Directional qualitative cluster sets
Discontinuity points of exactly -to-one functions
Discrete approximation of the Mumford-Shah functional in dimension two
The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.
Discrete fractional calculus with the nabla operator.
Discrete Models of Time-Fractional Diffusion in a Potential Well
Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity...
Distant bounded variation and products of derivatives
Distortion function and quasisymmetric mappings
We study the relationship between the distortion function and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.
Distortion theorems for fractional calculus of certain analytic functions with negative coefficients.
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
We give characterizations of the distributional derivatives , , of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Distributional fractional powers of the Laplacean. Riesz potentials
For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...
Division space axiomatics
Dynamical properties of maps derived from maps with strong negative Schwarzian derivative.
Dynamical stability of the typical continuous function
Dynamical systems on vector bundles.
Dynamics of a certain sequence of powers.
Dynamics of the radix expansion map.
Each nowhere dense nonvoid closed set in Rn is a σ-limit set
We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in , n ≥ 1, is a σ-limit set for some continuous map.
Effective decomposition of σ-continuous Borel functions
We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering of X such that is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.
Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Ein allgemeiner Satz der Integrirbarkeitslehre