Recently, necessary and sufficient conditions for output synchronization of linear systems via diffusive couplings have been reported. In this paper, we study the case when such conditions are not satisfied and exact synchronization is impossible. In particular, we study two kinds of heterogeneous linear networks: (i) non-identical harmonic oscillators and (ii) double-integrators. We show that ...

We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that non-exi...

Extending the results of Friedrich (2008 Class. Quantum Grav. 25 065012) we give a complete description of the asymptotically flat, conformally non-flat, static vacuum data which admit non-trivial, asymptotically smooth conformal mappings onto other such data. These data form a 3-parameter family which decomposes into 1-parameter families of data which are conformal to each other. The data and ...

We study the equations of black strings in spacetimes of arbitrary dimensions with a negative cosmological constant and construct numerically non uniform black strings solutions. Our results suggest the existence of a localised black hole in asymptotically locally AdS spacetime. We also present evidences for a dependence of the critical dimension on the horizon radius.The critical dimension rep...

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

Sequential Mand L-estimators of location minimizing the risk asymptotically as the cost of one observation tends to 0 are constructed. Their asymptotic risk efficiencies are shown to coincide with the asymptotic efficiencies of the respective non-sequential estimators; this enables to construct the asymptotically minimax sequential Mand L-estimators in the model of contaminacy. The asymptotic d...

We prove that the space-time developments of generic solutions of the vacuum constraint Einstein equations do not possess any global or local Killing vectors, when Cauchy data are prescribed on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to a constant, or for CMC asymptotically hyperbolic initial data sets. More generally, we show that non-exi...

Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.

Renormalization group techniques are used in order to obtain the improved non-local gravitational effective action corresponding to any asymptotically free GUT, up to invariants which are quadratic on the curvature. The corresponding non-local gravitational equations are written down, both for the case of asymptotically free GUTs and also for quantum Rgravity. The implications of the results wh...