In this article, we prove existence results for common fixed points of two or three relatively asymptotically regular mappings satisfying the orbital continuity of one of the involved maps on ordered orbitally complete metric spaces. We furnish suitable examples to demonstrate the validity of the hypotheses of our results.

Abstract In string theory, an important challenge is to show if the singularity of black holes can be smoothed out by complete $$\alpha ^{\prime }$$ α ′ corrections. The simplest case consider a 2D hole or 3D string. This problem was discussed in gauged Wess–Zumino–Witt...

We aim here at showing how some known Ramanujan Cayley graphs yield error-correcting codes that are asymptotically optimal in the class of cycle codes of graphs. The main reason why known constructions of Ramanujan graphs yield good cycle codes is that the number of their cycles of a given length behaves essentially like that of random regular graphs. More precisely we show that for actual cons...

We consider the Vlasov-Einstein system in a spherically symmetric setting and prove the existence of static solutions which are asymptotically flat and have finite total mass and finite extension of the matter. Among these there are smooth, singularity-free solutions, which have a regular center and may have isotropic or anisotropic pressure, and also solutions, which have a Schwarzschild-singu...

For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to...

Given a globally asymptotically controllable system, we derive from an existence theorem of a semiconcave control-Lyapunov function, the construction of a globally asymptotically stable feedback in the Euler sense. The feedback is rather regular in the case of control systems affine in the control. Abridged English Version In this paper, we study systems of the general form ẋ(t) = f(x(t), u(t))...

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased ...

We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express ω-regular conditions. The qualitative analysis...

A three dimensional black hole solution of Einstein equations with negative cosmological constant coupled to a conformal scalar field is given. The solution is static, circularly symmetric, asymptotically anti-de Sitter and nonperturbative in the conformal field. The curvature tensor is singular at the origin while the scalar field is regular everywhere. The condition that the Euclidean geometr...