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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.

This paper studies the optimal decision-making and coordination problem of a dual-channel fresh agricultural product (FAP) supply chain. The purpose is to analyze the impact of information sharing on optimal decisions and propose a coordination mechanism to encourage supply chain members to share information.

The two-echelon dual-channel FAP supply chain includes a manufacturer and a retailer. By using the Stackelberg game theory and the backward induction method, the optimal decisions are obtained under information symmetry and asymmetry and the coordination contract is designed.

The results show that supply chain members should comprehensively evaluate the specific situation of product attributes, coefficient of freshness-keeping cost and network operating costs to make decisions. Asymmetric information can exacerbate the deviation of optimal decisions among supply chain members and information sharing is always beneficial to manufacturers but not to retailers. The improved revenue-sharing and cost-sharing contract is an effective coordination mechanism.

The conclusions can provide theoretical guidance for supply chain managers to deal with information asymmetry and improve the competitiveness of the supply chain.

This paper combines the three characteristics that are most closely related to the reality of supply chains, including horizontal and vertical competition of different channels, the perishable characteristics of FAPs and the uncertainty generated by asymmetric demand information.

To explore how the blockchain affects the pricing and financing decisions in a low-carbon platform supply chain.

Considering the dual roles of the e-commerce platform as a seller and an initiator, a typical game-theoretical method is applied to analyze the behavior of supply chain decision-makers and the impact of key variables on equilibriums.

When loan interest rates are symmetric, whether blockchain is used or not, the e-commerce platform financing mode will always produce higher wholesale price and unit carbon emission reduction, while the retail price is the opposite. Higher unit additional income brought by the blockchain can bring higher economic and environmental performances, and the e-commerce platform financing mode is superior to bank financing mode. The application of blockchain may cause the manufacturer to change his/her financing choice. For bank financing, with the increase of loan interest rates, the advantages brought by blockchain will gradually disappear, but this situation will not occur under e-commerce platform financing.

Blockchain is known for its information transparency properties and its ability to enhance user trust. However, the impacts of applying blockchain in a low-carbon platform supply chain with different financing options are not clear. The authors examine the manufacturer's strategic choices for platform financing and bank financing, whether to adopt blockchain, and the impact of these decisions on carbon emissions reduction, consumer surplus and social welfare. The research conclusion can provide reference for the operation and financing decisions of platform supply chain under the carbon reduction target in the digital economy era.

This research focuses on the controlling irreversibilities in a radiative, chemically reactive electromagnetohydrodynamics (EMHD) flow of a nanofluid toward a stagnation point. Key considerations include the presence of Ohmic dissipation, linear thermal radiation, second-order chemical reaction with the multiple slips. With these factors, this study aims to provide insights for practical applications where thermal management and energy efficiency are paramount.

Lie group transformation is used to revert the leading partial differential equations into nonlinear ODE form. Hence, the solutions are attained analytically through differential transformation method-Padé and numerically using the Runge–Kutta–Fehlberg method with shooting procedure, to ensure the precise and reliable determination of the solution. This dual approach highlights the robustness and versatility of the methods.

The system’s entropy generation is enhanced by incrementing the magnetic field parameter (M), while the electric field (E) and velocity slip parameters (ξ) control its growth. Mass transportation irreversibility and the Bejan number (Be) are significantly increased by the chemical reaction rate (C_r). In addition, there is a boost in the rate of heat transportation by 3.66% while 0.05⩽ξ⩽0.2; meanwhile for 0.2⩽ξ⩽1.1, the rate of mass transportation gets enhanced by 12.87%.

This paper presents a novel approach to analyzing the entropy optimization in a radiative, chemically reactive EMHD nanofluid flow near a stagnation point. Moreover, this research represents a significant advancement in the application of analytical techniques, complemented by numerical approaches to study boundary layer equations.

Food quality and safety issues have always been imperative topics discussed by people. The anti-tampering of blockchain technology and the transparency of information make it possible to improve food traceability and safety quality. How to effectively apply blockchain traceability technology to food safety has great research significance for improving food safety and consumer quality trust.

The paper aims to analyze the differences in product quality levels and market participants’ profits before and after the use of blockchain-driven traceability technology in the food agricultural product supply chain (SC) in the dynamic game frameworks of supplier-led and retailer-led modes, respectively, and explores the willingness, social welfare and consumer surplus of each member of the agricultural product SC to participate in the blockchain. Besides, We investigate the SC performance improvement with the mechanism of central centralized decision-making and revenue-sharing contract, compared to the SC performance in dynamic games.

The results are obtained as follow: The adoption of blockchain traceability technology can help improve the quality of food agricultural products, consumer surplus and social welfare, but the application and popularization of technology is hindered by traceability technology installment costs. Compared with the supplier leadership model, retailer-led food quality level, customer surplus and social welfare are higher.

How to effectively apply blockchain traceability technology to food safety has great research significance for improving food safety and consumer quality trust.

Food quality and safety issues have always been hot topics discussed by people. The anti-tampering of blockchain technology and the transparency of information make it possible to improve food traceability and safety quality.

The research results enrich the theories related to food safety and quality, and provide a valuable reference for food enterprises involved in the decision-making exploration of blockchain technology.

Based on the characteristics of blockchain technology, the demand function is adjusted and the product loss risk of channel members is transferred through a Stackelberg game SC composed of agricultural products suppliers and retailers.

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  We introduce two features of blockchain: quality trust and product information tracking.

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  The willingness of each member of the supply chain to use blockchain for product traceability was explored.

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  The overall traceability effect of the retailer-led blockchain is better than that of the manufacturer-led blockchain.

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  The cost of blockchain technology is a barrier to its adoption.

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  Blockchain brings higher consumer surplus and social welfare.

We introduce two features of blockchain: quality trust and product information tracking.

The willingness of each member of the supply chain to use blockchain for product traceability was explored.

The overall traceability effect of the retailer-led blockchain is better than that of the manufacturer-led blockchain.

The cost of blockchain technology is a barrier to its adoption.

Blockchain brings higher consumer surplus and social welfare.

The purpose of this study is to investigate the interplay between fiscal dominance and monetary policy in South Africa from 1960 to 2023.

The study employs a structural vector autoregression (SVAR) medel to analyze the relationship between fiscal dominance and monetary policy. Short-term and long-term shocks of government borrowing and deficits are examined to understand their impact on inflation dynamics.

Fiscal dominance has a significant effect both in the short and long run. There is evidence that government debt and deficits increase inflation, overriding the effects of monetary policy aimed at maintaining price stability. On the other hand, the study reveals that money supply shocks have a greater effect in reducing fiscal dominance compared to interest rate shocks. The variance movement on inflation is significantly explained by government debt and deficits. This emphasizes the persistence of inflationary pressures associated with fiscal dominance, highlighting the importance of effective policy interventions to mitigate inflationary risks.

This study contributes to the existing literature by providing insights into the dynamics of fiscal dominance in South Africa. Moreover, this study extends the theoretical framework of the fiscal theory of the price level (FTPL) and the government budget constraint. This study contributes valuable insights into the dynamics of fiscal dominance in South Africa and offers guidance for policymakers in formulating strategies to safeguard economic stability.

This paper aims to present a study on stability analysis of Jeffrey fluids in the presence of emergent chemical gradients within microbial systems of anisotropic porous media.

This study uses an effective method that combines non-dimensionalization, normal mode analysis and linear stability analysis to examine the stability of Jeffrey fluids in the presence of emergent chemical gradients inside microbial systems in anisotropic porous media. The study focuses on determining critical values and understanding how temperature gradients, concentration gradients and chemical reactions influence the onset of bioconvection patterns. Mathematical transformations and analytical approaches are used to investigate the system’s complicated dynamics and the interaction of numerous characteristics that influence stability.

The analysis is performed using the Jeffrey-Darcy type and Boussinesq estimation. The process involves using non-dimensionalization, using the normal mode approach and conducting linear stability analysis to convert the field equations into ordinary differential equations. The conventional thermal Rayleigh Darcy number RDa,c is derived as a comprehensive function of various parameters, and it remains unaffected by the bio convection Lewis number Łe. Indeed, elevating the values of ζ and γ′ in the interval of 0 to 1 has been noted to expedite the formation of bioconvection patterns while concurrently expanding the dimensions of convective cells. The purpose of this investigation is to learn how the temperature gradient affects the concentration gradient and, in turn, the stability and initiation of bioconvection by taking the Soret effect into the equation. The results provide insightful understandings of the intricate dynamics of fluid systems affected by chemical and biological elements, providing possibilities for possible industrial and biological process applications. The findings illustrate that augmenting both microbe concentration and the bioconvection Péclet number results in an unstable system. In this study, the experimental Rayleigh number RDa,c was determined to be 4π2at the critical wave number ( δcˇ) of π.

The study’s novelty originated from its investigation of a novel and complicated system incorporating Jeffrey fluids, emergent chemical gradients and anisotropic porous media, as well as the use of mathematical and analytical approaches to explore the system’s stability and dynamics.

This study investigates the influence of nonfinancial 8-K disclosures released during the earnings announcement window on the abnormal trading activities of individual investors.

We employ regression analysis in this empirical study to examine the impact of nonfinancial 8-K filings on individual investors' abnormal trading activities.

Our results reveal that individual investors exhibit higher levels of abnormal trading activities when firms release nonfinancial 8-Ks during the (0,1) window of earnings announcements. This effect is observed for both buyer-initiated and seller-initiated transactions and is particularly pronounced for firms reporting an operating loss. Negative sentiment in 8-Ks significantly intensifies such effect. Additionally, we find that buy-sell consensus increases significantly with concurrent nonfinancial 8-Ks. This suggests that 8-Ks may reduce information noise, leading individuals to trade with greater conviction.

Our study examines the joint influence of nonfinancial 8-Ks and earnings announcements on individual investors' trading activities, thereby providing a novel perspective on the mechanisms through which 8-K filings affect individual investors' trading behaviors.

Omnichannel sales have provided new impetus for the development of catering merchants. The authors thus focus on how catering merchants should manage capacities at the ordering, production and delivery stages to meet customers’ needs in different channels under third-party platform delivery and merchant self-delivery. This is of great significance for the development of the omnichannel catering industry.

This paper formulates the capacity decisions of omnichannel catering merchants under the third-party platform delivery and merchant self-delivery mode. The authors mainly use queuing theory to analyze the queuing behavior of online and offline customers, and the impact of waiting time on customer shopping behavior. In addition, the authors also characterize the merchant’s capacity by the rate in queuing model.

The authors find that capacities at ordering stage and food production stage are composed of base capacities and safety capacities, but the delivery capacities only have the latter. And in the self-delivery mode, merchants can develop higher safety capacities by charging delivery fees. The authors prove that regardless of the delivery mode, omnichannel sales can bring higher profits to merchants by integrating demand.

The authors focus on analyzing the capacity management of omnichannel catering merchants at the ordering, production and delivery stages. And the authors also add the delivery process into the omnichannel for analysis, so as to solve the problem of capacity decision-making under different delivery modes. The management of delivery capacity and its impact on other stages’ capacities are not covered in other literature studies, which is one of the main innovations of this paper.

The purpose of this study is to develop a novel general mathematical model to find the optimal product mix of commercial graphite products, which has a complex production process with alternative sub-processes in the graphite mining production process.

The network optimization was adopted to model the complex graphite mining production process through the optimal allocation of raw graphite, byproducts, and saleable products with comparable sub-processes, which has different processing capacities and costs. The model was tested on a selected graphite manufacturing company, and the optimal graphite product mix was determined through the selection of the optimal production process. In addition, sensitivity and scenario analyses were carried out to accommodate uncertainties and to facilitate further managerial decisions.

The selected graphite mining company mines approximately 400 metric tons of raw graphite per month to produce ten types of graphite products. According to the optimum solution obtained, the company should produce only six graphite products to maximize its total profit. In addition, the study demonstrated how to reveal optimum managerial decisions based on optimum solutions.

This study has made a significant contribution to the graphite manufacturing industry by modeling the complex graphite mining production process with a network optimization technique that has yet to be addressed at this level of detail. The sensitivity and scenario analyses support for further managerial decisions.