Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops

We consider random Schr\"odinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.Comment: 25 pages, 4 figure

942-42 Is Mitral Valve Prolapse with Significant Mitral Regurgitation a Different Condition from Uncomplicated Mitral Prolapse? Results of Family Studies

Mild instances of mitral valve prolapse (MVP) have been suggested to represent variants of normal, whereas individuals with complicated forms of MVP have a distinct medical condition. This hypothesis would predict different phenotypic features and patterns of inheritance in relatives of index cases with complicated or uncomplicated MVP. Accordingly, we performed clinical and echocardiographic assessment of 16 MVP patients with and 76 without moderate to severe mitral regurgitation (MR+and MR– probands) and 60 and 256, respectively, first-degree relatives (MR+ and MR– relatives). MR+ probands were older (p=0.01), more likely to be male (p=0.002), were more overweight (p=0.004) and had higher systolic blood pressures (p=0.05) and larger aortic roots (p=0.034) after the effects of age and body size were taken into account. MR+ and MR– relatives had similar prevalences (27 and 32%) and age distribution of MVP, but affected MR+ relatives were younger (expected because more children and fewer parents of MR+ probands could be evaluated). and more likely to be male. MR+ and MR- relatives were virtually identical in regard to body habitus, blood pressure, the prevalence of auscultatory findings, thoracic bony abnormalities and palpitations and all echo measurements including anterior mitral leaflet thickness. Four instances of significant MR and two MVP-related complications (infective endocarditis and transient ischemic attack) occurred in the 82 relatives of MR– probands as opposed to none among relatives of MR+ probands. In 20 families, one proband or relative with MVP had severe MR and at least one other with MVP (presumably due to the same gene) was free of MR or complications. Thus, MVP with severe MR does not represent a heritable phenotype and commonly coexists with mild forms of MVP in the same family, making their classification as separate conditions illogical and potentially misleading

Surface materials of the Viking landing sites

Martian surface materials viewed by the two Viking landers (VL-1 and VL-2) range from fine-grained nearly cohesionless soils to rocks. Footpad 2 of VL-1, which landed at 2.30 m/s, penetrated 16.5 cm into very fine grained dunelike drift material; footpad 3 rests on a rocky soil which it penetrated ≈3.6 cm. Further penetration by footpad 2 may have been arrested by a hard substrate. Penetration by footpad 3 is less than would be expected for a typical lunar regolith. During landing, retroengine exhausts eroded the surface and propelled grains and rocks which produced craters on impact with the surface. Trenches excavated in drift material by the sampler have steep walls with up to 6 cm of relief. Incipient failure of the walls and failures at the end of the trenches are compatible with a cohesion near 10–10^2 N/m^2. Trenching in rocky soil excavated clods and possibly rocks. In two of five samples, commanded sampler extensions were not achieved, a situation indicating that buried rocks or local areas with large cohesions (≥10 kN/m^2) or both are present. Footpad 2 of VL-2, which landed at a velocity between 1.95 and 2.34 m/s, is partly on a rock, and footpad 3 appears to have struck one; penetration and leg strokes are small. Retroengine exhausts produced more erosion than occurred for VL-1 owing to increased thrust levels just before touchdown. Deformations of the soil by sampler extensions range from doming of the surface without visible fracturing to doming accompanied by fracturing and the production of angular clods. Although rocks larger than 3.0 cm are abundant at VL-1 and VL-2, repeated attempts to collect rocks 0.2–1.2 cm across imbedded in soil indicate that rocks in this size range are scarce. There is no evidence that the surface sampler of VL-2, while it was pushing and nudging rocks ≈25 cm across, spalled, chipped, or fractured the rocks. Preliminary analyses of surface sampler motor currents (≈25 N force resolution) during normal sampling are consistent with cohesionless frictional soils (ϕ ≈ 36°) or weakly cohesive frictionless soils (C < 2 kN/m^2). The soil of Mars has both cohesion and friction

Sensitivities of Key Parameters in the Preparation of Silver/Silver Chloride Electrodes Used in Harned Cell Measurements of pH

A questionnaire was completed by fourteen world leading national metrology institutes to study the influence of several variables in the preparation of Ag/AgCl electrodes on the accuracy of Harned cell measurements of pH. The performance of each institute in the last decade has been assessed based on their results in eight key comparisons, organized by the Bureau International des Poids et Measures Consultative Committee for Amount of Substance, involving the measurement of pH of phosphate, phthalate, carbonate, borate and tetroxalate buffer solutions. The performance of each laboratory has been correlated to the results of the questionnaire to determine the critical parameters in the preparation of Ag/AgCl electrodes and their sensitivities with respect to the accuracy of pH measurement. This study reveals that the parameters most closely correlated to performance in comparisons are area of electrode wire exposed to the electrolyte, diameter and porosity of the Ag sphere prior to anodisation, amount of Ag converted to AgCl during anodisation, stability times employed for electrodes to reach equilibrium in solution prior to measurement, electrode rejection criteria employed and purity of reagents

On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.Comment: (1 figure

Effect of Structural Design of Silver/Silver Chloride Electrodes on Stability and Response Time and the Implications for Improved Accuracy in pH Measurement

The response time of thermal electrolytic Ag/AgCl reference electrodes is defined by the porous structure that limits the rate at which traces of any previous solution are diluted by any new solution environment. The electrode stabilisation time when transferred from one electrolyte to another has been shown to change when different structural designs to the conventional sphere of Ag/AgCl are used. Electrodes fabricated with cylindrical architectures of Ag/AgCl have shown improved stability and reach equilibrium faster than spherical electrodes. This work has positive implications for the accuracy and throughput of primary pH measurements made using the Harned cell