Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations

This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook) schemes in the framework of finite volume method for the ultra-relativistic flows. Different from the existing kinetic flux-vector splitting (KFVS) or BGK-type schemes for the ultra-relativistic Euler equations, the present genuine BGK schemes are derived from the analytical solution of the Anderson-Witting model, which is given for the first time and includes the "genuine" particle collisions in the gas transport process. The BGK schemes for the ultra-relativistic viscous flows are also developed and two examples of ultra-relativistic viscous flow are designed. Several 1D and 2D numerical experiments are conducted to demonstrate that the proposed BGK schemes not only are accurate and stable in simulating ultra-relativistic inviscid and viscous flows, but also have higher resolution at the contact discontinuity than the KFVS or BGK-type schemes.Comment: 41 pages, 13 figure

A Cartographic Analysis of the Syntactic Structure of Mandarin Ba

This paper analyzes the syntactic properties of the “ba-construction” or “disposal form” in Mandarin Chinese under new theoretical frameworks. By introducing the event-decomposition method proposed by Ramchand (2008), it argues that the ba-construction conveys the causativity and the resultativity of the event at the same time, which can be shown from the syntactic representation. Then, this paper tests the position of ba, assuming that it is a functional head, and the result of the test indicates that ba is a voice head in the hierarchy of functional projections proposed by Cinque (1999, 2006). The final word order of a ba-construction can be derived by the argument movement of the direct object and by a head movement of ba or by the merge of ba at the head position of the higher functional head of a split VoiceP

Higher Ext-groups in the triple product case

In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.Comment: To appear in Math. Res. Let

MWPoW: Multiple Winners Proof of Work Protocol, a decentralisation strengthened fast-confirm blockchain protocol

Blockchain mining should not be a game among power oligarchs. In this paper, we present the Multiple Winners Proof of Work Protocol (MWPoW), a mining-pool-like decentralised blockchain consensus protocol. MWPoW enables disadvantaged nodes which post only a small amount of calculation resource in the mining game to create blocks together and compete with power oligarchs without centralised representatives. A precise Support Rate of blocks can be determined through the mining process; the mechanism of the mainchain determination is therefore changed and has become faster and more straightforward. A method that periodically adjusts the block size and the block interval is introduced into MWPoW, which increases the system flexibility in the changes of network conditions and data flow. Experiments suggest, without lifting calculation and bandwidth requirements, MWPoW is more attractive to disadvantaged nodes due to its mostly increased reward expectation for disadvantaged nodes. The transaction pending time is shortened chiefly, and either the block interval or the block size can be adapted amid the changes of overall network conditions