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About 5,203 papers for “Computable analysis”

Computable Real Analysis,

Bruce J. MacLennan · Defense Technical Information Center (DTIC) · 1984

We present a model of the real numbers that is completely finitistic. Every real number is represented by a finite structure-specifically, a finite sequence of symbols from a finite alphabet. All of the arithmetic operations on reals are also finite and can be evaluated on a computer. We allow nothing that cannot be described by a finite algorithm-whether numbers or sequences or functions. This development is carried through the fundamental theorem of calculus. (Author)

Cited by 1

Aspects of Computable Analysis

Michelle Porter · 2016

<p>Computable analysis has been well studied ever since Turing famously formalised the computable reals and computable real-valued function in 1936. However, analysis is a broad subject, and there still exist areas that have yet to be explored. For instance, Sierpinski proved that every real-valued function ƒ : ℝ → ℝ is the limit of a sequence of Darboux functions. This is an intriguing result, and the complexity of these sequences has been largely unstudied. Similarly, the Blaschke Selection Theorem, closely related to the Bolzano-Weierstrass Theorem, has great practical importance, but has not been considered from a computability theoretic perspective. The two main contributions of this thesis are: to provide some new, simple proofs of fundamental classical results (highlighting the role of ∏0/1 classes), and to use tools from effective topology to analyse the Darboux property, particularly a result by Sierpinski, and the Blaschke Selection Theorem. This thesis focuses on classical computable analysis. It does not make use of effective measure theory.</p>

Cited by 0

Aspects of Computable Analysis

Michelle Porter · 2016

<p>Computable analysis has been well studied ever since Turing famously formalised the computable reals and computable real-valued function in 1936. However, analysis is a broad subject, and there still exist areas that have yet to be explored. For instance, Sierpinski proved that every real-valued function ƒ : ℝ → ℝ is the limit of a sequence of Darboux functions. This is an intriguing result, and the complexity of these sequences has been largely unstudied. Similarly, the Blaschke Selection Theorem, closely related to the Bolzano-Weierstrass Theorem, has great practical importance, but has not been considered from a computability theoretic perspective. The two main contributions of this thesis are: to provide some new, simple proofs of fundamental classical results (highlighting the role of ∏0/1 classes), and to use tools from effective topology to analyse the Darboux property, particularly a result by Sierpinski, and the Blaschke Selection Theorem. This thesis focuses on classical computable analysis. It does not make use of effective measure theory.</p>

Cited by 1Open access

Aspects of Computable Analysis

Michelle Porter · Figshare · 2016

<p>Computable analysis has been well studied ever since Turing famously formalised the computable reals and computable real-valued function in 1936. However, analysis is a broad subject, and there still exist areas that have yet to be explored. For instance, Sierpinski proved that every real-valued function ƒ : ℝ → ℝ is the limit of a sequence of Darboux functions. This is an intriguing result, and the complexity of these sequences has been largely unstudied. Similarly, the Blaschke Selection Theorem, closely related to the Bolzano-Weierstrass Theorem, has great practical importance, but has not been considered from a computability theoretic perspective. The two main contributions of this thesis are: to provide some new, simple proofs of fundamental classical results (highlighting the role of ∏0/1 classes), and to use tools from effective topology to analyse the Darboux property, particularly a result by Sierpinski, and the Blaschke Selection Theorem. This thesis focuses on classical computable analysis. It does not make use of effective measure theory.</p>

Cited by 1Open access

COMPUTABLE GENERAL EQUILIBRIUM ANALYSIS

Serajul Hoque · 2006

We use a 86-industry CGE model of Bangladesh to simulate the employment effects of removing all tariffs in Bangladesh. We find that this would expand GDP and generate employment. The industries that experience the greatest positive effects on their output and employment are the export-oriented industries. There are also positive effects on the suppliers to these industries. Lightly-protected industries that rely heavily on imported intermediate inputs exhibit robust expansion as they benefit from a cost reduction. In contrast, highly-protected industries demonstrate contraction. The occupational pattern of the employment results indicates that expansion is felt most heavily in the export sector (export-related occupation experiences the largest increase).

Cited by 0

Lowness, randomness, and computable analysis

André Nies · arXiv (Cornell University) · 2016

Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th birthday.

Cited by 0Open access

Computable analysis and Blaschke products

Alec Matheson, Timothy H. McNicholl · Proceedings of the American Mathematical Society · 2007

We show that if a Blaschke product defines a computable function, then it has a computable sequence of zeros in which the number of times each zero is repeated is its multiplicity. We then show that the converse is not true. We finally show that every computable, radial, interpolating sequence yields a computable Blaschke product.

Cited by 7Open access

A Computable General Equilibrium Analysis

Zenebe Gebreegziabher, Jesper Stage, Alemu Mekonnen et al. · 2011

This paper analyses the economic impacts of climate change on Ethiopia’s agriculture using a countrywide computable general equilibrium model. The impacts on agriculture are based on results from a Ricardian model where current (and future) agricultural production is analyzed as a function of temperature and precipitation. We project that the effect of overall climate change will be relatively benign until approximately 2030 and then worsen considerably. Our simulation results indicate that, over a 50-year period, the projected

Cited by 0