By making fundamental use of the Farey shift map and employing infinite (but σ-finite) measures together with the Chacon-Ornstein ergodic theorem it is possible to find new metrical results for continued fractions. Moreover this offers a unified approach to several existing theorems. The application of ergodic theory to the study of continued fractions began with the Gauss transformation, G: [0...

where Ed= fl, bkEZ2,, k 2 1, and with some constraints on bk and sk. Usually we will assume that x is irrational, and thus that the expansion (1.1) is infinite. A special case of an SRCF is the regular continuedfraction, RCF, which is obtained by taking ck = 1 for every k in (1.1). The aim in introducing the OCF was to optimize two things simultaneously. In the first place one wishes the conver...

Kim, Sun-Hoi. 2002. The metrical dependency of tone placement in Optimality Theory. Studies in Phonetics, Phonology and Morphology 8.1. 17-38. In this paper, I examine the metrical dependency of tone placement in OT. In Creek and Shingazidja, the determination of tone placement heavily draws on the special relationship between high tone and the metrically prominent position in the prosodic doma...

This paper describes an automatic system of music analysis based on the generative theory of tonal music (GTTM). The system works by acquiring the metrical structure of the music. The GTTM is considered one of the most promising theories of music in regard to computer implementation; however, no order is given for applying its rules and as a result, they frequently conflict with each other. To ...

The fixed point alternative methods are implemented to giveHyers-Ulam  stability for  the quintic functional equation $ f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting ofintuitionistic fuzzy normed spaces (IFN-spaces).  This methodintroduces a met...