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CCA
2009
Springer
13 years 9 months ago
On the Computability of Rectifiable Simple Curve (Extended Abstract)
d Abstract) Robert Rettinger1 and Xizhong Zheng2,3 1 Lehrgebiet Algorithmen und Komplexit
Robert Rettinger, Xizhong Zheng
CCA
2009
Springer
13 years 9 months ago
Effective Choice and Boundedness Principles in Computable Analysis
Abstract. In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can...
Vasco Brattka, Guido Gherardi
CCA
2009
Springer
13 years 9 months ago
Effective Dispersion in Computable Metric Spaces
We investigate the relationship between computable metric spaces (X, d, ) and (X, d, ), where (X, d) is a given metric space. In the case of Euclidean space, and are equivalent u...
Zvonko Iljazovic
CCA
2009
Springer
13 years 9 months ago
From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interv
Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds ∆ on the measurement errors. In this case, ba...
Vladik Kreinovich
CCA
2009
Springer
13 years 11 months ago
Computability of Homology for Compact Absolute Neighbourhood Retracts
In this note we discuss the information needed to compute the homology groups of a topological space. We argue that the natural class of spaces to consider are the compact absolut...
Pieter Collins
CCA
2009
Springer
13 years 11 months ago
A Constructive Study of Landau's Summability Theorem
Josef Berger, Douglas S. Bridges
CCA
2009
Springer
13 years 11 months ago
Separations of Non-monotonic Randomness Notions
In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Mar...
Laurent Bienvenu, Rupert Hölzl, Thorsten Kr&a...
CCA
2009
Springer
13 years 11 months ago
Computing Conformal Maps onto Canonical Slit Domains
We extend the results of [2] by computing conformal maps onto the canonical slit domains in Nehari [14]. Along the way, we demonstrate the computability of solutions to Neuman prob...
Valentin V. Andreev, Timothy H. McNicholl