We survey multivariate limit laws for sequences of random vectors which satisfy distributional recursions as they appear under various models of randomness for parameters of trees, characteristics of divideand-conquer algorithms, or, more generally, for quantities related to recursive structures or branching processes. While the area of probabilistic analysis of algorithms, since its introducti...

Consider the equation div$(\varphi^2 \nabla \sigma)=0$ in $\mathbb{R}^N,$ where $\varphi>0$. It is well-known that if there exists $C>0$ such $\int_{B_R}(\varphi \sigma)^2 dx\leq CR^2$ for every $R\geq 1$ then $\sigma$ necessarily constant. In this paper we prove result not true replace $R^2$ by $R^k$ $k>2$ any dimension $N$. This question related to a conjecture De Giorgi.

Let $\Omega$ be a subdomain of $\mathbb{C}$ and let $\mu$ positive Borel measure on $\Omega$. In this paper, we study the asymptotic behavior eigenvalues compact Toeplitz operators $T\_\mu$ acting Bergman spaces $(\lambda n(T\mu))$ decreasing sequence $T\_\mu$, $\rho$ an increasing function such that $\rho (n)/n^A$ is for some $A>0$. We give explicit necessary sufficient geometric condition in ...

In this paper we prove a new version of Kransoselskii's fixed-point theorem under ($\psi, \theta, \varphi$)-weak contraction condition. The theoretical result is applied to the existence solution following fractional hybrid differential equation involving Riemann-Liouville and integral operators orders $0<\alpha<1$ $\beta>0:$ \begin{equation}\nonumber \left\{\begin{array}{ll} D^{\alpha}[x(t)-f(...

Methods for proving functional limit laws are developed for sequences of stochastic processes which allow a recursive distributional decomposition either in time or space. Our approach is an extension of the so-called contraction method to the space C[0, 1] of continuous functions endowed with uniform topology and the space D[0, 1] of càdlàg functions with the Skorokhod topology. The contractio...

A module $$M$$ is said to be distributive (resp., uniserial) if the submodule lattice of a chain) Any uniserial but ring integers non-uniserial as $$\mathbb{Z}$$ -module. Direct sums (resp. modules are called semidistributive serial) modules. If $$A$$ with automorphism $$\varphi$$ , then we denote by $$A((x,\varphi))$$ skew Laurent series coefficient in which addition naturally defined and mult...

We prove that under some mild conditions on the symbol $$\varphi ,$$ spectrum of corresponding composition operator $$C_\varphi $$ Korenblum type spaces $$A_{-}^{-\alpha }$$ and $$A_{+}^{-\alpha contains a closed ball positive radius.