We give a description of asymptotic quadratic growth rates for geodesic segments on covers of Veech surfaces in terms of the modular fiber parameterizing coverings of a fixed Veech surface. To make the paper self contained we derive the necessary asymptotic formulas from the Gutkin-Judge formula. As an application of the method we define and analyze d-symmetric elliptic differentials and their ...

In this paper, we introduce the notions of S-proximal Berinde g-cyclic contraction two nonself mappings and g-contractions first kind second in an S-metric space prove some coincidence best proximity point theorems for these types space. Also, give examples to analyze support our main results. The results presented here generalize existing literature.

In this paper we study the stability properties of a delay differential equation by means of contraction mappings. The paper is motivated by a number of difficulties encountered in the study of stability by means of Liapunov’s direct method. We notice that most of these difficulties vanish when applying fixed point theory. An asymptotic stability theorem with a necessary and sufficient conditio...

We consider a variety of subtrees of various shapes lying on the fringe of a recursive tree. We prove that (under suitable normalization) the number of isomorphic images of a given fixed tree shape on the fringe of the recursive tree is asymptotically Gaussian. The parameters of the asymptotic normal distribution involve the shape functional of the given tree. The proof uses the contraction met...

We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a ver...

We consider distributional recursions which appear in the study of random binary search trees with monomials as toll functions. This extends classical parameters as the internal path length in binary search trees. As our main results we derive asymptotic expansions for the moments of the random variables under consideration as well as limit laws and properties of the densities of the limit dist...

We derive asymptotic approximations for the sequence f(n) de5ned recursively by f(n) = min16j¡n {f(j) + f(n− j)}+ g(n), when the asymptotic behavior of g(n) is known. Our tools are general enough and applicable to another sequence F(n) = max16j¡n {F(j) + F(n − j) + min{g(j); g(n− j)}}, also frequently encountered in divide-and-conquer problems. Applications of our results to algorithms, group t...

We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β) be the asymptotic probability that a random integer n is semismooth with respect to nβ and nα. We present new recurrence relations for G and related functions. We then give numerica...

The novelty of our paper is to establish results on asymptotic stability mild solutions in $p$th moment Riemann-Liouville fractional stochastic neutral differential equations (for short FSNDEs) order $\alpha \in (\frac{1}{2},1)$ using a Banach's contraction mapping principle. core point this derive the solution FSNDEs involving time-derivative by applying version variation constants formula. ar...

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation process realized by a Recurrent Neural Network (RNN) are provided. Existence. convergence, and robustness of such a process are analyzed. This is undertaken based upon the Contraction Mapping Theorein (CMT) and the corresponding Fixed Point Iteration (FPI). Upper bounds for such a process are shown to be the conditions o...