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The purpose of this study is to investigate the nonlinear Schrödinger equation (NLS) incorporating spatiotemporal dispersion and other dispersive effects. The goal is to derive various soliton solutions, including bright, dark, singular, periodic and exponential solitons, to enhance the understanding of soliton propagation dynamics in nonlinear metamaterials (MMs) and contribute new findings to the field of nonlinear optics.

The research uses a range of powerful mathematical approaches to solve the NLS. The proposed methodologies are applied systematically to derive a variety of optical soliton solutions, each demonstrating unique optical behaviors and characteristics. The approach ensures that both the theoretical framework and practical implications of the solutions are thoroughly explored.

The study successfully derives several types of soliton solutions using the aforementioned mathematical approaches. Key findings include bright optical envelope solitons, dark optical envelope solitons, periodic solutions, singular solutions and exponential solutions. These results offer new insights into the behavior of ultrashort solitons in nonlinear MMs, potentially aiding further research and applications in nonlinear wave studies.

This study makes an original contribution to nonlinear optics by deriving new soliton solutions for the NLS with spatiotemporal dispersion. The diversity of solutions, including bright, dark, periodic, singular and exponential solitons, adds substantial value to the existing body of knowledge. The use of distinct and reliable methodologies to obtain these solutions underscores the novelty and potential applications of the research in advancing optical technologies. The originality lies in the novel approaches used to obtain these diverse soliton solutions and their potential impact on the study and application of nonlinear waves in MMs.

Experts may adjust their assessments through communication and mutual influence, and this dynamic evolution relies on the spread of internal trust relationships. Due to differences in educational backgrounds and knowledge experiences, trust relationships among experts are often incomplete. To address such issues and reduce decision biases, this paper proposes a probabilistic linguistic multi-attribute group decision consensus model based on an incomplete social trust network (InSTN).

In this paper, we first define the new trust propagation operators based on the operations of Probability Language Term Set (PLTS) with algebraic t-conorm and t-norm, which are combined with trust aggregation operators to estimate InSTN. The adjustment coefficients are then determined through trust relations to quantify their impact on expert evaluation. Finally, the particle swarm algorithm (PSO) is used to optimize the expert evaluation to meet the consensus threshold.

This study demonstrates the feasibility of the method through the selection of treatment plans for complex cases. The proposed consensus model exhibits greater robustness and effectiveness compared to traditional methods, mainly due to the effective regulation of trust relations in the decision-making process, which reduces decision bias and inconsistencies.

This paper introduces a novel probabilistic linguistic multi-attribute swarm decision consensus model based on an InSTN. It proposes a redefined trust propagation and aggregation approach to estimate the InSTN. Moreover, the computational efficiency and decision consensus accuracy of the proposed model are enhanced by using PSO optimization.

The main objective of the present investigation is to develop a novel efficient stochastic model for availability optimization of reverse osmosis machine system (ROMS) for water purification under the concepts of exponentially distributed decision variables and various redundancy strategies at the component level.

ROMS is a complex framework configured in a series structure using six subsystems. Initially, a state transition diagram is developed and Chapman–Kolmogorov differential-difference equations are derived using Markov birth death process. The steady-state availability of the ROMS is derived for a particular case. The impact of variation in failure and repair rates measured on availability. Furthermore, an effort is made to predict the optimal availability of the ROMS system using the metaheuristic algorithms, namely, dragonfly algorithm (DA), grasshopper optimization algorithm (GOA) and whale optimization algorithm (WOA).

It is observed that the ROMS system predicts optimal availability of 0.999926 after five iterations with a population size of 300 by the WOA. The findings of this study are significant for reliability engineers as well as for maintenance engineers to ensure the availability of ROMS for water purification.

In the present investigation, a novel stochastic model is developed for ROMS, and metaheuristics algorithms are applied to predict the optimal availability.

There are various uncertain and nonlinear problems in hydraulic legged robot systems, including parameter uncertainty, unmodeled dynamics and external disturbances. This study aims to eliminate uncertainties and improve the foot trajectory tracking control performance of hydraulic legged robots, a high-performance foot trajectory tracking control method based on fixed-time disturbance observers for hydraulic legged robots is proposed.

First, the robot leg mechanical system model and hydraulic system model of the hydraulic legged robot are established. Subsequently, two fixed-time disturbance observers are designed to address the unmatched lumped uncertainty and match lumped uncertainty in the system. Finally, the lumped uncertainties are compensated in the controller design, and the designed motion controller also achieves fixed-time stability.

Through simulation and experiments, it can be found that the proposed tracking control method based on fixed-time observers has better tracking control performance. The effectiveness and superiority of the proposed method have been verified.

Both the disturbance observers and the controller achieve fixed-time stability, effectively improving the performance of foot trajectory tracking control for hydraulic legged robots.

Megaproject supply chains involve multiple layers of stakeholders, leading to complex relationships and risks. The role of social interactions within these networks is unexplored. Therefore, an analysis of construction supply chain risk management from the perspective of social networks is essential to identify related stakeholders, their relationships and the social network risk factors.

About 65 risk factors, identified from literature and interviews, informed the development of a questionnaire for the study. Online questionnaires administered in Ghana and South Africa produced 120 valid responses. Feedback from the responses was ranked and assessed to determine the overall social network risk levels using the Normalised Mean and Fuzzy synthesis analysis methods.

About 24 risk factors were identified and classified into six groups: Client/Consultant-related, Community-related, Government-related, Industry Perception-related, Supplier-related and Stakeholder Opportunism. The top five social network risks identified include bribery, supplier monopoly, incomplete design teams, poor communication and lack of collaboration.

The study provides detailed evaluations of social network risks in Africa, and the findings will help in developing strategies to mitigate supply chain disruptions caused by these challenges.

This study contributes to the literature on supply chain risk management by offering context-specific insights into the social network perspective of megaprojects in Africa, which differs from those in developed countries.

This study explores the immobilisation of enzymes within porous catalysts of various geometries, including spheres, cylinders and flat pellets. The objective is to understand the irreversible Michaelis-Menten kinetic process within immobilised enzymes through advanced mathematical modelling.

Mathematical models were developed based on reaction-diffusion equations incorporating nonlinear variables associated with Michaelis-Menten kinetics. This research introduces fractional derivatives to investigate enzyme reaction kinetics, addressing a significant gap in the existing literature. A novel approximation method, based on the independent polynomials of the complete bipartite graph, is employed to explore solutions for substrate concentration and effectiveness factor across a spectrum of parameter values. The analytical solutions generated through the bipartite polynomial approximation method (BPAM) are rigorously tested against established methods, including the Bernoulli wavelet method (BWM), Taylor series method (TSM), Adomian decomposition method (ADM) and fourth-order Runge-Kutta method (RKM).

The study identifies two main findings. Firstly, the behaviour of dimensionless substrate concentration with distance is analysed for planar, cylindrical and spherical catalysts using both integer and fractional order Michaelis-Menten modelling. Secondly, the research investigates the variability of the dimensionless effectiveness factor with the Thiele modulus.

The study primarily focuses on mathematical modelling and theoretical analysis, with limited experimental validation. Future research should involve more extensive experimental verification to corroborate the findings. Additionally, the study assumes ideal conditions and uniform catalyst properties, which may not fully reflect real-world complexities. Incorporating factors such as mass transfer limitations, non-uniform catalyst structures and enzyme deactivation kinetics could enhance the model’s accuracy and broaden its applicability. Furthermore, extending the analysis to include multi-enzyme systems and complex reaction networks would provide a more comprehensive understanding of biocatalytic processes.

The validated bipartite polynomial approximation method presents a practical tool for optimizing enzyme reactor design and operation in industrial settings. By accurately predicting substrate concentration and effectiveness factor, this approach enables efficient utilization of immobilised enzymes within porous catalysts. Implementation of these findings can lead to enhanced process efficiency, reduced operating costs and improved product yields in various biocatalytic applications such as pharmaceuticals, food processing and biofuel production. Additionally, this research fosters innovation in enzyme immobilisation techniques, offering practical insights for engineers and researchers striving to develop sustainable and economically viable bioprocesses.

The advancement of enzyme immobilisation techniques holds promise for addressing societal challenges such as sustainable production, environmental protection and healthcare. By enabling more efficient biocatalytic processes, this research contributes to reducing industrial waste, minimizing energy consumption and enhancing access to pharmaceuticals and bio-based products. Moreover, the development of eco-friendly manufacturing practices through biocatalysis aligns with global efforts towards sustainability and mitigating climate change. The widespread adoption of these technologies can foster a more environmentally conscious society while stimulating economic growth and innovation in biotechnology and related industries.

This study offers a pioneering approximation method using the independent polynomials of the complete bipartite graph to investigate enzyme reaction kinetics. The comprehensive validation of this method through comparison with established solution techniques ensures its reliability and accuracy. The findings hold promise for advancing the field of biocatalysts and provide valuable insights for designing efficient enzyme reactors.

Recent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation.

The mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome.

The velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs).

Additionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry.

The originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers.

Analyses the emergence of tortious liability on solicitors and the damages awarded against them for negligence in preparing wills, ie testamentary disposition, when this causes losses to beneficiaries recognisable in law; it is no longer the case that actions by clients against solicitors are always for breach of contract. Traces how negligence has been established as an independent tort, and shows how absence of privity does not debar a claim. Discusses the landmark case of Ross v Caunters, which showed that liability could be to a third party, ie the beneficiary of a will that was made void by solicitor negligence; discusses how the duty of care was ascertained in this and other cases. Outlines the control mechanisms that a third party has to prove before a court decides that a solicitor is liable: reliance on the solicitor, whether there is a causal link between negligence and loss, proximity and foreseeability; there is also the concept of fair, just and reasonable. Covers lastly the issues of unjust enrichment of unintended beneficiaries, professional indemnity insurance, social policy objectives for awarding damages, and the bounds of liability.

Discusses how important perceptions of tax fairness can be in forming tax‐compliant behaviour in various jurisdictions, based on a crosscultural study of Australia and Hong Kong. Defines fairness and its relationship with legitimacy. Describes a tax survey questionnaire administered to business students, which is broken down by demographic data and includes extensive correlations between tax‐fairness perception and tax‐compliance behaviour. Concludes that legitimacy is a crucial normative influence in shaping how fair tax systems are perceived to be and how likely people are to comply with their tax obligations.