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The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

This study proposes a predictive neural network model reference decoupling control method for the coupling problem between the leg joints of hydraulic quadruped robots, and verifies its decoupling effect..

The machine–hydraulic cross-linking coupling is studied as the coupling behavior of the hydraulically driven quadruped robot, and the mechanical dynamics coupling force of the robot system is controlled as the disturbance force of the hydraulic system through the Jacobian matrix transformation. According to the principle of multivariable decoupling, a prediction-based neural network model reference decoupling control method is proposed; each module of the control algorithm is designed one by one, and the stability of the system is analyzed by the Lyapunov stability theorem.

The simulation and experimental research on the robot joint decoupling control method is carried out, and the prediction-based neural network model reference decoupling control method is compared with the decoupling control method without any decoupling control method. The results show that taking the coupling effect experiment between the hip joint and knee joint as an example, after using the predictive neural network model reference decoupling control method, the phase lag of the hip joint response line was reduced from 20.3° to 14.8°, the amplitude attenuation was reduced from 1.82% to 0.21%, the maximum error of the knee joint coupling line was reduced from 0.67 mm to 0.16 mm and the coupling effect between the hip joint and knee joint was reduced from 1.9% to 0.48%, achieving good decoupling.

The prediction-based neural network model reference decoupling control method proposed in this paper can use the neural network model to predict the next output of the system according to the input and output. Finally, the weights of the neural network are corrected online according to the predicted output and the given reference output, so that the optimization index of the neural network decoupling controller is extremely small, and the purpose of decoupling control is achieved.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

Throughout human history, the occurrence of disasters has been inevitable, leading to significant human, financial and emotional consequences. Therefore, it is crucial to establish a well-designed plan to efficiently manage such situations when disaster strikes. The purpose of this study is to develop a comprehensive program that encompasses multiple aspects of postdisaster relief.

A multiobjective model has been developed for postdisaster relief, with the aim of minimizing social dissatisfaction, economic costs and environmental damage. The model has been solved using exact methods for different scenarios. The objective is to achieve the most optimal outcomes in the context of postdisaster relief operations.

A real case study of an earthquake in Haiti has been conducted. The acquired results and subsequent management analysis have effectively assessed the logic of the model. As a result, the model’s performance has been validated and deemed reliable based on the findings and insights obtained.

Ultimately, the model provides the optimal quantities of each product to be shipped and determines the appropriate mode of transportation. Additionally, the application of the epsilon constraint method results in a set of Pareto optimal solutions. Through a comprehensive examination of the presented solutions, valuable insights and analyses can be obtained, contributing to a better understanding of the model’s effectiveness.

The purpose of this paper is to investigate the impact of near-wall treatment approaches, which are crucial parameters in predicting the flow characteristics of open channels, and the influence of different vegetation covers in different layers.

Ansys Fluent, a computational fluid dynamics software, was used to calculate the flow and turbulence characteristics using a three-dimensional, turbulent (k-e realizable), incompressible and steady-flow assumption, along with various near-wall treatment approaches (standard, scalable, non-equilibrium and enhanced) in the vegetated channel. The numerical study was validated concerning an experimental study conducted in the existing literature.

The numerical model successfully predicted experimental results with relative error rates below 10%. It was determined that nonequilibrium wall functions exhibited the highest predictive success in experiment Run 1, standard wall functions in experiment Run 2 and enhanced wall treatments in experiment Run 3. This study has found that plant growth significantly alters open channel flow. In the contact zones, the velocities and the eddy viscosity are low, while in the free zones they are high. On the other hand, the turbulence kinetic energy and turbulence eddy dissipation are maximum at the solid–liquid interface, while they are minimum at free zones.

This is the first study, to the best of the author’s knowledge, concerning the performance of different near-wall treatment approaches on the prediction of vegetation-covered open channel flow characteristics. And this study provides valuable insights to improve the hydraulic performance of open-channel systems.

The purpose of this paper is to solve the challenging problem of automatic carrier landing with the presence of environmental disturbances. Therefore, a global fast terminal sliding mode control (GFTSMC) method is proposed for automatic carrier landing system (ACLS) to achieve safe carrier landing control.

First, the framework of ACLS is established, which includes flight glide path model, guidance model, approach power compensation system and flight controller model. Subsequently, the carrier deck motion model and carrier air-wake model are presented to simulate the environmental disturbances. Then, the detailed design steps of GFTSMC are provided. The stability analysis of the controller is proved by Lyapunov theorems and LaSalle’s invariance principle. Furthermore, the arrival time analysis is carried out, which proves the controller has fixed time convergence ability.

The numerical simulations are conducted. The simulation results reveal that the proposed method can guarantee a finite convergence time and safe carrier landing under various conditions. And the superiority of the proposed method is further demonstrated by comparative simulations and Monte Carlo tests.

The GFTSMC method proposed in this paper can achieve precise and safe carrier landing with environmental disturbances, which has important referential significance to the improvement of ACLS controller designs.

This chapter of the book aims to introduce multiobjective linear programming (MLP) as an optimum tool to find the best quality engineering techniques (QET) in the main domains of supply chain management (SCM). The importance of finding the best quality techniques in SCM elements in the shortest possible time and at the least cost allows all organizations to increase the power of experts’ analysis in supply chain network (SCN) data under cost-effective conditions. In other words, this chapter aims to introduce an operations research model by presenting MLP for obtaining the best QET in the main domains of SCM. MLP is one of the most determinative tools in this chapter that can provide a competitive advantage. Under goal and system constraints, the most challenging task for decision-makers (DMs) is to decide which components to fund and at what levels. The definition of a comprehensive target value among the required goals and determining system constraints is the strength of this chapter. Therefore, this chapter can guide the readers to extract the best statistical and non-statistical techniques with the application of an operations research model through MLP in supply chain elements and shows a new innovation of the effective application of operations research approach in this field. The analytic hierarchy process (AHP) is a supplemental tool in this chapter to facilitate the relevant decision-making process.

The purpose of this paper is to study the spillover effects of foreign direct investment (FDI) on skilled–unskilled wage inequality in the Indian manufacturing industries.

The authors show theoretically with a model of spillover that if foreign firms (receiving FDI) have a negative spillover effect on domestic firms (not receiving FDI), then the level of capital and skilled workers in the domestic firms falls down. Consequently, the authors conduct an empirical analysis by using system GMM estimation technique on the firm-level data of the Indian organised manufacturing sector.

The authors show that wage inequality worsens when there is negative spillover effects like competition spillover or skill spillover effect of FDI in India.

To the best of the authors’ knowledge, this is the first attempt to measure the various spillover effects of FDI on the wage inequality in the Indian manufacturing industries by using firm-level data.

Pre-positioning and distributing relief items are important parts of disaster management as it simultaneously considers activities from both pre- and post-disaster stages. This study aims to address this problem with a novel mathematical model.

In this research, a bi-objective mixed-integer linear programming model is developed to tackle pre-positioning and distributing relief items, and it is formulated as an integrated location-allocation-routing problem with uncertain parameters. The humanitarian supply chain consists of relief facilities (RFs) and demand points (DPs). Perishable and imperishable relief commodities (RCs), different types of vehicles, different transportation modes, a time window for delivering perishable commodities and the occurrence of unmet demand are considered. A scenario-based game theory is applied for purchasing RCs from different suppliers and an integrated best-worst method-technique for order of preference by similarity to ideal solution technique is implemented to determine the importance of DPs. The proposed model is used to solve several random test problems for verification, and to validate the model, Iran’s flood in 2019 is investigated as a case study for which useful managerial insights are provided.

Managers can effectively adjust their preferences towards response time and total cost of the network and use sensitivity analysis results in their decisions.

The model locates RFs, allocates DPs to RFs in the pre-disaster stage, and determines the routing of RCs from RFs to DPs in the post-disaster stage with respect to minimizing total costs and response time of the humanitarian logistics network.

Motivated by the wide application of procurement strategies in retailing, this paper aims to examine the effect of procurement strategies on decisions and profits and strategic inventory (SI) is considered.

The game-theoretic models are developed under a two-period fresh product supply chain (FSC), and consist of the mode of purchasing products only in the first period without SI (Scenario S), the mode of purchasing products in every period without SI (Scenario T) and the mode of purchasing products in every period with SI (Scenario TS).

Conducting the calculating and comparing, some major findings can be concluded. In general, two-period purchasing strategies (Scenarios T and TS) promote a higher freshness-keeping effort than the single buying strategy (Scenario S). Regarding the pricing strategy, SI and Scenario S can both contribute to obtaining a lower wholesale price, the retailer's pricing is relatively complicated and hinges on the consumer's sensitivity to freshness-keeping effort and the holding cost. Besides, comparing the sales quantity and the profit, the authors find that Scenario TS stimulates more demands and brings more profits for the manufacturer. However, Scenario TS is not the optimal selection for the reason that SI sometimes hurts the retailer and even the whole supply chain. Whereas, when the holding cost is in a certain range, Scenario TS will lead to a win-win situation.

The main findings of this study can give the enterprises some advice on the procurement strategies of fresh products and the decisions of pricing and the freshness-keeping effort.