A note of pointwise estimates on Shishkin meshes

We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.Comment: 10pages, 1 figur

Some notes on the paper "The mean value of a new arithmetical function"

In reference [2], we used the elementary method to study the mean value prop- erties of a new arithmetical function, and obtained two mean value formulae for it, but there exist some errors in that paper. The main purpose of this paper is to correct the errors in reference [2], and give two correct conclusions

Compliments and compliment responses in Philippine English

Compliment is a speech act that frequently occurs in everyday conversations. It is often used to start a conversation or to ‘lubricate’ the conversational interaction by reinforcing the rapport between the interlocutors. One line of academic research on compliments is to investigate similarities and differences across varieties of English (Jucker, 2009). So far, many varieties of English, such as American English, New Zealand English, and African English have been explored and it was found that compliments are formulaic in terms of both the meaning and the syntactic forms (e.g. Manes & Wolfson, 1981; Holmes, 1986; Herbert & Straight, 1989). However, only few studies have been done on Philippine English. This paper aims to fill the gap. A Discourse Completion Test (Henceforth DCT) was used to elicit data of giving and receiving compliments from 30 college students in a Philippine University. An analysis is provided of the compliment strategies, the syntactic and lexical patterns characterizing compliments, and the compliment response strategies. It was found that Philippine English speakers tend to use explicit compliments plus a bound semantic formula most frequently. The compliments in Philippine English are as formulaic at syntactic and lexical levels as other varieties of English. Filipinos are more likely to accept the compliment, rather than reject it, when they receive one

A tight-binding model for the excitonic band structure of a one-dimensional molecular chain: UV-Vis spectra, Zak phase and topological properties

Recently organic optics becomes a hot topic due to the rapid development of organic light-emitting diodes, organic solar cells, and organic photon detectors. The optical spectra of the molecular semiconductors are difficult to solve an model from first-principles because (i) the very large number of atoms in a unit cell and (ii) the accurate theoretical excited state is still under development. Here we present a tight-binding model of an exciton band structure in a molecular chain. We take into account the intra-molecule and charge-transfer excitation within a molecular dimer in a unit cell, then we apply the tight-binding model by including the coupling between two types of excitations. We not only found that our calculations can explain a body of UV-Vis optical spectra of transition-metal phthalocyanines, but also a one-dimensional excitonic topological band structure if we fine-tune the couplings in a dimerized molecular chain. We have found a large space to obtain the topological Zak phase in the parameter space, in which there is a simple linear relationship between the hopping integrals between cells and within cell.Comment: 5 pages, 5 figure