Exact Solutions to Sourceless Charged Massive Scalar Field Equation on Kerr-Newman Background

The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated angular part is an ordinary spheroidal wave equation. General exact solutions in integral forms and in power series expansion as well as several special solutions with physical interest are given for the radial equation in the non-extreme case. In the extreme case, power series solution to the radial equation is briefly studied. Recurrence relations between coefficients in power series expansion of general solutions and connection between the radial equation are discussed in both cases.Comment: 22 Pages, in LaTex, no figure, to appear in J. Math. Phy

Constrained structure of ancient Chinese poetry facilitates speech content grouping

Ancient Chinese poetry is constituted by structured language that deviates from ordinary language usage [1, 2]; its poetic genres impose unique combinatory constraints on linguistic elements [3]. How does the constrained poetic structure facilitate speech segmentation when common linguistic [4, 5, 6, 7, 8] and statistical cues [5, 9] are unreliable to listeners in poems? We generated artificial Jueju, which arguably has the most constrained structure in ancient Chinese poetry, and presented each poem twice as an isochronous sequence of syllables to native Mandarin speakers while conducting magnetoencephalography (MEG) recording. We found that listeners deployed their prior knowledge of Jueju to build the line structure and to establish the conceptual flow of Jueju. Unprecedentedly, we found a phase precession phenomenon indicating predictive processes of speech segmentation—the neural phase advanced faster after listeners acquired knowledge of incoming speech. The statistical co-occurrence of monosyllabic words in Jueju negatively correlated with speech segmentation, which provides an alternative perspective on how statistical cues facilitate speech segmentation. Our findings suggest that constrained poetic structures serve as a temporal map for listeners to group speech contents and to predict incoming speech signals. Listeners can parse speech streams by using not only grammatical and statistical cues but also their prior knowledge of the form of language