Congruence Property In Conformal Field Theory

The congruence subgroup property is established for the modular representations associated to any modular tensor category. This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of any rational, C_2-cofinite vertex operator algebra is a congruence subgroup. In particular, the q-character of each irreducible module is a modular function on the same congruence subgroup. The Galois symmetry of the modular representations is obtained and the order of the anomaly for those modular categories satisfying some integrality conditions is determined.Comment: References are updated. Some typos and grammatical errors are correcte

Twisted Verlinde formula for vertex operator algebras

For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules to the $S$-matrix in the orbifold theory is established. As an application of the twisted Verlinde formula, a twisted analogue of the Kac-Walton formula is proved, which gives fusion rules between twisted modules of affine vertex operator algebras in terms of Clebsch-Gordan coefficients associated to the corresponding finite dimensional simple Lie algebras.Comment: 48 page

Data De-Duplication with Adaptive Chunking and Accelerated Modification Identifying

The data de-duplication system not only pursues the high de-duplication rate, which refers to the aggregate reduction in storage requirements gained from de-duplication, but also the de-duplication speed. To solve the problem of random parameter-setting brought by Content Defined Chunking (CDC), a self-adaptive data chunking algorithm is proposed. The algorithm improves the de-duplication rate by conducting pre-processing de-duplication to the samples of the classified files and then selecting the appropriate algorithm parameters. Meanwhile, FastCDC, a kind of content-based fast data chunking algorithm, is adopted to solve the problem of low de-duplication speed of CDC. By introducing de-duplication factor and acceleration factor, FastCDC can significantly boost de-duplication speed while not sacrificing the de-duplication rate through adjusting these two parameters. The experimental results demonstrate that our proposed method can improve the de-duplication rate by about 5 %, while FastCDC can obtain the increase of de-duplication speed by 50 % to 200 % only at the expense of less than 3 % de-duplication rate loss

The chemical composition and manufacturing technology of glass beads excavated from the Hetian Bizili site, Xinjiang

The Hetian Bizili site in Lop County, located on the southern route of the Silk Road in Xinjiang, China, was a trade and cultural hub between the East and the West in ancient times. In 2016, a large number of glass beads were unearthed from the 40 tombs excavated on this site. In this study we determined the chemical compositions and manufacturing technology of bodies and decorations of twelve glass beads from the M5 tomb of Bizili by using LA-ICP-AES, EDXRF, Raman Spectrometry, and SR-μCT. The chemical compositions of the beads were all Na2O–CaO–SiO2, with plant ash mainly used as a flux. Lead antimonate and lead stannate were used as the opacifying agents. We detected elevated levels of boron and high levels of phosphorus in some beads: this is discussed in the context of the type of flux used and the possible use of a P-rich opacifier. Some of the beads with high contents of aluminum may potentially come from Pakistan. In terms of manufacturing technology, the craftsmen made ‘eye’ beads in different ways and also trail decorated beads

A Multivariate Generalizability Theory Approach to College Students' Evaluation of Teaching

Teachers' teaching level evaluation is an important component in classroom teaching and professional promotion in the institutions of higher learning in China. Many self-made questionnaires are currently being administered to Chinese college students to evaluate teachers' classroom teaching performance. Quite often, due to the absence of strong educational, and psychological measurements and theoretical foundations for these questionnaires, their dependability remains open to doubt. Evaluation time points, the number of students, major type, and curriculum type were examined in relation to college students' perceptions on their teachers' classroom teaching performance, using Teachers' Teaching Level Evaluation Scale for Colleges (TTLES-C). Data were collected in a sample of 556 students at two time points from three Chinese universities and were analyzed using multivariate generalizability theory. Results showed that evaluations at the beginning of the spring semester produced better outcomes than did evaluations at the end of the fall semester, and 20 student evaluators were sufficient to ensure good dependability. Results also revealed that the evaluation dependability of science curriculum appeared higher than that of liberal arts curriculum. Recommendations were discussed on the evaluation criteria and mode

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions

High-quality free-standing InAs nanosheets are emerging layered semiconductor materials with potentials in designing planar Josephson junction devices for novel physics studies due to their unique properties including strong spin-orbit couplings, large Land\'e g-factors and the two dimensional nature. Here, we report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures, and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating forefront physics, such as the two-dimensional topological superconductivity

Mechanical-force-induced non-local collective ferroelastic switching in epitaxial lead-titanate thin films.

Ferroelastic switching in ferroelectric/multiferroic oxides plays a crucial role in determining their dielectric, piezoelectric, and magnetoelectric properties. In thin films of these materials, however, substrate clamping is generally thought to limit the electric-field- or mechanical-force-driven responses to the local scale. Here, we report mechanical-force-induced large-area, non-local, collective ferroelastic domain switching in PbTiO3 epitaxial thin films by tuning the misfit-strain to be near a phase boundary wherein c/a and a1/a2 nanodomains coexist. Phenomenological models suggest that the collective, c-a-c-a ferroelastic switching arises from the small potential barrier between the degenerate domain structures, and the large anisotropy of a and c domains, which collectively generates much larger response and large-area domain propagation. Large-area, non-local response under small stimuli, unlike traditional local response to external field, provides an opportunity of unique response to local stimuli, which has potential for use in high-sensitivity pressure sensors and switches