Results 1 to 10 of about 270 (49)

Infinitesimals via Cauchy sequences: Refining the classical equivalence

Open Mathematics, 2021
A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that a null sequence “becomes” an infinitesimal.
Emanuele Bottazzi, Mikhail G Katz
exaly   +2 more sources

Monotone subsequence via ultrapower

Open Mathematics, 2018
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and ...
Piotr Błaszczyk, Vladimir Kanovei, Tahl Nowik   +2 more
exaly   +2 more sources

Metric completions, the Heine-Borel property, and approachability

Open Mathematics, 2020
We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space.
Kanovei Vladimir, Katz Mikhail G., Nowik Tahl   +2 more
doaj   +1 more source

Connectedness and compactness on standard sets [PDF]

, 2010
We present a nonstandard characterization of connected compact sets. (C) 2010 WILEY-VCH Verlag GmbH & Co KGaA.
Almeida, R
core   +2 more sources

Cost-effectiveness of ranibizumab in treatment of diabetic macular oedema (DME) causing visual impairment : evidence from the RESTORE trial [PDF]

, 2012
Background/aims To evaluate the cost-effectiveness of ranibizumab as either monotherapy or combined with laser therapy, compared with laser monotherapy, in the treatment of diabetic macular oedema (DME) causing visual impairment from a UK healthcare ...
Mitchell, Paul, Annemans, Lieven, Gallagher, Meghan, Hasan, Rafiq, Thomas, Simu, Gairy, Kerry, Knudsen, Martin, Onwordi, Henrietta   +7 more
core   +2 more sources

A strong form of almost differentiability [PDF]

, 2009
We present a uniformization of Reeken's macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor's theorem, mean value ...
Almeida, R., Neves, V.
core   +2 more sources

Stevin numbers and reality [PDF]

, 2012
We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures.
A. H. Lightstone, A. L. Cauchy, A. Malet, A. Robinson, A. Tarski, A.-L. Cauchy, B. L. Waerden van der, C.S. Peirce, C.S. Peirce, D. Fearnley-Sander, D. H. Fowler, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sherry, D. Tall, D. Tall, E. Hewitt, G. Hellman, G. Lakoff, G. Schubring, H. Freudenthal, H. Sinaceur, J. Bair, J. Burgess, J. Dauben, J. Dauben, J. Havenel, J. L. Bell, K. Bråting, K. Katz, Karin Usadi Katz, L. Arkeryd, L. Arkeryd, L. Magnani, M. Moore, M. Moore, Mikhail G. Katz, N. Cutland, P. Ehrlich, P. Roquette, R. Dossena, R. Ely, R. Goldblatt, S. Gandz, Th. Skolem   +46 more
core   +1 more source

Generalized solutions of variational problems and applications

Advances in Nonlinear Analysis, 2018
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ*⊃ℝ{\mathbb{R}^{*}\supset\mathbb{R}} that allow to solve variational problems with no classical solutions.
Benci Vieri, Luperi Baglini Lorenzo, Squassina Marco   +2 more
doaj   +1 more source

Deconvolving the pre-Himalayan Indian margin – tales of crustal growth and destruction [PDF]

, 2018
The metamorphic core of the Himalaya is composed of Indian cratonic rocks with two distinct crustal affinities that are defined by radiogenic isotopic geochemistry and detrital zircon age spectra.
Ahmad, Ali, Ali, Ali, Ali, Ali, Ali, Amato, Aoki, Be’eri-Shlevin, Be’eri-Shlevin, Blades, Botev, Cawood, Cawood, Cawood, Chen, Chen, Clift, Collins, Collins, Cui, DeCelles, DeCelles, Ding, Dyck, Gansser, Ge, Gehrels, Gehrels, Griffin, Guynn, Gürsu, Han, Hassanzadeh, Hawkesworth, Hopkinson, Horstwood, Hu, Hu, Huang, Iizuka, Iizuka, Isozaki, Kaur, Kay, Keppie, Kohn, Le Fort, Le Fort, Lee, Li, Li, Li, Li, Li, Li, Long, Long, Martin, Martin, McQuarrie, McQuarrie, Merdith, Morag, Morag, Mottram, Myrow, Myrow, Myrow, Nowell, Pan, Parrish, Richards, Roberts, Roberts, Robinson, Robinson, Scholl, Searle, Shen, Shu, Singh, Sláma, Song, Spakman, Spencer, Spencer, Spencer, Spencer, Spencer, Stern, Stern, Su, Tate, Thimm, Thomas, Veevers, von Huene, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Wang, Webb, Webb, Woodhead, Woodhead, Yakymchuk, Yan, Yao, Yao, Yao, Yao, Yao, Yin, Yu, Yu, Yu, Yu, Zhang, Zhang, Zhou, Zhou, Zhu, Zhu, Zou   +132 more
core   +4 more sources

Antibiotic prescribing in primary healthcare: Dominant factors and trade-offs in decision-making [PDF]

, 2018
Background: This study aims to establish dominant factors influencing general practitioner (GP) decision-making on antibiotic prescribing in the Australian primary healthcare sector.
Australian Commission on Safety and Quality in Health Care, Australian Commission on Safety and Quality in Health Care, Australian Government, Bech, Bell, Biesta, Bridges, Broom, Broom, Butler, Butler, Charani, Choice Metrics, Coenen, Coenen, Creswell, Dallas, Department of Health, Department of Health, Drekonja, Edwards, Fereday, Fletcher-Lartey, Gerard, Hall, Hardy-Holbrook, Hauber, Henriksen, Hensher, Hoffman, Hoffmann, Jefferson, Kumar, Lancaster, Lancsar, Lum, Marshall, McCullough, McDonnell Norms Group, McFadden, NPS MedicineWise, NPS MedicineWise, OECD, Public Health England, Russo, Ryan, Ryan, Saldana, Sargent, Sargent, Spurling, Tashakkori, Teixeira Rodrigues, van Driel, Wong, World Health Organization   +55 more
core   +2 more sources