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We introduce three different classes of linguistic variables. Each of these classes can assume values defined via a fuzzy subset.

Omnichannel has become increasingly important with the development of e-commerce. In omnichannel, merchants expect customers to get the products and services at anytime, anywhere and in any way, and the same is true for customers. This drives multihoming in online platforms for both merchants and customers. Thus, once both customers and merchants are multihomed, what price and subsidy decisions should be made between platforms to compete to obtain optimal profits? The main purpose of this paper is to solve these problems and provide decision-making for two-sided platforms in omnichannel.

This study builds a dual Hotelling model to capture the utility and network effects of customers and merchants on two-sided platforms. This study introduces the exposure effect and convenience effect of multihomed customers and merchants in the model and analyzes the impact of these effects in the market with multihoming on one side. Then, this study extends the model to the market with multihoming on both sides and makes the pricing decision for two-sided platform when considering the exposure effect and convenience effect through an equilibrium solution. Finally, this study also uses numerical analysis to simulate the decision and profit of the platform.

This paper finds that the convenience effect will only increase social welfare when customers are single-homed and merchants are multihomed. In addition, when both users are multihomed, the platform will subsidize to attract merchants and customers if the convenience effect and exposure effect are relatively high. This study also finds that network effects come not only from the same platform but also from another platform in the case with multihoming on both sides. And network effects in the heterogeneous platform will be reduced by the convenience effect and exposure effect.

According to the behavioral characteristics of merchants and customers in omnichannel, this paper first adopts the dual Hotelling model to study the pricing of two-sided platforms with multihoming on both sides. This paper shows that network effects originate not only from the same platform but also from another platform and that the exposure effect and the convenience effect can exist as cross-platform network effects, which provides a new explanation for network effects in markets with multihoming on both sides. This research extends the theory of network effects and plays an important role in the development of two-sided platforms in omnichannel.

This paper aims to show the proposed energy method for inductance calculation is valid for any number of poles, phases and any winding layout.

A two-dimensional (2-D) analytical energy-based approach is presented to calculate self-inductances and mutual inductances of brushless surface-mounted permanent-magnet machines.

The proposed calculation procedure is valid for brushless permanent-magnet machines with slotted or slotless stator structure. Comparisons between energy method and flux linkage method are presented based on simulation and experimental results. It shows that the energy method has an excellent agreement with the result obtained from finite element method (FEM) and experimental study.

This paper compares energy-based method with flux linkage method and FEM for inductance calculations in slotless and slotted permanent-magnet motors. The relations for inductance calculation are presented which are obtained based on 2-D analytical representation of magnetic field.

The purpose of this paper is to find the optimal power structure that drives green practices in the supply chain and coordinate the costs and benefits of green practices in supply chain under different power structures.

This paper developed a supply chain of one supplier and one manufacturer, in which the supplier and the manufacturer are responsible for the “greening” of products. Then, the game theory modeling method is used to explore the influence of different power structures on green practices in the supply chain. Finally, the authors developed a green cost-sharing contract made by the leader; regarding optimal supply chain profits and green performance, the proposed contracts and the non-coordination situation are compared and tested by a numerical simulation.

The increase of the green practice difficulty of any member in the supply chain will not only reduce the greenness of products at that stage but will also reduce the green investment of the supply chain partner. Becoming a channel leader does not necessarily mean being more profitable than being a follower, and when the green practice difficulty of the leader is less than a certain threshold, ceding dominant power to the follower may benefit both sides. A green cost-sharing contract made by the leader is not necessarily beneficial to all enterprises.

This paper helps to better understand the role of the power relation in realizing the industry's green goals and helps decision-makers to achieve win-win cooperation by adjusting power relations and optimizing green cost-sharing contracts.

The purpose of this article is to determine the optimal use of collateral in order to maximize the borrower's wealth by reducing the interest rate payments. This analysis is to shed light on the fundamental question whether good or bad borrowers pledge more collateral.

The analysis bases on a simple firm value model similar to Merton's but with the additional feature that the borrower can bring in collateral. This article not only presents the case with perfect information between borrowers and lenders but also regards the consequences arising from asymmetric information.

A bad borrower, who is characterized by higher bankruptcy costs, riskier projects, and a lower contribution to the project value, typically pledges more collateral than a good borrower. These relationships base on the existence of perfect information between borrowers and lenders. If asymmetric information in terms of the project's riskiness or the contribution of the borrower to the project is present, these relationships invert and good borrowers tend to pledge more collateral. As a result, the allocation of information between a borrower and a lender is crucial for the optimal choice of collateral.

This research underlines the potential for firms to add firm value by pledging collateral because collateral reduces interest rates and therefore results in more attractive terms of the loan. On the other hand, further empirical research can be done to verify our theoretical finding that under perfect information bad borrowers pledge more collateral, while under asymmetric information primarily good borrowers use collateral.

This paper introduces a new motive for the use of collateral and explains – in contrast to many other theoretical models – why bad borrowers tend to pledge more collateral.

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology.

First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations.

This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space.

This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

Multi-robots simultaneously coverage and tracking (SCAT) is the problem of simultaneously covering area and tracking targets, which is essential for many applications, such as delivery service, environment monitor, traffic surveillance, crime monitor, anti-terrorist mission and so on. The purpose of this paper is to improve the performance of detected target quantity, coverage rate and less deadweight loss by designing a self-organized method for multi-robots SCAT.

A self-organized reciprocal control method is proposed, coupling task assignment, tracking and covering, equipped with collision-avoiding ability naturally. First, SCAT problem is directly modeled as optimal reciprocal coverage velocity (ORCV) in velocity space. Second, the preferred velocity is generated by calculating the best velocity to the center of some robot detected targets. ORCV is given by adjusting the velocity relative to neighbor robots’ toward in optimal coverage velocity (OCV); it is proven that OCV is collision-free assembly. Third, some corresponding algorithms are designed for finding optimal velocity under two situations, such as no detected targets and empty ORCV.

The simulation results of two cases for security robots show that the proposed method has detected more targets with less deadweight loss and decision time and no collisions anytime.

In this paper, a self-organized reciprocal control method is proposed for multi-robots SCAT problem, which is modeled in velocity space directly, different to the traditional method modeling in configuration space. What is more, this method considers the reciprocal of robots that contributes to the better accomplishment of SCAT cooperatively.

The purpose of this paper is to propose a seamless autonomous navigation method based on the motion constraint of the mobile robot, which is able to meet the practical need of maintaining the navigation accuracy during global positioning system (GPS) outages.

The seamless method uses the motion constraint of the mobile robot to establish the filter model of the system, in which the virtual observation about the speed is used to overcome the shortage of the navigation accuracy during GPS outages. The corresponding motion constraint model of the mobile robot is established. The proposed seamless navigation scheme includes two parts: the micro inertial navigation system (MINS)/GPS-integrated filter model and the motion constraint filter model. When the satellite signals are good, the system works on the MINS/GPS-integrated mode. If some obstacles block the GPS signals, the motion constraint measurement equation will be effective so as to improve the navigation accuracy of the mobile robot.

Three different vehicle tests of the mobile robot show that the seamless navigation method can overcome the shortage of the navigation accuracy during GPS outages, so as to improve the navigation performance in practical applications.

A seamless navigation system based on the motion constraint of the mobile robot is proposed to overcome the shortage of the navigation accuracy during GPS outages, thus improving the adaptability of the robot navigation.

This paper aims to present the estimation of the output voltage of metal oxide semiconductor field effect transistor (MOSFET) using the extended Kalman filter (EKF) method.

The method uses EKF for MOSFET output voltage estimation. To implement the EKF method, the state space model has been obtained using Kirchhoff’s current law and Enz-Krummenacher-Vittoz model of the MOSFET circuit.

The proposed method can be used for any mode of MOSFET operation besides near the quiescent point region. The nonlinearity that occurs in the saturation region of MOSFET can also be considered in the proposed method. The proposed method can also be used for a large input signal. Though Kalman filter can be used for the small amplitude input signal, it results in inaccurate estimation due to the linearization of the nonlinear system.

The method is able to track the parameters when they are slowly changing with time.

The proposed method presents maximal precision of simulation as the maximal precision of simulation requires modeling of the circuit in terms of device parameters and circuit elements.