A Weighted Estimate for the Square Function on the Unit Ball in \C^n

We show that the Lusin area integral or the square function on the unit ball of \C^n, regarded as an operator in weighted space $L^2(w)$ has a linear bound in terms of the invariant $A_2$ characteristic of the weight. We show a dimension-free estimate for the ``area-integral'' associated to the weighted $L^2(w)$ norm of the square function. We prove the equivalence of the classical and the invariant $A_2$ classes.Comment: 11 pages, to appear in Arkiv for Matemati

Sharp weighted estimates for classical operators

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. Our method is flexible enough to prove the corresponding sharp one-weight norm inequalities for some operators of harmonic analysis: the maximal singular integrals associated to $T$, Dyadic square functions and paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein. Also we can derive a very sharp two-weight bump type condition for $T$.Comment: We improve different parts of the first version, in particular we show the sharpness of our theorem for the vector-valued maximal functio

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor

Effect of temperature on passive film formation of UNS N08031 Cr-Ni alloy in phosphoric acid contaminated with different aggressive anions

tThe influence of temperature and the effect of aggressive anions on the electrochemical behaviour of UNSN08031 stainless steel in a contaminated phosphoric acid solution were evaluated. Stabilisation of thepassive film was studied by potentiodynamic polarisation curves, potentiostatic tests, electrochemicalimpedance spectroscopy (EIS) measurements, Mott Schottky analysis and X-ray photoelectron spec-troscopy (XPS). The stability of the passive film was found to decrease as temperature increases. The filmformed on the stainless steel surface was a n-type semiconductor and the XPS spectrum revealed thepresence of fluoride ions.Authors express their gratitude to the Ministry of Education of Spain (MHE2011-00202) for its financial support during the stay at University of Manchester, to MAEC of Spain (PCI Mediterraneo C/8196/07, C/018046/08, D/023608/09 and D/030177/10) and to the Generalitat Valenciana (GV/2011/093) for the financial support. The authors would also like to acknowledge the support of the School of Materials at the University of Manchester for providing analytical and technical support for the study.Escrivá Cerdán, C.; Blasco Tamarit, ME.; García García, DM.; García Antón, J.; Akid, R.; Walton, J. (2013). Effect of temperature on passive film formation of UNS N08031 Cr-Ni alloy in phosphoric acid contaminated with different aggressive anions. Electrochimica Acta. 111:552-561. https://doi.org/10.1016/j.electacta.2013.08.040S55256111

Bounds for the Hilbert transform with matrix A2 weights

International audienceWe establish a new estimate for the Hilbert transform in L^2 space endowed with a matrix weight

Passive and transpassive behaviour of Alloy 31 in a heavy brine LiBr solution

The passive and transpassive behaviour of Alloy 31, a highly alloyed austenitic stainless steel (UNS N08031), has been investigated in a LiBr heavy brine solution (400 g/l) at 25 °C using potentiostatic polarisation combined with electrochemical impedance spectroscopy and Mott-Schottky analysis. The passive film formed on Alloy 31 has been found to be p-type and/or n-type in electronic character, depending on the film formation potential. The thickness of the film formed at potentials within the passive region increases linearly with applied potential. The film formed at transpassive potentials is thinner and more conductive than the film formed within the passive region. These observations are consistent with the predictions of the Point Defect Model for passive and transpassive films on metals and alloys