Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of planar rarefaction wave for 3D Boltzmann equation, while the corresponding results for the shock and contact discontinuities are still completely open.Comment: 45pages. We correct some typoes. The paper will be published on Kinetic and Related Model

Intrinsic coherence in assisted sub-state discrimination

We study intrinsic coherence in the tripartite process to unambiguously discriminate two nonorthogonal states of a qubit, entangled with another one, and assisted by an auxiliary system. The optimal success probability is found to be benefited by initial intrinsic coherence, but no extra one is required. The transformations among different contributions of intrinsic coherence are necessary in this procedure, which increase with the overlap between the states to recognize. Such state discrimination is a key step of the probabilistic teleportation protocol. Entanglement of the quantum channel decreases the coherence characterizing the reliance on an ancilla.Comment: 6 pages with 4 figure

Understanding changes in teacher beliefs and identity formation: A case study of three novice teachers in Hong Kong

Novice teachers often undergo an identity shift from learner to teacher. Along this process, their instructional beliefs change considerably which in turn affect their teacher identity formation. Drawing on data collected mainly through interviews with three novice English teachers formore than one year, the present study examines their firstyear teaching experience in Hong Kong secondary schools, focusing on changes of their English teaching beliefs and the impact of these changes on their identity construction. Findings reveal that while the teachers’ initial teaching beliefs were largely shaped in their prior school learning and learning-to-teach experience, these beliefs changed and were reshaped a great deal when encountering various contextual realities, and these changes further influenced their views on their teacher identity establishment, unfortunately in a more negative than positive direction. The study sheds light on the importance of institutional support in affording opportunities for novice teachers’ workplace learning and professional development