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

Relativistic Astronomy. III. Test of Special Relativity via Doppler Effect

The Breakthrough Starshot program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Because the probe velocity is designed to be a good fraction of the light speed, Zhang & Li recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including the parametric general Doppler effect and the Doppler effect with massive photons. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Additionally, using the imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity v ~ 0.2c, aperture D ~ 3.5 cm, and spectral resolution R ~ 100 (or 1000), we find that the probe velocity uncertainty can be constrained to σ v ~ 0.01c (or 0.001c), and the time dilation factor uncertainty can be constrained to (or 0.001), where is the time dilation factor and γ is the Lorentz factor. Meanwhile, the photon mass limit is set to m γ 10−33 g, which is slightly lower than the energy of the optical photon

Pilot Power Allocation Through User Grouping in Multi-Cell Massive MIMO Systems

In this paper, we propose a relative channel estimation error (RCEE) metric, and derive closed-form expressions for its expectation $\rm {Exp}_{rcee}$ and the achievable uplink rate holding for any number of base station antennas $M$, with the least squares (LS) and minimum mean squared error (MMSE) estimation methods. It is found that RCEE and $\rm {Exp}_{rcee}$ converge to the same constant value when $M\rightarrow\infty$, resulting in the pilot power allocation (PPA) is substantially simplified and a PPA algorithm is proposed to minimize the average $\rm {Exp}_{rcee}$ per user with a total pilot power budget $P$ in multi-cell massive multiple-input multiple-output systems. Numerical results show that the PPA algorithm brings considerable gains for the LS estimation compared with equal PPA (EPPA), while the gains are only significant with large frequency reuse factor (FRF) for the MMSE estimation. Moreover, for large FRF and large $P$, the performance of the LS approaches to the performance of the MMSE, which means that simple LS estimation method is a very viable when co-channel interference is small. For the achievable uplink rate, the PPA scheme delivers almost the same average achievable uplink rate and improves the minimum achievable uplink rate compared with the EPPA scheme.Comment: 30 pages, 5 figures, submitted to IEEE Transactions on Communication

Integral and Rxte/Asm Observations on Igr J17098-3628

To probe further the possible nature of the unidentified source IGR J17098-3628, we have carried out a detailed analysis of its long-term time variability as monitored by RXTE/ASM, and of its hard X-ray properties as observed by INTEGRAL. INTEGRAL has monitored this sky region over years and significantly detected IGR J17098-3628 only when the source was in this dubbed active state. In particular, at $\ge$ 20 keV, IBIS/ISGRI caught an outburst in March 2005, lasting for $\sim$5 days with detection significance of 73$\sigma$ (20-40 keV) and with the emission at $<$200 keV. The ASM observations reveal that the soft X-ray lightcurve shows a similar outburst to that detected by INTEGRAL, however the peak of the soft X-ray lightcurve either lags, or is preceded by, the hard X-ray ($>$20 keV) outburst by $\sim$2 days. This resembles the behavior of X-ray novae like XN 1124-683, hence it further suggests a LMXB nature for IGR J17098-3628. While the quality of the ASM data prevents us from drawing any definite conclusions, these discoveries are important clues that, coupled with future observations, will help to resolve the as yet unknown nature of IGR J17098-3628.Comment: 15 pages, 7 figure, accepted in PAS