Fourth order quasi-compact difference schemes for (tempered) space fractional diffusion equations

The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its corresponding Fokker-Planck equation has space fractional derivative, which characterizes L\'{e}vy flights. Sometimes the infinite variance of L\'{e}vy flight discourages it as a physical approach; exponentially tempering the power-law jump length of CTRW makes it more `physical' and the tempered space fractional diffusion equation appears. This paper provides the basic strategy of deriving the high order quasi-compact discretizations for space fractional derivative and tempered space fractional derivative. The fourth order quasi-compact discretization for space fractional derivative is applied to solve space fractional diffusion equation and the unconditional stability and convergence of the scheme are theoretically proved and numerically verified. Furthermore, the tempered space fractional diffusion equation is effectively solved by its counterpart of the fourth order quasi-compact scheme; and the convergence orders are verified numerically.Comment: 27 pages, 1 figur

A Study of Students’ Silence and Teachers’ Questioning Strategies in College English Classroom

With the development of English language teaching, teachers have paid more and more attention to communicative language teaching and made efforts to encourage classroom interaction. However, many college students are in the habit of keeping silent which discourage teachers and restrict the effective communication between teachers and students. As one of the biggest problems, it has attracted much attention from more and more researchers. This paper here aims to investigate the major causes of students’ silence by means of questionnaire and class observation. Through a detailed description and analysis of the collected data, students’ learning motivation and reasons for silence in classroom are made clear, anxiety being the main cause triggering students’ silence. Meanwhile on the basis of analysis of teachers’ teaching mode, the paper points out that teachers’ questioning strategies have large influence on students’ silence in class, and improper teaching mode are bound to make students feel anxious. Finally, suggestions about improving teaching strategies are put forward for the purpose of lessening students’ feeling of anxiety and decreasing their silence in classrooms

A Discussion of Color Metaphors From the Perspective of Cognition and Culture

Metaphor is a pervasive phenomenon which has traditionally been considered as a figure of speech used for special effects in a speech or an essay. It is pervasive in everyday life. Color terms are usually used to depict the colors of objects in the world. Every object in the world has its own color. There are a large number of metaphorical expressions with color serving as the source domain in both English and Chinese. As a very important human experience, colors have attracted many scholars attention. The study revealed that possible reasons for the similarities of color metaphor in the two languages can be attributed to the common perceptual and cultural experience, while the dissimilarities originated from the different living environment, religion, custom, and philosophy etc.This essay makes a comparison of color metaphor about the similarities and differences between English and Chinese. Understanding similarities and differences of color metaphor between English and Chinese is of great importance in the cross-cultural communication. It’s beneficial for us to do English teaching, English translation, and appreciation of English culture

Uncertainty Measures in Ordered Information System Based on Approximation Operators

This paper focuses on constructing uncertainty measures by the pure rough set approach in ordered information system. Four types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy, roughness, approximation quality, approximation accuracy, dependency degree, and importance degree are investigated. Theoretical analysis indicates that all the four types can be used to evaluate the uncertainty in ordered information system, especially that we find that the essence of the first type and the third type is the same. To interpret and help understand the approach, experiments about real-life data sets have been conducted to test the four types of uncertainty measures. From the results obtained, it can be shown that these uncertainty measures can surely measure the uncertainty in ordered information system

Planning Skip-Stop Transit Service under Heterogeneous Demands

Transit vehicles operating under skip-stop service visit only a subset of the stops residing along a corridor. It is a strategy commonly used to increase vehicle speeds and reduce patron travel times. The present paper develops a continuous approximation model to optimally design a select form of skip-stop service, termed AB-type service. The model accounts for spatially-heterogeneous demand patterns. An efficient heuristic is developed to obtain solutions. These are shown to be near-optimal for a variety of numerical examples. Results also indicate that optimal AB-type designs outperform optimized all-stop service in a variety of cases. The AB-type service is found to be especially competitive when travel demands are high, trip origins are unevenly distributed along a corridor, and patrons have relatively high values of time. In these cases, AB-type service is found to reduce system costs by as much as 8%.Comment: 24 pages, 7 figures, 2 table