All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 15 Next

Displaying 281 – 300 of 2145

Showing per page

Approximate and L p Peano derivatives of nonintegral order

J. Marshall Ash, Hajrudin Fejzić (2005)

Studia Mathematica

Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. L p , 1 ≤ p ≤ ∞) sense at x ∈ ℝ m if there are numbers f α ( x ) , |α| ≤ n, such that f ( x + h ) - ∑ | α | ≤ n f α ( x ) h α / α ! is O ( h u ) in the approximate (resp. L p ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or L p sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and f = g on Π....

Area functionals and Godbillon-Vey cocycles

Takashi Tsuboi (1992)

Annales de l'institut Fourier

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the topology...

Arrow-Hahn economic models with weakened conditions of continuity

Inese Bula, Dace Rika (2006)

Banach Center Publications

In this article we give descriptions of some economic models that are based on Arrow-Hahn economic model. Finally we consider a model with two major assumptions: first, there is discontinuous excess demand function and, second, if price goes to zero, then it is possible that excess demand may approach infinity. For this last new economic model the existence of quasi-equilibrium is proved.

Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

Jaroslav Jaroš, Kusano Takaŝi, Jelena Manojlović (2013)

Open Mathematics

Positive solutions of the nonlinear second-order differential equation ( p ( t ) | x ' | α - 1 x ' ) ' + q ( t ) | x | β - 1 x = 0 , α > β > 0 , are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.

Currently displaying 281 – 300 of 2145