Search results for "Applied Mathematics"

Some fixed point theorems for generalized contractive mappings in complete metric spaces

2015

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Resonance between Cantor sets

2007

Let $C_a$ be the central Cantor set obtained by removing a central interval of length $1-2a$ from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if $\log b/\log a$ is irrational, then \[ \dim(C_a+C_b) = \min(\dim(C_a) + \dim(C_b),1), \] where $\dim$ is Hausdorff dimension. More generally, given two self-similar sets $K,K'$ in $\RR$ and a scaling parameter $s>0$, if the dimension of the arithmetic sum $K+sK'$ is strictly smaller than $\dim(K)+\dim(K') \le 1$ (``geometric resonance''), then there exists $r<1$ such that all contraction ratios of the similitudes defining $K$ and $K'$ are powers of $r$ (``algebraic resonance…

Finite 2-groups with odd number of conjugacy classes

2016

In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly $k$ real conjugacy classes. On the other hand we construct infinitely many finite 2-groups with exactly 25 real conjugacy classes. Both resuls are proven using pro-$p$ techniques and, in particular, we use the Kneser classification of semi-simple $p$-adic algebraic groups.

Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)

2018

A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enou…

Weakly compact composition operators between algebras of bounded analytic functions

1999

Lattice property of $p$-admissible weights

2015

$(BV,L^p)$-decomposition, $p=1,2$, of Functions in Metric Random Walk Spaces

2019

In this paper we study the $(BV,L^p)$-decomposition, $p=1,2$, of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the case $p=1$ we also study the associated geometric problem and the thresholding parameters.

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.

Generic unfoldings with the same bifurcation diagram which are not (C0, C0)— equivalent

1997

A decidable word problem without equivalent canonical term rewriting system

1989

We present a weak associative single-axiom system having the following property: the word problem is decidable with an efficient algorithm even though there does not exist any finite equivalent canonical term rewriting system.