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With the rapid development of the digital economy, an increasing number of digitalized two-sided platforms have deployed the tying strategy to leverage their market power from the core two-sided product to other two-sided products in the competitive market, which transforms the competition among single platforms into that among platform ecological networks. To clarify the mechanism of the formation of the digital platform ecological networks, this paper aims to analyze the expansion and stability of platform ecology by exploring the impacts of network externalities and sellers’ heterogeneity on the tying strategy of two-sided platforms.

This paper develops a game model of two-sided platforms based on Choi and Jeon (2021), which highlights the decisive influence of non-negative price constraints (NPC) on platforms’ tying motivation. Taking the operating systems market as an example, we expand from the perspective of platform service differences to relax the NPC and explore the internal logic of platform ecosystem expansion.

Platforms have an incentive to charge lower prices or even subsidize buyers when the network externalities on the sellers’ side are relatively strong. When the product is highly differentiated and heterogenous, platforms are motivated to tie to capture more buyers with a lower price and grab excess profits from sellers. Eventually, tying is able to consolidate the two-sided platform ecological networks by excluding competitors, capturing user value and deterring entry.

In order to describe the characteristics of platform ecological network more generally, this paper extends the research based on the analyses of Choi and Jeon (2021) by (1) allowing horizontal differences between tied products and (2) relaxing the NPC. Unlike Choi and Jeon (2021), this paper allows platforms to charge users of two-sided platforms at negative prices (or to subsidize them). (3) Setting simultaneous pricing in two-sided platforms. Classical two-sided market theory stresses that the presence of cross-network externalities can give rise to a “chicken and egg” problem.

Developing general closed-form solutions for six-degrees-of-freedom (DOF) serial robots is a significant challenge. This paper thus aims to present a general solution for six-DOF robots based on the product of exponentials model, which adapts to a class of robots satisfying the Pieper criterion with two parallel or intersecting axes among its first three axes.

The proposed solution can be represented as uniform expressions by using geometrical properties and a modified Paden–Kahan sub-problem, which mainly adopts the screw theory.

A simulation and experiments validated the correctness and effectiveness of the proposed method (general resolution for six-DOF robots based on the product of exponentials model).

The Rodrigues rotation formula is additionally used to turn the complex problem into a solvable trigonometric function and uniformly express six solutions using two formulas.

The aim of this chapter is to determine the relationship between labor productivity and economic development. In this context, the annual data of Turkey on a range of 1970–2017 are included in the study period. On the other hand, these data are tested with the help of Toda Yamamoto causality analysis. Thus, it will be possible to determine whether there is a strong relationship between the two variables. According to the obtained results of the analysis, it is defined that there is a causal relationship from labor productivity to economic growth in Turkey. Based on these results, it can be said that labor productivity should rise in order to increase economic development in Turkey. For this purpose, educational programs in Turkey can be revised with the help of a detailed study. In this process, cooperation with companies to understand the needs in the market plays a key role. Additionally, regulations should also be prepared related to the salaries of the employees. If it can be possible to prevent employees from receiving wages below a certain amount by placing a minimum legal limit on salaries, it will be possible to increase the motivation of the employees. This situation has a positive and significant contribution to the labor productivity.

This paper aims to explore the future path of agricultural development in China toward 2060 under the dual carbon goals, so as to inform better policy choices for facilitating agricultural and rural transformation toward the goal of maintaining food security, sustainable income growth and low carbon emission.

This study employs a single-country, multi-sectoral computable general equilibrium model, CHINAGEM model and develops eight illustrative scenarios to simulate the impacts of attaining dual carbon goals on agricultural development in China. Additional two scenarios have also been designed to inform better policy making with the aim to offset the negative impact of the decarbonization schemes through facilitating agricultural technology progress.

Dual carbon goals are projected to impose substantial negative impact on agricultural productions and consumptions in China in the coming four decades. Under the assumption of business as usual, agricultural production will reduce by 0.49–8.94% along with the attainment of carbon neutrality goal by 2060, with the production of cereals and high-value being more severely damaged. To mitigate the adverse impact of the decarbonization schemes, it is believed that fastening technology progress in agriculture is one of the most efficient ways for maintaining domestic food security without harming the dual carbon goals. In particular, if agricultural productivity (particularly, for cereals and high-value products) can be increased by another 1% per year, the production losses caused by carbon emission mitigation will be fully offset. This implies that promoting technology progress is still the best way to facilitate agricultural development and rural transformation in future China.

The paper contributes to the literature in better informing the impact of dual carbon goals on China's agriculture and the effectiveness of technology progress in agriculture on buffering the adverse impact of the decarbonization schemes and promoting agricultural development.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.