Circular Twin Value Sets for Continued Fractions and How They Imply Convergence

Author(s):  
Lisa Lorentzen
2020 ◽  
Author(s):  
Sung Won Jung ◽  
Sungchul Bae ◽  
Donghyeong Seong ◽  
Byoung-Kee Yi

BACKGROUND Through several years of the healthcare information exchange based on the HIE project, some problems were found in the CDA documents generated. OBJECTIVE To fix some problems, we developed the K-CDA Implementation Guide (K means S. Korea) that conforms to the HL7 CDA, and suits the domestic conditions regarding the healthcare information. METHODS We achieved by analyzing HIE guideline and the U.S. C-CDA, and comparing each item. The items that required further discussion were reviewed by the expert committee. Based on the reviews, the previously developed templates were revised. RESULTS A total of 35 CDA templates were developed: five document-level templates, fourteen section-level templates, and sixteen entry-level templates. The 28 value sets used in the templates have been improved and the OIDs for HIE have been redefined CONCLUSIONS The K-CDA IG allows management in the form of a template library based on the definition of the General K-Header and the structured templates. This enables the K-CDA IG to respond to the expansion of national HIE templates with flexibility. For the K-CDA IG, the CDA template in current use was incorporated to the greatest extent possible, to minimize the scope of modifications. It enables the national HIE and the HIE with countries abroad.


Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 255
Author(s):  
Dan Lascu ◽  
Gabriela Ileana Sebe

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.


Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 840
Author(s):  
Maxim Sølund Kirsebom

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.


2020 ◽  
Vol 23 ◽  
pp. S680
Author(s):  
T. Pan ◽  
B. Mulhern ◽  
R. Viney ◽  
R. Norman ◽  
J. Hanmer ◽  
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