We assume that the reader is familiar with the value distribution theory of meromorphic function (see [1, 2]) and its associated standard notations, such as (T r,f)), (m r,f)), (N r,f)) etc.
Once a way had been found to write music down – a "technology" which developed out of the medieval monastery, with its imprecise neumes, and achieved a new beginning with the staff notation associated with the 11th-century Italian, Guido of Arezzo, which we still use – a conflict was implicit between music as performance and music as text.
Section 2 provides definitions and notation associated with an IFS and its attractors.
A variety of notation associated with this model and its dynamics will be introduced throughout the paper, which we summarize in Table 1.
In contrast, the children commented that the images used in the graphical interface were attractive and that its icons were organized consistently with the curriculum structure and were associated with phonetic notation, which enabled easy use of trial-and-error methods without breakdown after a failed search.
In the proof of the theorem for NUS and the rest of the appendices, we make extensive use of the useful CDFs that have been grouped together in Appendix B, so we highly encourage the readers to go through the previous appendix for proper understanding of these proofs and the notation associated to those CDFs.
To do this effectively, it is helpful to have a picture in mind as well as the appropriate notation associated to this picture.
Assuming the reader is familiar with the basics of Nevanlinna's value distribution theory, we shall adopt the standard notations associated with the theory, such as the characteristic function T ( r, f ), the counting function of the poles N ( r, f ), and the proximity function m ( r, f ) (see, e.g., [1, 2]).
Previous empirical observations on different data-sources [20, 23 26] have shown out that the TTE probability distribution (p(T)) (see Table 1 for a list of notations), associated to a single mean of transportation, is characterised by an exponential tail p(T) = beta^{-1}exp -T/beta),quad text{for } T > 1 text{ hour,} (1) where β is a fit parameter.
