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This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.

The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.

This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.

The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.

This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.

The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.

This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.

Green innovation in supply chains is crucial for socioeconomic development and stability. Factors that influence collaborative green innovation in the supply chain are complex and diverse. Exploring the main influencing factors and their mechanisms is essential for promoting collaborative green innovation in supply chains. Therefore, this study analyzes how upstream and downstream enterprises in the supply chain collaborate to develop green technological innovations, thereby providing a theoretical basis for improving the overall efficiency of the supply chain and advancing green innovation technology.

Based on evolutionary game theory, this study divides operational scenarios into pure market and government-regulated operations, thereby constructing collaborative green innovation relationships in different scenarios. Through evolutionary analysis of various entities in different operational scenarios, combined with numerical simulation analysis, we compared the evolutionary stability of collaborative green innovation behavior in supply chains with and without government regulation.

Under pure market mechanisms, the higher the green innovation capability, the stronger the willingness of various entities to collaborate in green innovation. However, under government regulation, a decrease in green innovation capability increases the willingness to collaborate with various entities. Environmental tax rates and green subsidy levels promote collaborative innovation in the short term but inhibit collaborative innovation in the long term, indicating that policy orientation has a short-term impact. Additionally, the greater the penalty for collaborative innovation breaches, the stronger the intention to engage in collaborative green innovation in the supply chain.

We introduce the factors influencing green innovation capability and social benefits in the study of the innovation behavior of upstream and downstream enterprises, expanding the research field of collaborative innovation in the supply chain. By comparing the collaborative innovation behavior of various entities in the supply chain under a pure market scenario and government regulations, this study provides a new perspective for analyzing the impact of corresponding government policies on the green innovation capability of upstream and downstream enterprises, enriching theoretical research on green innovation in the supply chain to some extent.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

This study aims to minimize the cost and time of blood delivery in the whole blood supply chain network (BSCN) in disaster conditions. In other words, integrating all strategic, tactical and operational decisions of three levels of blood collection, processing and distribution leads to satisfying the demand at the right time.

This paper proposes an integrated BSCN in disaster conditions to consider four categories of facilities, including temporary blood collection centers, field hospitals, main blood processing centers and medical centers, to optimize demand response time appropriately. The proposed model applies the location of all permanent and emergency facilities in three levels: blood collection, processing and distribution. Other essential decisions, including multipurpose facilities, emergency transportation, inventory and allocation, were also used in the model. The LP metric method is applied to solve the proposed bi-objective mathematical model for the BSCN.

The findings show that this model clarifies its efficiency in the total cost and blood delivery time reduction, which results in a low carbon transmission of the blood supply chain.

The researchers proposed an integrated BSCN in disaster conditions to minimize the cost and time of blood delivery. They considered multipurpose capabilities for facilities (e.g. field hospitals are responsible for the three purposes of blood collection, processing and distribution), and so locating permanent and emergency facilities at three levels of blood collection, processing and distribution, support facilities, emergency transportation and traffic on the route with pollution were used to present a new model.

This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems.

Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given.

This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices.

A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

The purpose of this paper is to study an extended hierarchy of nonlinear evolution equations including the sixth-order dispersion Korteweg–de Vries (KdV6), eighth-order dispersion KdV (KdV8) and many other related equations.

The newly developed models have been handled using the simplified Hirota’s method, whereas multiple soliton solutions are furnished using Hirota’s criteria.

The authors show that every member of this hierarchy is characterized by distinct dispersion relation and distinct resonance branches, whereas the phase shift retains the KdV type of shifts for any member.

This paper presents an efficient algorithm for handling a hierarchy of integrable equations of diverse orders.

Multisoliton solutions are derived for each member of the hierarchy, and then generalized for any higher-order model.

This work presents useful algorithms for finding and studying integrable equations of a hierarchy of nonlinear equations. The developed models exhibit complete integrability, by investigating the compatibility conditions for each model.

This paper presents an original work with a variety of useful findings.

This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.

The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.

The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.

The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.

As supply chain excellence matters, designing an appropriate health-care supply chain is a great consideration to the health-care providers worldwide. Therefore, the purpose of this paper is to benchmark several potential health-care supply chains to design an efficient and effective one in the presence of mixed data.

To achieve this objective, this research illustrates a hybrid algorithm based on data envelopment analysis (DEA) and goal programming (GP) for designing real-world health-care supply chains with mixed data. A DEA model along with a data aggregation is suggested to evaluate the performance of several potential configurations of the health-care supply chains. As part of the proposed approach, a GP model is conducted for dimensioning the supply chains under assessment by finding the level of the original variables (inputs and outputs) that characterize these supply chains.

This paper presents an algorithm for modeling health-care supply chains exclusively designed to handle crisp and interval data simultaneously.

The outcome of this study will assist the health-care decision-makers in comparing their supply chains against peers and dimensioning their resources to achieve a given level of productions.

A real application to design a real-life pharmaceutical supply chain for the public ministry of health in Morocco is given to support the usefulness of the proposed algorithm.

The novelty of this paper comes from the development of a hybrid approach based on DEA and GP to design an appropriate real-life health-care supply chain in the presence of mixed data. This approach definitely contributes to assist health-care decision-makers design an efficient and effective supply chain in today’s competitive word.