In this paper, we develop a more general framework of block-structured Markov processes in the queueing study of blockchain systems, which can provide analysis both for the stationary performance measures and for the sojourn times of any transaction or block. Note that an original aim of this paper is to generalize the two-stage batchservice queueing model studied in Li et al. [56] both "from exponential to phase-type" service times and "from Poisson to MAP" transaction arrivals. In general, the MAP transaction arrivals and the two stages of PH service times make our blockchain queue more suitable to various practical conditions of blockchain systems with crucial factors, for example, the mining processes, the block-generations, the blockchain-building and so forth. For such a more general blockchain queueing model, we focus on two basic research aspects: (1) By using the matrix-geometric solution, we first obtain a sufficient stable condition of the blockchain system. Then we provide simple expressions for the average stationary number of transactions in the queueing waiting room, and the average stationary number of transactions in the block. (2) However, comparing with Li et al. [56], analysis of the transaction-confirmation time becomes very difficult and challenging due to the complicated blockchain structure. To overcome the difficulties, we develop a computational technique of the first passage times by means of both the PH distributions of infinite sizes and the RG-factorizations. Finally, we hope that the methodology and results given in this paper will open a new avenue to queueing analysis of more general blockchain systems in practice, and can motivate a series of promising future research on development of blockchain technologies. 1

Light interference is an essential topic for understanding the wavelike nature of light, however, there are limited studies on modeling and assessing students' misconceptions and learning difficulties in this area. Based on the knowledge integration modeling approach, a conceptual framework for light interference is developed and used to model student understanding and guide the development of an assessment tool on light interference. The conceptual framework provides a representation of students' reasoning pathways to clearly show their connections through different conceptual components and contextual features of problem-solving settings. This type of representation focuses on showing students' knowledge structures regarding the features of integration and fragmentation. Experts' reasoning pathways always flow through a central idea of a concept with well-established connections to a wide range of contextual features and conditions. These connections form an integrated knowledge structure, which demonstrates deep understanding. In contrast, novices often focus on surface details without linking the central idea, forming fragmented local connections that link directly between contextual features and task outcomes. As a result, novice students' problem solving often relies on memorization of formula and solutions without any deep understanding. Through testing and interviews at a large Chinese university, a light interference test (LIT) has been developed and validated. Assessment results also demonstrate that students with a strong conceptual understanding of the central idea are able to apply expertlike reasoning to familiar and novel questions regardless of the contextual details. Meanwhile, students with weaker or nonexistent understanding of the central idea often struggle when novel situations are presented. LIT provides a useful tool to measure students' conceptual understanding on light interference and probe thought pathways of students' reasoning that can further indicate students' knowledge structure and levels of deep understanding.

Diode-pumped Yb:LuAG laser has been passively mode locked with a SESAM for the first time to the authors' knowledge. The pulses as short as 7.63ps were generated, without negative dispersion elements. The output power achieved 610mW at pump of 11.2W with repetition rate of 86MHz. The continuous-wave operation and wavelength tuning pumped at 940nm were also examined, and its tuning can cover the range of 1033nm-1079nm.

Rural school consolidation has significantly changed the landscape of rural education in China. Based on a study carried out in nine provinces, this article analyzes the effect of this policy initiative. It has led to increased school dropout rates in rural schools.

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