Results 11 to 20 of about 187 (58)
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 +2 more
doaj +1 more source
The general set in the MCIM Isotopic Model [PDF]
, 2005 To obtain a bigger number of mathematical and physical applications of the Santilli’s isotheory, the latest studies have shown the necessity of analyzing isotopic models which use non associative laws.
Falcón Ganfornina, Raúl Manuel +1 more
core +2 more sources
An embedding of Schwartz distributions in the algebra of asymptotic functions
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 417-428, 1998., 1997 We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper “asymptotic function,” similar to but different from J. F Colombeau′s algebras of new generalized functions.
Michael Oberguggenberger, Todor Todorov
wiley +1 more source
The Caccioppoli ultrafunctions
Advances in Nonlinear Analysis, 2017 Ultrafunctions are a particular class of functions defined on a hyperreal field ℝ∗⊃ℝ{\mathbb{R}^{\ast}\supset\mathbb{R}}. They have been introduced and studied in some previous works [2, 6, 7].
Benci Vieri +2 more
doaj +1 more source
The rapid points of a complex oscillation [PDF]
, 2012 By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion.
Potgieter, Paul
core +2 more sources
Algebraic Approach to Colombeau Theory [PDF]
, 2013 We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology.
Todorov, Todor D.
core +3 more sources
Hypernatural Numbers as Ultrafilters [PDF]
, 2015 In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of ...
A Blass +27 more
core +2 more sources
A Correspondence Principle for the Gowers Norms
, 2012 We give a variation of the Furstenberg Correspondence which preserves the Gowers uniformity norms.Comment: Journal of Logic and Analysis, 4; February ...
Towsner, Henry
core +2 more sources
A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets [PDF]
, 2017 Results of Smale (1957) and Dugundji (1969) allow to compare the homotopy groups of two topological spaces $X$ and $Y$ whenever a map $f:X\to Y$ with strong connectivity conditions on the fibers is given.
Achille, Alessandro +1 more
core +2 more sources
Axiomatics for the external numbers of nonstandard analysis [PDF]
, 2017 Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix.
Berg, Imme van den, Dinis, Bruno
core +2 more sources