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This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

This paper aims to address a pollution-routing problem with one general period of congestion (PRP-1GPC), where the start and finish times of this period can be set freely.

In this paper, three sets of decision variables are optimized, namely, travel speeds before and after congestion and departure times on given routes, aiming to minimize total cost including green-house gas emissions, fuel consumption and driver wages. A two-phase algorithm is introduced to solve this problem. First, an adaptive large neighborhood search heuristic is used where new removal and insertion operators are developed. Second, an analysis of optimal speed before congestion is presented, and a tailored speed-and-departure-time optimization algorithm considering congestion is proposed by obtaining the best node to be served first over the congested period.

The results show that the newly developed operator of congested service-time insertion with noise is generally used more than other insertion operators. Besides, compared to the baseline methods, the proposed algorithm equipped with the new operators provides better solutions in a short time both in PRP-1GPC instances and time-dependent pollution-routing problem instances.

This paper considers a more general situation of the pollution-routing problem that allows drivers to depart before the congestion. The PRP-1GPC is better solved by the proposed algorithm, which adds operators specifically designed from the new perspective of the traveling distance, traveling time and service time during the congestion period.

The purpose of this paper is to maximize the average profit of the supply chain by calculating the order quantity, the number of shipments during the production time of the vendor, the number of shipments during the supply cycle of the vendor and the time when the retailer’s inventory level reaches to zero.

A production and inventory model for degrading commodities with stochastic demand and two-level partial trade credit in a supply chain is presented. The model’s applicability and the processes' feasibility for solving are verified by GAMS software with BARON.

The impact of the model’s parameters on the vendor and retailer’s average profit was found through sensitivity analysis. The effect of the model’s parameters on the supply chain’s average profit was also found. Moreover, the reasons for this effect were given.

First, decision-makers may use this model to increase the supply chain's average profit. Second, the proposed model takes a general form. Third, the policymakers can also adjust the model’s parameters according to their preferences to get the desired results.

First, this paper develops an inventory and production model for perishable goods. Second, it is believed that the demand is random because the demand is affected by many factors, which make the study more realistic. Third, this paper studies production and inventory problems from the supply chain perspective. Finally, the interest for partial trade credit is calculated. The interest caused by stochastic shortages is also considered and calculated.

The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The authors establish a result concerning the L²-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the observed Fisher information of a local-to-unity parameter. In contrast to the Dickey–Fuller (DF) test statistic, the sequential test statistic has asymptotic normality. The authors derive the joint limit of the test statistic and the stopping time, which can be characterized using a 3/2-dimensional Bessel process driven by a time-changed Brownian motion. The authors obtain their limiting joint Laplace transform and density function under the null and local alternatives. In addition, simulations are conducted to show that the theoretical results are valid.

The purpose of this study is to investigate the influencing mechanism of consumers' continuous purchase intention toward the subscriber-based knowledge payment platforms (SBKPPs).

This study obtained 226 valid samples through questionnaire surveys and used partial least square structural equation modeling (PLS-SEM) and fuzzy-set qualitative comparative analysis (fsQCA) methods to elucidate the complex causal patterns of consumers' continuous purchase intention toward the SBKPPs.

The findings revealed that perceived utilitarian value, perceived hedonic value and perceived social value directly affected consumers' continuous purchase intention, while content quality and service quality indirectly affected consumers' continuous purchase intention. In addition, this study also demonstrated that all factors must be combined to play a role, and there exist four configurations resulting in consumers' continuous purchase intention toward the SBKPPs.

The results can help researchers and practitioners better understand the causal patterns of consumers' continuous purchase intention toward the SBKPPs.

This study contributes to the knowledge payment literature by investigating consumers' continuous purchase intention toward the SBKPPs. This study also provides practical enlightenment for the SBKPPs' marketing.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

The importance of service firms cooperating with digital platforms is widely acknowledged. The authors study three contractual relationships (fixed-cost, cost-sharing, and profit-sharing) between service firms (specifically hotels) and digital platforms in a highly fragmented service supply chain to examine which of these contract types optimizes profits.

The authors extend prior models analyzing the optimal expected total profit from the travel service firm (hotel)–digital platform relationship, providing new insights into each contract type’s ability to coordinate decentralized systems and optimize profits for both parties.

This study finds that fixed cost contracts cannot coordinate the decentralized system. Cost-sharing contracts can coordinate the decentralized system but only allow one channel profit split. In contrast, profit-sharing contracts may not always perfectly coordinate the decentralized system but support alternative profit allocations. Practically, both profit-sharing and cost-sharing contracts are preferable to fixed-cost contracts.

The paper includes implications for travel service firm managers to consider when structuring contracts with digital platforms to focus on profit optimization. Profit-sharing contracts are most preferable when cost and revenue data are fully shared between parties, while cost-sharing contracts are preferable over fixed-cost contracts.

This study extends prior investigations into the utility of different contract types on the optimal profit of a travel service firm (hotel)-digital platform provider relationship. The research fills a gap in the literature concerning the contracts used in these relationship types.

The growing availability of naturalistic driving datasets (NDDs) presents a valuable opportunity to develop various models for autonomous driving. However, while current NDDs include data on vehicles with and without intended driving behavior changes, they do not explicitly demonstrate a type of data on vehicles that intend to change their driving behavior but do not execute the behaviors because of safety, efficiency, or other factors. This missing data is essential for autonomous driving decisions. This study aims to extract the driving data with implicit intentions to support the development of decision-making models.

According to Bayesian inference, drivers who have the same intended changes likely share similar influencing factors and states. Building on this principle, this study proposes an approach to extract data on vehicles that intended to execute specific behaviors but failed to do so. This is achieved by computing driving similarities between the candidate vehicles and benchmark vehicles with incorporation of the standard similarity metrics, which takes into account information on the surrounding vehicles' location topology and individual vehicle motion states. By doing so, the method enables a more comprehensive analysis of driving behavior and intention.

The proposed method is verified on the Next Generation SIMulation dataset (NGSim), which confirms its ability to reveal similarities between vehicles executing similar behaviors during the decision-making process in nature. The approach is also validated using simulated data, achieving an accuracy of 96.3 per cent in recognizing vehicles with specific driving behavior intentions that are not executed.

This study provides an innovative approach to extract driving data with implicit intentions and offers strong support to develop data-driven decision-making models for autonomous driving. With the support of this approach, the development of autonomous vehicles can capture more real driving experience from human drivers moving towards a safer and more efficient future.

As the quality of the environment decreases, enterprises and consumers' awareness of environmental protection is constantly improving. More and more enterprises begin to increase their investment in carbon emission reduction and attract environmentally friendly consumers to buy low-carbon products through advertising. The purpose of this paper is to utilize a realistic differential game model to provide dynamic carbon emission reduction strategies, advertising strategies and cooperation methods for complex supply chain members from a long-term perspective.

This paper uses the extend Vidale-Wolfe model (V-W model) to discuss the dynamic joint emission reduction strategy in the supply chain.

(1) When consumers' awareness of environmental protection increases, on the whole, carbon emission reduction and profit of products show an upward trend. (2) From a long-term perspective, the manufacturer's advertising subsidy to one of the retailers is the best choice. If the strength of the two retailers is unbalanced, the manufacturer will choose to cooperate with the dominant retailer. (3) Advertising, as a marketing means for retailers to promote low-carbon products, can alleviate the adverse effects of prisoner's dilemma in a semi-cooperative state, but it cannot achieve the Pareto optimization result.

This paper focuses on the analysis of the situation that when the manufacturer is the leader and thinks that consumers are active advocates of low-carbon products.

The results of this paper can provide theoretical basis for the joint emission strategy of supply chain members in low-carbon environment.