scholarly journals On the period length of some special continued fractions

1992 ◽  
Vol 4 (1) ◽  
pp. 19-42 ◽  
Author(s):  
R. A. Mollin ◽  
H. C. Williams
Keyword(s):  
Continued Fractions ◽  
Period Length

scholarly journals CLASSIFICATION AND SYMMETRIES OF A FAMILY OF CONTINUED FRACTIONS WITH BOUNDED PERIOD LENGTH

2012 ◽  
Vol 93 (1-2) ◽  
pp. 53-76
Author(s):  
K. H. F. CHENG ◽  
R. K. GUY ◽  
R. SCHEIDLER ◽  
H. C. WILLIAMS
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Period Length ◽  
Continued Fraction Expansion ◽  
Quadratic Irrational ◽  
Continued Fraction Expansions

AbstractIt is well known that the regular continued fraction expansion of a quadratic irrational is symmetric about its centre; we refer to this symmetry as horizontal. However, an additional vertical symmetry is exhibited by the continued fraction expansions arising from a family of quadratics known as Schinzel sleepers. This paper provides a method for generating every Schinzel sleeper and investigates their period lengths as well as both their horizontal and vertical symmetries.

scholarly journals A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe
Keyword(s):  
Dynamical Systems ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Unit Interval ◽  
Probability Measures ◽  
Absolutely Continuous ◽  
Continued Fraction Expansions ◽  
Absolutely Continuous Invariant

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aim to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan’s continued fractions, θ-expansions, N-continued fractions, and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

scholarly journals Extreme Value Theory for Hurwitz Complex Continued Fractions

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 840
Author(s):  
Maxim Sølund Kirsebom
Keyword(s):  
Invariant Measure ◽  
Extreme Value Theory ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Value Theory ◽  
Extreme Value ◽  
Poisson Law ◽  
Complex Continued Fractions

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.

Effects of dry period length on milk yield and content and metabolic status of high-producing dairy cows under heat stress

2021 ◽  
Vol 53 (2) ◽  
Author(s):  
A. Boustan ◽  
V. Vahedi ◽  
M. Abdi Farab ◽  
H. Karami ◽  
R. Seyedsharifi ◽  
...  
Keyword(s):  
Heat Stress ◽  
Dairy Cows ◽  
Milk Yield ◽  
Period Length ◽  
Metabolic Status ◽  
Dry Period
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