A collection of n anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robo...

Based on research done on a small corpus of comment articles, this paper reconsiders the relation between topic entity, subject function and given status and explores their role in the construction and maintenance of the global discourse topic. It claims that even though it is pertinent to say that at sentence level much of the topical information is non-subject and/or frequently postverbal wit...

In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function. The notation and terminology used here are introduced in the following papers:

(Def. 2) cosec = 1 the function sin . For simplicity, we follow the rules: x, a, b, c are real numbers, n is a natural number, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. One can prove the following propositions: (1) If (the function cos)(x) 6= 0, then sec is differentiable in x and (sec)′(x) = (the function sin)(x) (the function cos)(x)2 . (2) If (the function s...