Interpolation of bilinear operators and compactness

The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some gaps in the original proof of Theorem 4.3, Here we give a new proof. For this, we change the Lemma 4.

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, like for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precise the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.Comment: 15 pages, 8 figures. Version accepted for publication in JSTA

The out-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory

We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job at describing the spatial shape of the correlation function of the out-equilibrium Edwards-Anderson Ising model in two dimensions.Comment: 20 pages + 5 Figure

Why a Single-Star Model Cannot Explain the Bipolar Nebula of Eta Carinae

I examine the angular momentum evolution during the 1837-1856 Great Eruption of the massive star Eta Carinae. I find that the new estimate of the mass blown during that eruption implies that the envelope of Eta Car substantially spun-down during the 20 years eruption. Single-star models, most of which require the envelope to rotate close to the break-up velocity, cannot account for the bipolar nebula (the Homunculus) formed from matter expelled in that eruption. The kinetic energy and momentum of the Homunculus further constrains single-star models. I discuss how Eta Car can fit into a unified model for the formation of bipolar lobes where two oppositely ejected jets inflate two lobes (or bubbles). These jets are blown by an accretion disk, which requires stellar companions in the case of bipolar nebulae around stellar objects.Comment: ApJ, in press. New references and segments were adde

Douglas-FIR Bark. II. Isolation and Characterization of A Glucomannan

A glucomannan has been isolated from the holocellulose fraction of the inner bark of Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco], and its structure and physical constants have been determined. The molar ratio of o-mannose, d-glucose, and d-galactose was 2:1:0.3. The glucomannan was completely methylated and hydrolyzed. Gas-liquid chromatographic and mass spectrometric analyses showed the presence of 2,3,4,6-tetra-, 2,3,6-tri-, and 2,3-di-O-methyl-d-glucopyranose, 2,3,6-tri- and 2,3-di-O-methyl-d-mannopyranose, and 2,3,4,6-tetra-O-methyl-d-galactopyranose. The proposed glucomannan structure consists of a linear chain of β-d-(1 → 4)-linked mannose and glucose units with α-d-(1 → 6)-linked galactose as intermittent, single-unit branches. The structural and physical properties of this glucomannan place it within the alkali-soluble family of polysaccharides known to be contained in the wood of all gymnosperms

FeNi-based magnetoimpedance multilayers: Tailoring of the softness by magnetic spacers

The microstructure and magnetic properties of sputtered permalloy films and FeNi(170 nm)/X/FeNi(170 nm) (X=Co, Fe, Gd, Gd-Co) sandwiches were studied. Laminating of the thick FeNi film with various spacers was done in order to control the magnetic softness of FeNi-based multilayers. In contrast to the Co and Fe spacers, Gd and Gd-Co magnetic spacers improved the softness of the FeNi/X/FeNi sandwiches. The magnetoimpedance responses were measured for [FeNi/Ti(6 nm)] 2/FeNi and [FeNi/Gd(2 nm)] 2/FeNi multilayers in a frequency range of 1-500 MHz: for all frequencies under consideration the highest magnetoimpedance variation was observed for [FeNi/Gd(2 nm)] 2/FeNi multilayers. © 2012 American Institute of Physics