Results 21 to 30 of about 270 (49)

Scale Free Analysis and the Prime Number Theorem [PDF]

, 2010
We present an elementary proof of the prime number theorem. The relative error follows a golden ratio scaling law and respects the bound obtained from the Riemann's hypothesis.
Choudhuri, Anuja Roy, Datta, Dhurjati Prasad   +1 more
core   +1 more source

Ten Misconceptions from the History of Analysis and Their Debunking [PDF]

, 2012
The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems.
A. Connes, A. Fraenkel, A. H. Lightstone, A. L. Cauchy, A. L. Cauchy, A. Malet, A. Robinson, A. Tarski, A. Weil, A. Weil, A.L. Cauchy, B. L. Waerden van der, B. Pourciau, B. Russell, C. Baltus, C. Boyer, D. E. Smith, D. Fearnley-Sander, D. H. Fowler, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Laugwitz, D. Sepkoski, D. Sherry, D. Sherry, D. Tall, D. Tall, David Sherry, E. Hewitt, E. Knobloch, E. Madison, E. Nelson, E.T. Bell, F. Faltin, F. W. Lawvere, G. Fisher, G. Leibniz, G. Schubring, H. Freudenthal, H. J. Keisler, H. J. M. Bos, H. Putnam, H. Rust, H. Sinaceur, Huygens, I. Grattan-Guinness, I. Kleiner, I. Lakatos, J. Crossley, J. Dauben, J. Grabiner, J. Gray, J. L. Bell, J. Lützen, J. Naets, K. Andersen, K. Bråting, K. Hrbacek, K. Hrbacek, K. Hrbáček, K. Katz, L. Arkeryd, L. Arkeryd, L. Magnani, M. Dehn, M. J. Barany, Mikhail G. Katz, N. Cutland, P. Ehrlich, P. Ehrlich, P. Giordano, P. Giordano, P. Mancosu, P. Mancosu, P. Roquette, P. Strømholm, Piotr Błaszczyk, R. Anderson, R. B. McClenon, R. Dedekind, R. Dedekind, R. Dossena, R. Ely, R. Lutz, S. Albeverio, S. H. Levy, S. Smale, T. Koetsier, T. Mormann, T. Tao, Th. Skolem, V. Benci, V. J. Katz, W. Felscher, W. Felscher   +95 more
core   +1 more source

Basic properties of ultrafunctions

, 2013
Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions.
Baglini, Lorenzo Luperi, Benci, Vieri
core   +1 more source

A mean value theorem for internal functions and an estimation for the diifferential mean point [PDF]

, 2008
In this paper we present several results about the mean value theorem (MVT) with nonstandard analysis techniques. Using only the intermediate value theo- rem, we present a nonstandard proof of the MVT.
Almeida, R
core  

A mu-differentiable Lagrange multiplier rule [PDF]

, 2009
We present some properties of the gradient of a mu-differentiable function.
Almeida, R, Torres, DFM
core  

Compact linear operators, a survey [PDF]

, 2007
In this paper we approach the Compact Linear Operators Theory by methods of Nonstandard Analysis.
Almeida, R
core  

Nonstandard analysis and differentiable manifolds - Foundations [PDF]

, 2009
We approach the study of di erentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the category of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations ...
Almeida, R
core  

On the continuity of functions [PDF]

, 2007
Some theorems on continuity are presented. First we will prove that every convex function f :Rn -> R is continuous using nonstandard analysis methods. Then we prove that if the image of every compact (resp. convex) is compact (resp.
Almeida, R
core  

On the Darboux property of derivative multifunction [PDF]

, 2015
Kwiecińska, Grażyna
core   +1 more source

Angles corniculaires et nombres superréels [PDF]

, 2008
Bair, Jacques, Henry, Valérie
core   +1 more source