We extend the construction of the manifold structure of smooth mapping spaces even further, and show that the mapping functor takes regular maps to regular maps.

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like a...

Pollard’s rho method is the asymptotically fastest known attack for the elliptic curve discrete logarithm problem (ECDLP) except special cases. It works by giving a pseudo-random sequence defined by an iteration function and then detecting a collision in the sequence. We note that the number of iterations before obtaining a collision is significant for the running time of the rho method and dep...

We show that any embedding $\mathbb {R}^d \to \mathbb {R}^{2d+2^{\gamma (d)}-1}$ inscribes a trapezoid or maps three points to line, where $2^{\gamma (d)}$ is the smallest power of $2$ satisfying (d)} \geq \rho (d)$ , and $\rho denotes Hurwitz–Radon function. The proof elementary includes novel application nonsingular bilinear maps. As an application, we recover recent results on nonexistence a...

Asymptotically Anti-de Sitter (AdS) Black Hole (BH) space–times are of theoretical and mathematical interest attractive. On the other hand, in last few decades, theory regular (nonsingular) BHs has gained many researchers enthusiasts. Therefore, asymptotically AdS free (essential) singularities can have a double attraction. An example such space–time is Regular Gaussian (RGBH). In this paper, s...

This paper deals with the study of the Bayes estimator’s asymptotic properties on Differentiable in Quadratic Mean (DQM) models in the case of independent and identically distributed observations. The investigation is led in order to define weak assumptions on the model under which this estimator is asymptotically efficient, regular and asymptotically of minimal risk. The results of the paper a...

Numerical solutions of the Einstein-Yang-Mills equations with a negative cosmological constant are constructed. These axially symmetric solutions approach asymptotically the anti-de Sitter spacetime and are regular everywhere. They are characterized by the winding number n > 1, the mass and the non-Abelian magnetic charge. The main properties of the solutions and the differences with respect to...

Numerical arguments are presented for the existence of regular and black hole solutions of the EinsteinSkyrme equations with a positive cosmological constant. These classical configurations approach asymptotically the de Sitter spacetime. The main properties of the solutions and the differences with respect to the asymptotically flat ones are discussed. It particular our results suggest that, f...

Given a convex function $$\Phi :[0,1]\rightarrow {\mathbb {R}}$$ and the mean $${\mathbb {E}}f({\textbf{X}})=a\in [0,1]$$ , which Boolean f maximizes $$ -stability {E}}[\Phi (T_{\rho }f({\textbf{X}}))]$$ of f? Here $${\textbf{X}}$$ is random vector uniformly distributed on discrete cube $$\{-1,1\}^{n}$$ $$T_{\rho }$$ Bonami–Beckner operator. Special cases this problem include (symmetric asymmet...