On the degree of approximation of functions in C2π1 with operators of the Jackson type

AbstractLet C2π1 be the class of real functions of a real variable that are 2π-periodic and have a continuous derivative. The positive linear operators of the Jackson type are denoted by Ln,p(n ∈ N), where p is a fixed positive integer. The object of this paper is to determine the exact degree of approximation when approximating functions f ϵ C2π1 with the operators Ln,p. The value of maxx¦Ln,p(f x) − f(x)¦ is estimated in terms of ω1(f; δ), the modulus of continuity of f′, with δ = πn. Exact constants of approximation are obtained for the operators Ln,p (n ∈ N, p ≥ 2) and for the Fejér operators Ln,1 (n ∈ N). Furthermore, the limiting behaviour of these constants is investigated as n → ∞, and p → ∞, separately or simultaneously

Checklist for One Health Epidemiological Reporting of Evidence (COHERE).

One Health is defined as the intersection and integration of knowledge regarding humans, animals, and the environment, yet as the One Health scientific literature expands, there is considerable heterogeneity of approach and quality of reporting in One Health studies. In addition, many researchers who publish such studies do not include or integrate data from all three domains of human, animal, and environmental health. This points to a critical need to unify guidelines for One Health studies. This report details the Checklist for One Health Epidemiological Reporting of Evidence (COHERE) to guide the design and publication format of future One Health studies. COHERE was developed by a core writing team and international expert review group that represents multiple disciplines, including human medicine, veterinary medicine, public health, allied professionals, clinical laboratory science, epidemiology, the social sciences, ecohealth and environmental health. The twin aims of the COHERE standards are to 1) improve the quality of reporting of observational or interventional epidemiological studies that collect and integrate data from humans, animals and/or vectors, and their environments; and 2) promote the concept that One Health studies should integrate knowledge from these three domains. The 19 standards in the COHERE checklist address descriptions of human populations, animal populations, environmental assessment, spatial and temporal relationships of data from the three domains, integration of analyses and interpretation, and inclusion of expertise in the research team from disciplines related to human health, animal health, and environmental health