A communicative English-speaking supplementary curriculum: Using WeChat to develop Chinese EFL learners’ speaking fluency

The development of English communication skills is ignored by most EFL learners in China. This problem attributes to sufficient practice during their English-learning process in class, since most public schools in China, grammar-translation is still the mainstream teaching approach. Which means that Chinese not English is used to give lectures. Students do grammatical analysis and vocabulary memorizing instead of communicating in the target language. However, this approach cannot help the development of students’ speaking fluency. The deficiency of English speaking a variety of problems when students need to communicate with English speakers. Besides, the inner shy personality and face-saving culture cause anxiety when Chinese EFL learners speak English. Thus, this project provides a curriculum for EFL instructors, which aims at increasing more oral practice opportunities to help EFL learners enhance English-speaking skills. The whole curriculum is conducted on WeChat which is the most popular social mobile application in China and all of the lessons are task-based learning. Through completing tasks on WeChat, students can gain English-speaking practice without time and space constraint. What’s more, speaking English on social network sites can help Chinese EFL learners reduce anxiety effectively

Spontaneous symmetry breakings in two-dimensional kagome lattice

We study spontaneous symmetry breakings for fermions (spinless and spinful) on a two-dimensional kagome lattice with nearest-neighbor repulsive interactions in weak coupling limit, and focus in particular on topological Mott insulator instability. It is found that at $\frac{1}{3}$-filling where there is a quadratic band crossing at $\Gamma$-point, in agreement with Ref. 1, the instabilities are infinitesimal and topological phases are dynamically generated. At $\frac{2}{3}$-filling where there are two inequivalent Dirac points, the instabilities are finite, and no topological phase is favored at this filling without breaking the lattice translational symmetry. A ferromagnetic quantum anomalous Hall state with infinitesimal instability is further proposed at half-filling of the bottom flat band.Comment: 5 pages, 3 figures, Published in Phys. Rev.

On Score Sequences ofk-Hypertournaments

AbstractGiven two nonnegative integers n and k withn≥k> 1, a k -hypertournament on n vertices is a pair (V, A), where V is a set of vertices with | V | =n and A is a set of k -tuples of vertices, called arcs, such that for any k -subset S ofV , A contains exactly one of the k!k -tuples whose entries belong to S. We show that a nondecreasing sequence (r1, r2,⋯ , rn) of nonnegative integers is a losing score sequence of a k -hypertournament if and only if for each j(1 ≤j≤n),with equality holding whenj=n. We also show that a nondecreasing sequence (s1,s2 ,⋯ , sn) of nonnegative integers is a score sequence of somek -hypertournament if and only if for each j(1 ≤j≤n),with equality holding whenj=n. Furthermore, we obtain a necessary and sufficient condition for a score sequence of a strong k -hypertournament. The above results generalize the corresponding theorems on tournaments

on On Score Sequences of k-Hypertournaments †

Given two nonnegative integers n and k with n ≥ k> 1, a k-hypertournament on n vertices is a pair (V, A), where V is a set of vertices with |V | = n and A is a set of k-tuples of vertices, called arcs, such that for any k-subset S of V, A contains exactly one of the k! k-tuples whose entries belong to S. We show that a nondecreasing sequence (r1, r2,..., rn) of nonnegative integers is a losing score sequence of a k-hypertournament if and only if for each j (1 ≤ j ≤ n), j� ri ≥ i=

Ultrasensitive magnetic tuning of optical properties of films of cholesteric cellulose nanocrystals

Chiral photonic crystals derived from the self-assembly of cellulose nanocrystals (CNCs) have found important applications in optical devices due to the capacity to adjust the chiral nematic phase under external stimulus, in particular an applied magnetic field. To date, strong magnetic fields have been required to induce an optical response in CNC films. In this work, the self-assembly of films of CNCs can be tuned by applying an ultrasmall magnetic field. The CNCs, decorated with Fe3O4 nanoparticles (Fe3O4/CNCs), were dispersed in suspensions of neat CNCs so as to alter the magnetic response of the CNCs. A subsequent process of dispersion not only prevents the clumping of the magnetic nanoparticles but also enhances the sensitivity to an applied magnetic field. A small magnetic field of 7 mT can tune the self-assembly and the microstructure of the CNCs. The pitch of the chiral structure decreased with an increase in applied magnetic field, from 302 to 206 nm, for fields from 7 to 15 mT. This phenomenon is opposite that observed for neat CNCs, in which the pitch is observed to increase with an increase in the external magnetic strength. The optical response under application of an ultrasmall magnetic field could help with theoretical research and enable more applications, such as sensors or nanotemplating agents