Related papers: An entire function with simply and multiply connec…
The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected…
We consider the iteration of quasiregular maps of transcendental type from $\mathbb{R}^d$ to $\mathbb{R}^d$. In particular we study quasi-Fatou components, which are defined as the connected components of the complement of the Julia set.…
The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems…
It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties. We verify this conjecture for projective manifolds whose universal cover…
In this paper, we study conditions which ensure the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain $D$. More precisely, the problem is the following. Given a…
For many transcendental entire functions, the escaping set has the structure of a Cantor bouquet, consisting of uncountably many disjoint curves. Rippon and Stallard showed that there are many functions for which the escaping set has a new…
Approximation of entire functions by their pad\'e approximants has been examined in the past. It is true that generically such an approximation holds. However, examining this problem from another viewpoint, we obtain stronger generic…
We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.
We consider the dynamical properties of transcendental entire functions and their compositions. We give several conditions under which Fatou set of a transcendental entire function $f$ coincide with that of $f\circ g,$ where $g$ is another…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
Rabi and Sherman [RS97] presented novel digital signature and unauthenticated secret-key agreement protocols, developed by themselves and by Rivest and Sherman. These protocols use ``strong,'' total, commutative (in the case of multi-party…
This paper is concerned with the existence and uniqueness of transition fronts of a general reaction-diffusion-advection equation in domains with multiple branches. In this paper, every branch in the domain is not necessary to be straight…
In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the…
We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P^2(C). We also find real examples with wandering…
A complex projective manifold is rationally connected, resp. rationally simply connected, if finite subsets are connected by a rational curve, resp. the spaces parameterizing these connecting rational curves are themselves rationally…
Guided by classical concepts, we define the notion of \emph{ends} of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points…
A question whether sufficiently regular manifold automorphisms may have wandering domains with controlled geometry is answered in the negative for quasiconformal or smooth homeomorphisms of $n$-tori, $n\ge2$, and hyperbolic surfaces.…
An arbitrary outward cuspidal domain is shown to be bi-Lipschitz equivalent to a Lipschitz outward cuspidal domain via a global transformation. This allows us to extend earlier Sobolev extension results on Lipschitz outward cuspidal domains…
We provide explicit expression of squeezing function for infinitely connected planar domain obtained by removing a convergent sequence of points from the unit disk converging to the boundary of unit disk. We also discuss Fridman invariant…
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…