Experiencing War as the \u27Enemy Other\u27: Italian Scottish experience in World War II (Book Review) by Wendy Ugolini

Review of Experiencing War as the \u27Enemy Other\u27: Italian Scottish experience in World War II. Wendy Ugolini. Manchester: Manchester University Press, 2011. Pp. 288

On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian

We prove the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y)$, for $0<\alpha<2$ and all real $m$, in the lattice ${\mathbf Z}^{d}$ as well as in the continuum ${\mathbf R}^{d}$ for dimension $d\ge 2$. This resolvent occurs as the covariance of the Gaussian measure underlying weakly self- avoiding walks with long range jumps (stable L\'evy walks) as well as continuous spin ferromagnets with long range interactions in the long wavelength or field theoretic approximation. The finite range decomposition should be useful for the rigorous analysis of both critical and off-critical renormalisation group trajectories. The decomposition for the special case $m=0$ was known and used earlier in the renormalisation group analysis of critical trajectories for the above models below the critical dimension $d_c =2\alpha$. This revised version makes some changes, adds new material, and also corrects some errors in the previous version. It refers to the author's published article with the same title in J Stat Phys (2016) 163: 1235-1246, as well as to an erratum to be published in J Stat Phys.Comment: 20 pages, 1 figure, errors corrected, references added, two new appendice

The Capacity of Channels with Feedback

We introduce a general framework for treating channels with memory and feedback. First, we generalize Massey's concept of directed information and use it to characterize the feedback capacity of general channels. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity. Fifth, scenarios with simple sufficient statistics are described

Thermodynamics of the Casimir effect

A complete thermodynamic treatment of the Casimir effect is presented. Explicit expressions for the free and the internal energy, the entropy and the pressure are discussed. As an example we consider the Casimir effect with different temperatures between the plates ($T$) resp. outside of them ($T'$). For $T'<T$ the pressure of heat radiation can eventually compensate the Casimir force and the total pressure can vanish. We consider both an isothermal and an adiabatic treatment of the interior region. The equilibrium point (vanishing pressure) turns out instable in the isothermal case. In the adiabatic situation we have both an instable and a stable equilibrium point, if $T'/T$ is sufficiently small. Quantitative aspects are briefly discussed.Comment: 12 pages, 3 EPS-figure