31,101 research outputs found

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

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    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

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    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

    Synchrotron Radiation from Electrons with a Pitch-angle Distribution

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    In most astrophysical processes involving synchrotron radiation, the pitch-angle distribution of the electrons is assumed to be isotropic. However, if electrons are accelerated anisotropically, e.g., in a relativistic shock wave with an ordered magnetic field or in magnetic reconnection regions, the electron pitch angles might be anisotropic. In this Letter, we study synchrotron radiation from electrons with a pitch-angle distribution with respect to a large-scale uniform magnetic field. Assuming that the pitch-angle distribution is normal with a scatter of σ p and that the viewing direction is where the pitch-angle direction peaks, we find that for electrons with a Lorentz factor γ, the observed flux satisfies F ν ∝ ν 2/3 for ν ν cr (ν cr is the critical frequency of synchrotron), if σ p 1/γ is satisfied. On the other hand, if σ p 1/γ, the spectrum below ν cr is a broken power law with a break frequency , e.g., for ν ν br and for . Thus, the ultimate synchrotron line of death is F ν ∝ ν 2/3. We discuss the application of this theory to blazars and gamma-ray bursts

    Dispersion Measure Variation of Repeating Fast Radio Burst Sources

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    The repeating fast radio burst (FRB) 121102 was recently localized in a dwarf galaxy at a cosmological distance. The dispersion measure (DM) derived for each burst from FRB 121102 so far has not shown significant evolution, even though an apparent increase was recently seen with newly detected VLA bursts. It is expected that more repeating FRB sources may be detected in the future. In this work, we investigate a list of possible astrophysical processes that might cause DM variation of a particular FRB source. The processes include (1) the cosmological scale effects such as Hubble expansion and large-scale structure fluctuations; (2) the FRB local effects such as gas density fluctuation, expansion of a supernova remnant, a pulsar wind nebula, and an HII region; and (3) the propagation effect due to plasma lensing. We find that the DM variations contributed by the large-scale structure are extremely small, and any observable DM variation is likely caused by the plasma local to the FRB source. Besides mechanisms that produce decreasing DM with time, we suggest that an FRB source in an expanding supernova remnant around a nearly neutral ambient medium during the deceleration (Sedov-Taylor and snowplow) phases or in a growing HII region can introduce DM increasing. Some effects (e.g. an FRB source moving in an HII region or plasma lensing) can give either positive or negative DM variations. Future observations of DM variations of FRB 121102 and other repeating FRB sources can bring important clues for the physical origin of these sources.Comment: 12 pages. Accepted for publication in Ap