A remark on one-sided approximation

Eggan, L. C.; Niven, Ivan

doi:10.1090/s0002-9939-1961-0131398-5

Cited by 2 publications

(2 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding BLDA (2) (figure (a)), take grid points [q, p] ∈ N 2 that lie immediately below the graph of f (x) = αx, i.e. [1,2], [2,4], [3,6], [4, 8] and [5,11]. Their vertical distances to the graph are approximately 0.24, 0.47, 0.71, 0.94 and 0.18, respectively.…”

Section: Approximations Of the First And Second Kindmentioning

confidence: 99%

See 1 more Smart Citation

One-sided Diophantine approximations

Hančl¹,

Turek²

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The paper deals with best one-sided (lower or upper) Diophantine approximations of the -th kind ( ∈ N). We use the ordinary continued fraction expansions to formulate explicit criteria for a fraction p q ∈ Q to be a best lower or upper Diophantine approximation of the -th kind to a given α ∈ R. The sets of best lower and upper approximations are examined in terms of their cardinalities and metric properties. Applying our results in spectral analysis, we obtain an explanation for the rarity of so-called Bethe-Sommerfeld quantum graphs.

show abstract

Section: Approximations Of the First And Second Kindmentioning

confidence: 99%

“…Robinson [16] used continued fractions to provide an alternative proof of Segre's theorem. Another and very short proof was later published by Eggan and Niven [5]. Then Finkelshtein [9] studied best upper Diophantine approximations of the 2nd kind.…”

Section: Introductionmentioning

confidence: 98%

One-sided Diophantine approximations

Hančl¹,

Turek²

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Klein polygons and reduced regular continued fractions

Finkel'shtein¹

1993

Russ. Math. Surv.

View full text Add to dashboard Cite

We investigated the influence of the irradiation conditions of the coherent length and the polarization of the laser beam, the incident angle i , the pulse number, the fluence, the substrate temperature and the a-Si film thickness on the meltingcrystallization of an a-Si film and the controllability of the periodic grain boundary location by using a linearly polarized laser beam. For formation of periodic grain boundary in the crystallized Si film, the linear polarization is key factor rather than the coherent length. Also, the a-Si film thickness should be around 60 nm for large optical absorption, and the high substrate temperature and the large pulse number are preferable. By using a p-polarized beam, the grain boundary width can be expanded proportional to 1=ð1 À sin i Þ roughly. In order to suppress the ablation of the film and to increase the productivity, the fluence should be adjusted precisely.

show abstract

A remark on one-sided approximation

Cited by 2 publications

References 3 publications

One-sided Diophantine approximations

One-sided Diophantine approximations

Klein polygons and reduced regular continued fractions

Contact Info

Product

Resources

About