Every open ball within R∞ has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam-Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam-Thron Theorem and...

Inspired by questions of convergence in continued fraction theory, Erdős, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Möbius maps acting on the Riemann sphere, S. By identifying S with the boundary of three-dimensional hyperbolic space, H, we show that these sets of divergence are precisely the sets that arise as conical limit sets of subsets of H. Usin...

D. DeMuth , G. J. Alner , D. Ayres , W. L. Barrett , P. Border , D. J. A. Cockerill , J. H. Cobb , H. Courant , T. Fields , H. Gallagher , M. C. Goodman , R. Gran , T. Joffe-Minor , T. Kafka , S. Kasahara , P. J. Litchfield , W. A. Mann , M. Marshak , R. Milburn , W. Miller , L. Mualem , A. Napier , W. Oliver , G. F. Pearce , E. Peterson , D. Petyt , K. Ruddick , M. Sanchez e J. Schneps , A. So...

We study the dynamics of a circadian oscillator model proposed by Tyson, Hong, Thron and Novak. This describes molecular mechanism for rhythm in Drosophila. After giving detailed its equilibria, we investigate cases that rate mRNA degradation is sufficiently high or low. When high, prove there are no periodic orbits region with biological meaning. low, this transformed into slow–fast system. Th...

Für die meisten schulischen Arbeitsaufgaben wird geräuscharmes, aufrechtes Sitzen als unverzichtbar angesehen. Der folgende Artikel geht der Frage nach, wie sich das auf einem Sitzgestell zunehmend demokratisiert und vom Thron über den Caféhaustuhl Eingang in Alltag gefunden hat. Die Rolle Schule bei Einübung Festigung dieser Körpertechnik ebenso dabei beleuchtet damit verbundene Disziplinardis...

background: decay products of radon and thoron present in indoor environment are the most important sources of radiation from natural sources which affect human beings, since general public spend at lest 80% of their time in indoor. materials and methods: air samples were collected for measuring the concentration of radon and thoron daughter products from various indoor environments during four...

ABSTRACf. In [3], Reed establishes a bijection between the (equivalence classes of) principal Tt-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the To case by obtaining a one-to-one correspondence between the principal To-extensions of a space X and the collections of sets (called "t-grill sets") which generate a cer...

D. DeMuth , G. J. Alner , D. Ayres , W. L. Barrett , P. Border , D. J. A. Cockerill , J. H. Cobb , H. Courant , T. Fields , H. Gallagher , M. C. Goodman , R. Gran , T. Joffe-Minor , T. Kafka , S. Kasahara , P. J. Litchfield , W. A. Mann , M. Marshak , R. Milburn , W. Miller , L. Mualem , A. Napier , W. Oliver , G. F. Pearce , E. Peterson , D. Petyt , K. Ruddick , M. Sanchez e J. Schneps , A. So...