A Multiple Aspects Quantitative Indicator for Ability of English Vocabulary: Vocabulary Quotient

tudents of EFL have a common problem with insufficient vocabulary. Some studies argue that English vocabulary is one of the most difficult parts. This paper applied the idea of KPI (Key Performance Indicator) from management science to EFL vocabulary learning and teaching. A vocabulary quotient (VQ in short) with four test models, including a listening com­prehension test, was proposed as KPIs. Based on VQ, VQ testing software was developed. To test the validity and reliability of the assessment tool based on VQ, assessments with 54 junior high students (n=54) was conducted. The findings of this study were generalized as the following: (1) the relationships between the score of general English proficiency test and scores of VQ tests were significant positive correlations respectively and (2) the relationships among scores of VQ tests were significant positive correlations. Results of this study suggest that VQ could be considered to be a KPI of EFL vocabulary teaching and learning. The proposed method is suggested to estimate one’s vocabulary sizes

Similarity solutions of Fokker-Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulted ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker-Planck equations are presented, and their properties analyzed.Comment: 13 pages, 8 figures. Version to appear in Ann. Phys. Presentation improved. Discussions and figures of easy examples remove

Optical transitions between Landau levels: AA-stacked bilayer graphene

The low-frequency optical excitations of AA-stacked bilayer graphene are investigated by the tight-binding model. Two groups of asymmetric LLs lead to two kinds of absorption peaks resulting from only intragroup excitations. Each absorption peak obeys a single selection rule similar to that of monolayer graphene. The excitation channel of each peak is changed as the field strength approaches a critical strength. This alteration of the excitation channel is strongly related to the setting of the Fermi level. The peculiar optical properties can be attributed to the characteristics of the LL wave functions of the two LL groups. A detailed comparison of optical properties between AA-stacked and AB-stacked bilayer graphenes is also offered. The compared results demonstrate that the optical properties are strongly dominated by the stacking symmetry. Furthermore, the presented results may be used to discriminate AABG from MG, which can be hardly done by STM