Results 11 to 20 of about 195 (57)
Relative set theory: Some external issues
Journal of Logic and Analysis, 2010 The paper establishes equivalence of two axiomatizations of the relative set theory GRIST, examines dependence of nonstandard concepts on the choice of the level, and proves that several nonstandard definitions of Lebesgue measure are equivalent.
K. Hrbacek
semanticscholar +1 more source
Time averaging for functional differential equations
Journal of Applied Mathematics, Volume 2003, Issue 1, Page 1-16, 2003., 2003 We present a result on the averaging for functional differential equations on finite time intervals. The result is formulated in both classical mathematics and nonstandard analysis; its proof uses some methods of nonstandard analysis.
Mustapha Lakrib
wiley +1 more source
Regions in the nonstandard plane that contain no standard points
Journal of Logic and Analysis, 2012 Nonstandard methods are applied to continuum theory in the plane. The main result concerns internal regions V that contain no standard points and have the property that st(V) does not disconnect the plane and are bounded by simple closed curves that have
Steven C. Leth
semanticscholar +1 more source
The method of averaging and functional differential equations with delay
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 8, Page 497-511, 2001., 2001 We present a natural extension of the method of averaging to fast oscillating functional differential equations with delay. Unlike the usual approach where the analysis is kept in an infinite‐dimensional Banach space, our analysis is achieved in ℝn. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is
Mustapha Lakrib
wiley +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 +2 more
doaj +1 more source
Relative set theory: Strong stability
Journal of Logic and Analysis, 2012 GRIST is an axiomatic framework for nonstandard set theory with many "levels of standardness." The paper establishes a number of general consequences of GRIST, in particular, a very strong form of Transfer principle.
K. Hrbacek
semanticscholar +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
Diffusion processes via parabolic equations: an infinitesimal approach to Lindeberg's limit theorem
Journal of Logic and Analysis, 2009 We approach infinitesimal diffusion processes via a linkage to the diffu- sion equation. By this we obtain Lindeberg's limit theorem and a Lindeberg type limit theorem for diffusion processes by an application of the underspill principle.
H. Weisshaupt
semanticscholar +1 more source
Categories of First-Order Quantifiers [PDF]
, 2018 One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories
Adam Nowaczyk +13 more
core +2 more sources