A continuum growth model is introduced. The state at time t, St, is a subset of R and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs somewhere in St after an exponentially distributed time with expected value |St| −1 and the location of the outburst is uniformly distributed over St. The main result is that ...

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of N = 4 super Yang-Mills theory in D = 4 and the (2, 0) tensor multiplet in D = 6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. For strongly coupled CFTs with AdS duals, we show that t...

In this paper we prove an approximate controllability result for the bilinear Schrödinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrödinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the controllability result to the density matrices. The proof ...

The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in R under uniform random shift is proportional to the (d + 1)st power of the grid scaling factor. This result remains valid for a bounded set in R with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to t...

We study the ratio of the entropy to the total energy in conformal field theories at finite temperature. For the free field realizations of N = 4 super Yang-Mills theory in D = 4 and the (2, 0) tensor multiplet in D = 6, the ratio is bounded from above. The corresponding bounds are less stringent than the recently proposed Verlinde bound. For strongly coupled CFTs with AdS duals, we show that t...

The quasigeostrophic model is a simpli ed geophysical uid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there see...

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with than that in four dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bound...

Bounds for the bulk heat transport in Rayleigh-Benard convection for an infinite Prandtl number fluid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the nondimensional temperature difference across the layer (the Rayleigh number Ra) according to Nu ≤ c Ra where c < 1 is an absolute co...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms o er a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthe...