Relation between the boundary point spectrum of a generator and of its adjoint

In this paper we get some relations between the boundary point spectrum of the generator A of a C0-semigroup and the generator A* of the dual semigroup. These relations combined with the results due to Lyubich-Phóng and Arendt-Batty, yield stability results on positive Cosemigroup

A new notion of solutions to the pp-Laplacian evolution equation in metric measure spaces

The $p$-Laplacian evolution equation in metric measure spaces has been studied as the gradient flow in $L^2$ of the $p$-Cheeger energy (for $1 < p < \infty$). In this paper, using the first-order differential structure on a metric measure space introduced by Gigli, we characterize the subdifferential in $L^2$ of the $p$-Cheeger energy. This gives rise to a new definition of the $p$-Laplacian operator in metric measure spaces, which allows us to work with this operator in more detail. In this way, we introduce a new notion of solutions to the $p$-Laplacian evolution equation in metric measure spaces. For $p = 1$, we obtain a Green-Gauss formula similar to the one by Anzellotti for Euclidean spaces, and use it to characterise the $1$-Laplacian operator and study the total variation flow. We also study the asymptotic behaviour of the solutions of the $p$-Laplacian evolution equation, showing that for $1 \leq p < 2$ we have finite extinction time.Comment: 56 page

Low-cost and easy experiments about water in the atmosphere

Peer ReviewedPostprint (published version

Asymptotic approach to Special Relativity compatible with a relativistic principle

We propose a general framework to describe Planckian deviations from Special Relativity (SR) compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to SR going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the non-trivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.Comment: 12 page

About Locality and the Relativity Principle Beyond Special Relativity

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality \cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-called Doubly Special Relativity theories.Comment: 10 pages, no figure

Variaciones fisiológicas observadas en tubérculos de patata (solanum tuberosum L.) después de un tratamiento con radiación gamma

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Químicas, leída en 1975.Fac. de Ciencias QuímicasTRUEProQuestpu

A nonlocal 1-Laplacian problem and median values

In this paper, we study solutions to a nonlocal 1-Laplacian equation. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled

Variaciones fisiológicas observadas en tubérculos de patata (solanum tuberosum L.) después de un tratamiento con radiación gamma

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Químicas, leída en 1975.Fac. de Ciencias QuímicasTRUEProQuestpu