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A Proposal for the Automatic Computation of Envelopes of Families of Plane Curves

Journal of Systems Science & Complexity 2019年第1期32卷 150-157页

作者： botana francisco RECIO Tomás Depto. de Matemática Aplicada I Universidad de Vigo Campus A Xunqueira Depto. de Matemáticas Estad'?stica y Computación Universidad de Cantabria

The idea of envelope of a family of plane curves is an elementary notion in differential geometry. As such, its implementation in dynamic geometry environments is quite universal(Cabri,The Geometer's Sketchpad, Cinderella, Geo Gebra,...). Nevertheless, most of these programs return,when computing certain envelopes, both some spurious solutions and the curves that truly ?t in the intuitive de?nition of envelope. The precise distinction between spurious and genuine parts has not been made before: This paper proposes such distinction in an algorithmic way, ready for its implementation in interactive geometry systems, allowing a ?ner classi?cation of the different parts resulting from the current, advanced approach to envelope computation and, thus, yielding a more precise output, free from extraneous components.

关键词： Automated deduction in geometry dynamic geometry envelopes parametric polynomial systems symbolic computation

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New environmental factors related to diabetes risk in humans:Emerging bisphenols used in synthesis of plastics

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World Journal of Diabetes 2023年第8期14卷 1301-1313页

作者： Rafael Moreno-Gómez-Toledano María Delgado-Marín Alberto Cook-Calvete Claudia González-Cucharero Nunzio Alcharani Beatriz Jiménez-Guirado Ignacio Hernandez Rafael Ramirez-Carracedo Laura Tesoro Laura botana Sandra Sánchez-Esteban Javier Diez-Mata Jose Luis Zamorano Ricardo J.Bosch Carlos Zaragoza Marta Saura Universidad de Alcalá Department of Biological Systems/PhysiologyAlcaláde Henares 28871Spain Cardiology Department University Hospital Ramón y CajalMadrid 28034Spain Laboratory of Cardiovascular Pathophysiology Joint Translational Research UnitUniversity Francisco de Vitoria School of MedicineMadrid 28034Spain Instituto Ramón y Cajal de Investigación Sanitaria-IRYCIS Madrid 28034Spain

BACKGROUND Diabetes mellitus(DM)is one of the largest global health emergencies of the 21st *** recent years,its connection with environmental pollutants,such as bisphenol A(BPA),has been demonstrated;consequently,new structurally similar molecules are used to replace BPA in the plastics industry(BPS,BPF and BPAF).AIM To carry out a systematic review to allow coherent evaluation of the state of the ***,a meta-analysis was performed to unify the existing quantitative *** Firstly,a systematic review was carried out,using the terms“(bisphenol)AND(Diabetes OR Hyperglycemia)”,to maximize the number of ***,three authors analyzed the set of ***,a meta-analysis was performed for each BP,using RevMan *** addition,funnel plots were developed to study publication *** The systematic analysis of the literature revealed 13 recent articles(2017–2023)related to the study *** qualitative analysis showed interesting data linking diabetes to the three most widely used substitute BPs in the industry:BPS,BPF and ***,the meta-analysis determined a positive relationship with BPS,BPF and BPAF,which was only statistically significant with *** There is a need to apply the precautionary principle,regulating the use of new ***,replacing BPA with BPS,BPF or BPAF is unlikely to protect the population from potential health risks,such as DM.

关键词： Bisphenol S Bisphenol F Bisphenol AF Diabetes mellitus Systematic review Meta-analysis

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