Nonstandard analysis and generalized Riemann integrals
Non-standard analysis and homology
Nonstandard analysis and the theory of shape
Non-standard characterisations of ideals in C(X).
Nonstandard methods for Navier-Stokes equations
Non-transitive points and porosity
We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems. We also show...
Nonwhere differentiable solutions of a system of functional equations. (Summary).
Norm comparison inequalities for the composite operator.
Norm estimates for Bessel-Riesz operators on generalized Morrey spaces
We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent , and obtain a new estimate for their norm.
Norm inequalities for integral operators on cones
Norm inequalities in weighted amalgam
Hardy inequalities for the Hardy-type operators are characterized in the amalgam space which involves Banach function space and sequence space.
Normal bases of rings of continuous functions constructed with the (qₙ)-digit principle
Normal numbers and subsets of N with given densities
For X ⊆ [0,1], let denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of . For α ≥ 3, X is properly iff is properly . We also show that for every nonempty set X ⊆[0,1], is -hard. For each nonempty set X ⊆ [0,1], in particular for X = x, is -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is -complete. Moreover, , the...
Normal spaces and the Lusin-Menchoff property
We study the relation between the Lusin-Menchoff property and the -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.
Normalization of almost conformal parabolic germs.
Note on a discretization of a linear fractional differential equation
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
Note on a theorem by Reshetnyak-Gurov
Note on a Theorem of Kuratowski-Sierpiński
Note on an inequality involving .
Note on an inequality of F. Qi and L. Debnath.