We study static black hole solutions in Einstein and Einstein–Gauss–Bonnet gravity with the topology of the product of two spheres,Sn × Sn, in higher dimensions. There is an unusual new feature of the Gauss–Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of > 0. For an Einstein–Gauss–Bonnet black hole a limited window of ne...

Aim of this work is to study the possibility existence multistability near boundary generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz have been chosen as an object study, and a modified auxiliary system method has used detect presence synchronous regime. Result proof unidirectionally topology attractor. For purpose, basins attraction asynch...

The reliability of the distributed system has been an important topic of research. Consensus protocols, which allow the correct nodes to agree on a common value, have been brought up to aid the reliable execution of tasks. In previous works, fully connected networks, generalized connected networks or multicasting network with fallible components were proposed to solve the consensus problem. How...

We use the idea of a scalarization of a cone metric to prove that the topology generated by any cone metric is equivalent to a topology generated by a related metric. We then analyze the case of an ordering cone with empty interior and we provide alternative definitions based on the notion of interior cone. Finally we discuss the implications of such cone metrics in the theory of iterated funct...

We study certain generalized topological structures, called closure operations, that are associated with -ary relations ( ¿ 1 an ordinal). It turns out that some of these structures are well-behaved with respect to connectedness and so are suitable for applications in digital topology. In particular, for any natural number n¿ 1 we ,nd an appropriate closure operation on Z, which is associated w...

The Leibler theory [L. Leibler, Macromolecules 13 1602 (1980)] for mi-crophase separation in AB block copolymer melts is generalized for systems with arbitrary topology of molecules. A diagrammatic technique for calculation of the monomeric correlation functions is developed. The free energies of various mesophases are calculated within the second-harmonic approximation. Model highly-branched t...

1. Introduction Mac Lane and Moerdijk, 1992, in their thorough introduction to topos theory, start their Prologue by saying – A startling aspect of topos theory is that it unifies two seemingly wholly distinct mathematical subjects: on the one hand, topology and algebraic geometry, and on the other hand, logic and set theory. Indeed , a topos can be considered both as a " generalized space " an...