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Full-Text Articles in Physical Sciences and Mathematics
Noncomputable Functions In The Blub-Shub-Smale Model, Wesley Calvert, Ken Kramer, Russell Miller
Noncomputable Functions In The Blub-Shub-Smale Model, Wesley Calvert, Ken Kramer, Russell Miller
Publications and Research
Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is insufficient to allow an oracle BSS-machine to decide membership in the set of algebraic numbers of degree d + 1. We add a number of further results on relative computability of these sets and their unions. Then we show that the halting problem for BSS-computation is not decidable below any countable oracle set, and give a more …
The Maximum Rectilinear Crossing Number Of The Wheel Graph, Elie Feder
The Maximum Rectilinear Crossing Number Of The Wheel Graph, Elie Feder
Publications and Research
We find and prove the maximum rectilinear crossing number of the wheel graph. First, we illustrate a picture of the wheel graph with many crossings to prove a lower bound. We then prove that this bound is sharp. The treatment is divided into two cases for n even and n odd.
Holomorphic Motions And Extremal Annuli, Zhe Wang
Holomorphic Motions And Extremal Annuli, Zhe Wang
Dissertations, Theses, and Capstone Projects
Holomorphic motions, soon after they were introduced, became an important subject in complex analysis. It is now an important tool in the study of complex dynamical systems and in the study of Teichmuller theory. This thesis serves on two purposes: an expository of the past developments and a discovery of new theories.
First, I give an expository account of Slodkowski's theorem based on the proof given by Chirka. Then I present a result about infinitesimal holomorphic motions. I prove the |ε log ε| modulus of continuity for any infinitesimal holomorphic motion. This proof is a very well application of Schwarz's …