indicative of intense tectonic stresses. Slope stability analysis indicated factors of safety (FoS) and strength reduction factor (SRF) less than 1, suggesting the potential for further failure in the lower sections of the landslide. Multiple factors, including slope geometry, active tectonics, material composition, and anthropogenic factors (i.e., slope loading and cutting for road and building construction, improper drainage distribution), contributed to the landslide's occurrence, however, the rainfall emerged as the primary triggering event. [ABSTRACT FROM AUTHOR]

Halide perovskites with carboneous materials put magical foundation for energy concern, specifically for supercapacitor electrodes, because of their flexible chemistry and high electronic/ionic conductivity. Here, the inorganic halide perovskite composites with rGO and PANI, i.e.; (KNiBr3, KNiBr3/rGO, and KNiBr3/PANI) were synthesize by employing facile hydrothermal approach. The physio-chemical characteristics of these composites were investigated in detail by using various advance characterization tools, including XRD, FE-SEM, EDX, I-V, CV, GCD, and EIS, respectively. XRD confirmed the phase purity and high crystallinity. Whereas FE-SEM attached with EDX, revealed the porous nature and confirmed the presence of the desired elements. I-V measurements represents the ohmic behavior, resulting to higher conductivity. In electrochemical measurements, CV confirmed the pesudocapacitive behavior of all the fabricated electrodes. GCD analysis showed that the electrode incorporated with PANI exhibited superior specific capacitance (944.25 F/g), power density (1374.31 W/kg), and energy density (79.087 Wh/kg) at 1 A/g. EIS confirmed that KNiBr3/PANI electrode showed small semi-circle, indicating the small polarization and solution resistance, support the FE-SEM and I-V analysis. In addition, stability test was performed over 3000th charging/discharging cycles at 5 mV/s, indicate that PANI-based electrode retained 94% of original capacitance. Based on these findings, it is confidently suggested that studied halide perovskite materials can be effectively used for next generation supercapacitor electrodes. [ABSTRACT FROM AUTHOR]

The paper introduce a novel auxiliary equation method for the successful derivation of traveling wave solutions for the non-linear Kairat-X (K-X) equation. Along with other novel results, soliton, singular, triangular periodic, and doubly periodic topological solutions are among the solutions obtained. The study revisits the concept of optical solitary waves, enhancing our understanding of the model. Previous studies have already derived analytical solutions using diverse approaches, contributing to the discovery of new soliton solutions within this framework. These solutions are characterized through three-dimensional, contour plot, and two-dimensional profile analyses. Additionally, the impact of time on the propagation of wave patterns is explored. The outcomes show how well our suggested approach works to solve non-linear evolution equations by producing fresh, more thorough solutions, making it a powerful mathematical tool for doing so. Through this article, we elucidate how leveraging NAEM with the Kairat-X equation can lead to optimized optical systems, improved data transmission rates, and the evolution of nonlinear optics towards more efficient and reliable communication technologies. [ABSTRACT FROM AUTHOR]

This work tackles the Heisenberg ferromagnet-type integrable Akbota equation. The Akbota equation is significant model to visualize and study the surface geometry and curve analysis. The Akbota equation is an integrable coupled system of differential equations with soliton solutions. It is a crucial tool for researching nonlinear phenomena in differential geometry of curves and surfaces, magnetism, and optics. The generalized projective Riccati equation method, the Sardar sub-equation method, and the G ′ G 2 -expansion method are the three separate analytical techniques used in this work. By using these approaches, exact analytical solutions for soliton waves are obtained, including dark, bright, singular, singular periodic, trigonometric, and hyperbolic waves. The creation of theoretical frameworks and the generalization of findings are made possible by analytical solutions. Researchers can frequently find patterns and relationships that apply more broadly by developing analytical solutions to particular cases, which results in the development of new theories and principles. The manuscript includes graphical representations, such as contour plots and two- or three-dimensional visualizations, in addition to theoretical derivations. These examples examine the propagation properties of the obtained soliton solutions and provide a promising basis for further research. Before this study, there is not existing any study in which, someone used these approaches and found solitons solutions. [ABSTRACT FROM AUTHOR]

Current communication deals with the flow impact of blood inside cosine shape stenotic artery. The under consideration blood flow is treated as Newtonian fluid and flow is assumed to be two dimensional. The governing equation are modelled and solved by adopting similarity transformation under the stenosis assumptions. The important quantities like Prandtl number, flow parameter, blood flow rate and skin friction are attained to analyze the blood flow phenomena in stenosis. The variations of different parameters have been shown graphically. It is of interest to note that velocity increases due to change in flow parameter gamma and temperature of blood decreases by increasing nanoparticles volume fraction and Prandtl number. In the area of medicine, the most interesting nanotechnology approach is the nanoparticles applications in chemotherapy. This study provides further motivation to include more convincing consequences in the present model to represent the blood rheology. [ABSTRACT FROM AUTHOR]

Alpha-cypermethrin interacts with the sodium channel and causes nerve blockage in insects. It is used to manage Aedes aegypti (Linnaeus) (Diptera: Culicidae), a primary vector of dengue worldwide. It not only affects both target and non-target organisms, but overuse of this insecticide increases the chances of resistance development in insect pests. In this study, resistance development, biological parameters, and stability of alpha-cypermethrin resistance were studied in a laboratory-selected strain of Ae. aegypti. The alpha-cypermethrin selected strain (Alpha Sel) developed an 11.86-fold resistance level after 12 rounds of alpha-cypermethrin selection compared to the unselected strain (Unsel). In biological parameters, Alpha Sel and Cross1 (Unsel ♂ and Alpha Sel♀) had shorter larval durations compared to Unsel and Cross2 (Unsel ♀ and Alpha Sel ♂) populations. The pupal duration of Alpha Sel and both crosses was shorter than that in the Unsel strain. The relative fitness of Alpha Sel, Cross1, and Cross2 was significantly less than that of the Unsel strain. These results indicate that alpha-cypermethrin resistance comes with fitness costs. Moreover, the frequency of alpha-cypermethrin resistance decreased when the Alpha Sel population was reared without further selection pressure for four generations. So, resistance was unstable and reversed when insecticide pressure ceased. We concluded that the judicious and rotational use of different insecticides with different modes of action and the adoption of other IPM-recommended practices would suppress resistance development for more extended periods in Ae. aegypti. [ABSTRACT FROM AUTHOR]

Advancements in additive manufacturing have significantly increased the use of cellular structures in product development, especially in the automotive, aerospace, and biomedical industries, due to their enhanced strength-to-weight ratio and energy-absorbing capabilities. This study investigates the tensile properties of 3D-printed PLA prismatic cellular structures, focusing on the effects of fillet radius, wall thickness, and cell size on tensile strength, Young's modulus, and strength-to-weight ratio. Using a full factorial design and ANOVA, we examined the impact and interaction of each geometrical parameter. Our findings show that triangular cellular structures exhibit a higher stiffness of 1.36 GPa and tensile strength of 24.28 MPa, resulting in a notable 5.78 MPa/gram strength-to-weight ratio. Increasing cell count and wall thickness enhances both tensile strength and Young's modulus, whereas adding fillet radii at corners reduces these properties. Fracture behaviors are influenced by geometrical design: shorter, thicker walls lead to progressive crack propagation, while longer, thinner walls tend to fail catastrophically. Fillet radius introduction shifts the fracture initiation point from the nodes. ANOVA results indicate that wall thickness and cell size significantly affect tensile strength and Young's modulus, contributing 36.53% and 53.54%, respectively. [ABSTRACT FROM AUTHOR]

Key message: Boron is essential for plants, but excess can induce toxicity. Boron (B) is a vital micronutrient for plants, but excess B can induce toxicity symptoms and reduce crop yields. B bioavailability depends on soil properties, including clay type, pH, and organic matter content. Symptoms of B toxicity include reduced shoot and root growth, leaf chlorosis and necrosis, impaired photosynthesis, and disrupted pollen development. This review paper examines the current knowledge on B toxicity mechanisms, tolerance strategies, and management approaches in plants. This review covers (1) factors affecting B bioavailability; (2) toxicity symptoms in plants; (3) uptake, transport, and detoxification mechanisms; and (4) strategies. To mitigate toxicity, plants reduce B uptake, activate efflux transporters, compartmentalize B, and enhance antioxidant systems. On the basis of this review, future research should focus on identifying novel tolerance mechanisms, exploring genetic strategies for improved B management, and developing innovative agronomic interventions. These insights will facilitate the breeding and management of crops for enhanced productivity under B toxicity stress. [ABSTRACT FROM AUTHOR]

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal–fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal–fractional alcohol addiction model are shown using the Picard–Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam–Hyers coupled with the Ulam–Hyers–Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community. [ABSTRACT FROM AUTHOR]

The continuously reinforced concrete pavement (CRCP) system grapples with challenges such as non-uniform transverse crack patterns and the need for substantial reinforcement. Field research on the Belgian CRCP sections along motorway E313 indicates that active cracking induced by partial surface saw-cuts consistently leads to transverse crack patterns. This study introduces an innovative modification to the CRCP: the actively reinforced concrete pavement design (ARCP). The ARCP leverages partial surface saw-cuts to reduce reinforcement needs by replacing continuous-length steel bars with partial-length counterparts. The main objective of the present study is to develop a 3D finite element (FE) model capturing the active cracking behavior of ARCP under realistic external temperature variations. Comparative analysis with CRCP considers early-age crack patterns, crack strain development, and the distribution of maximum steel stress for different steel ratios (0.67%, 0.75%, and 0.85%). FE simulation results align with field data, indicating that ARCP exhibits similar early-age cracking behavior to CRCP but with a significant 24 to 42% reduction in total reinforcement. This innovation presents a promising avenue for addressing CRCP challenges while optimizing material usage in pavement construction. [ABSTRACT FROM AUTHOR]

The dynamic behavior of the Vakhnenko-Parkes equation is examined in this manuscript. This is an important subject because of its implications for comprehending intricate mathematical models describing traveling wave phenomena and solitons. The construction of traveling wave solutions for the Vakhnenko-Parkes equation in closed form is the main issue addressed in the study. The modified auxiliary equation approach and the extended (G ′ G 2) -expansion method are used to address this because they are effective in producing precise solutions of a large class of nonlinear partial differential equations. A visual component to comprehending the behavior of the equation is added by employing 3D-surface graphs, 2D-line graphs, and contour plots to explore these solutions graphically. A variety of traveling wave behavior is observed from the obtained solutions. These results imply that the Vakhnenko-Parkes equation and its solutions are complex, offering important insights into the underlying dynamics. The proposed techniques are applied for the first time to study the considered model in this work. A comparison of the obtained results with the previous works is presented to confirm the significance and novelty of the reported results. [ABSTRACT FROM AUTHOR]

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations. [ABSTRACT FROM AUTHOR]

The Eocene Kuldana Formation (KF) in the Yadgar area of Pakistan, comprises a diverse range of sedimentary facies, including variegated red beds of shales, mudstones, and sandstones, as well as interbedded limestone and marl. In this study, we conducted an integrated micropaleontological, sedimentological, mineralogical, and geochemical investigation to determine the depositional setting, biochronology, provenance, and paleoclimate of the KF. The study identified six lithofacies and six microfacies, which indicate a variety of environments ranging from floodplains and channels to the margins and shallow marine settings. The nannofossil biostratigraphy places the KF in the Early Eocene, more precisely the NP10 zone (Ypresian), and the fossil zone of benthic foraminifera classifies the study section as the Shallow Benthic Zone SBZ-8 (Middle Ilerdian 2). In terms of petrography, the KF sandstone was classified as litharenite and feldspathic litharenite, while the QtFL diagram suggests a recycled orogen. Geochemical proxies indicate an oxidizing environment, a high-to-low regular sedimentation rate, moderate-to-intense chemical weathering in the source region, and a warm-humid to dry climate during the deposition of KF. Overall, the findings suggest that the deposition of KF marks the end of Neo-Tethys due to the Early Eocene Indian–Kohistan collision and that the uplifting of the Himalayas provided the source for the deposition of KF in the foreland basin. The study provides new insights into the depositional environment, biochronology, provenance, and paleoclimate of KF, and highlights the potential for red beds as reliable indicators of oxygenation levels in proximity to mineral deposits. [ABSTRACT FROM AUTHOR]

Lead (Pb) is toxic to the development and growth of rice plants. Nanoparticles (NPs) have been considered one of the efficient remediation techniques to mitigate Pb stress in plants. Therefore, a study was carried out to examine the underlying mechanism of iron (Fe) and silicon (Si) nanoparticle-induced Pb toxicity alleviation in rice seedlings. Si–NPs (2.5 mM) and Fe-NPs (25 mg L−1) were applied alone and in combination to rice plants grown without (control; no Pb stress) and with (100 µM) Pb concentration. Our results revealed that Pb toxicity severely affected all rice growth-related traits, such as inhibited root fresh weight (42%), shoot length (24%), and chlorophyll b contents (26%). Moreover, a substantial amount of Pb was translocated to the above-ground parts of plants, which caused a disturbance in the antioxidative enzyme activities. However, the synergetic use of Fe- and Si–NPs reduced the Pb contents in the upper part of plants by 27%. It reduced the lethal impact of Pb on roots and shoots growth parameters by increasing shoot length (40%), shoot fresh weight (48%), and roots fresh weight (31%). Both Si and Fe–NPs synergistic application significantly elevated superoxide dismutase (SOD), peroxidase (POD), catalase (CAT), and glutathione (GSH) concentrations by 114%, 186%, 135%, and 151%, respectively, compared to plants subjected to Pb stress alone. The toxicity of Pb resulted in several cellular abnormalities and altered the expression levels of metal transporters and antioxidant genes. We conclude that the synergistic application of Si and Fe-NPs can be deemed favorable, environmentally promising, and cost-effective for reducing Pb deadliness in rice crops and reclaiming Pb-polluted soils. [ABSTRACT FROM AUTHOR]

In recent years, alcohol addiction has become a major public health concern and a global threat due to its potential negative health and social impacts. Beyond the health consequences, the detrimental consumption of alcohol results in substantial social and economic burdens on both individuals and society as a whole. Therefore, a proper understanding and effective control of the spread of alcohol addictive behavior has become an appealing global issue to be solved. In this study, we develop a new mathematical model of alcohol addiction with treatment class. We analyze the dynamics of the alcohol addiction model for the first time using advanced operators known as fractal–fractional operators, which incorporate two distinct fractal and fractional orders with the well-known Caputo derivative based on power law kernels. The existence and uniqueness of the newly developed fractal–fractional alcohol addiction model are shown using the Picard–Lindelöf and fixed point theories. Initially, a comprehensive qualitative analysis of the alcohol addiction fractional model is presented. The possible equilibria of the model and the threshold parameter called the reproduction number are evaluated theoretically and numerically. The boundedness and biologically feasible region for the model are derived. To assess the stability of the proposed model, the Ulam–Hyers coupled with the Ulam–Hyers–Rassias stability criteria are employed. Moreover, utilizing effecting numerical schemes, the models are solved numerically and a detailed simulation and discussion are presented. The model global dynamics are shown graphically for various values of fractional and fractal dimensions. The present study aims to provide valuable insights for the understanding the dynamics and control of alcohol addiction within a community. [ABSTRACT FROM AUTHOR]