627 research outputs found

    Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product

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    Given two positive integers nn and kk and a parameter t(0,1)t\in (0,1), we choose at random a vector subspace VnCkCnV_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n} of dimension NtnkN\sim tnk. We show that the set of kk-tuples of singular values of all unit vectors in VnV_n fills asymptotically (as nn tends to infinity) a deterministic convex set Kk,tK_{k,t} that we describe using a new norm in Rk\R^k. Our proof relies on free probability, random matrix theory, complex analysis and matrix analysis techniques. The main result result comes together with a law of large numbers for the singular value decomposition of the eigenvectors corresponding to large eigenvalues of a random truncation of a matrix with high eigenvalue degeneracy.Comment: v3 changes: minor typographic improvements; accepted versio

    New Frontier in Cooking Technology - 'Cooking Green'

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    An insulating carbon neutrality bag has been designed, tested and commissioned for green cooking. This has provided an eco - solution that has reduced the amount of energy needed for cooking, save money, reduce emission rate, create employment for the youths/ women and allows for waste to wealth conversion. The Okada Wonder Bag (OWB) was designed, fabricated, and the performance of the bag was critically evaluated using different food stuffs (Beans, Rice, Yam, plantain, Maize, beef, goat meat and Skin/beef ('special kpomo' from the head of a cow) to ascertain the reliability of the bag. Results obtained show a high degree of reliability/correlation as the bag displayed maximum performance in terms of heat conservation and cooking efficiency. Performance characteristics also reveal that the bag with expanded polystyrene insulation was better than that with wood shavings as insulating material. Also, an attempt was made using cooking gas as a case in point to show how much gas/money can be saved and emission reduction by the application ofthe insulation cooking technique and the results were encouragin

    Roughness distributions for 1/f^alpha signals

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    The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some references were correcte

    The Norwich Patellar Instability Score:validity, internal consistency and responsiveness for people conservatively-managed following first-time patellar dislocation

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    Background: This paper assessed the validity, internal consistency, responsiveness and floor-ceiling effects of the Norwich Patellar Instability (NPI) Score for a cohort of conservatively managed people following first-time patellar dislocation (FTPD).  Methods: Fifty patients were recruited, providing 130 completed datasets over 12 months. The NPI Score, Lysholm Knee Score, Tegner Level of Activity Score and isometric knee extension strength were assessed at baseline, six weeks, six and 12 months post-injury.  Results: There was high convergent validity with a statistically significant correlation between the NPI Score and the Lysholm Knee Score (p < 0.001), Tegner Level of Activity Score (p < 0.001) and isometric knee extension strength (p < 0.002). Principal component analysis revealed that the NPI Score demonstrated good concurrent validity with four components account for 70.4% of the variability. Whilst the NPI Score demonstrated a flooring-effect for 13 of the 19 items, no ceiling effect was reported. There was high internal consistency with a Cronbach Alpha value of 0.93 (95% CI: 0.91 to 0.93). The NPI Score was responsive to change over the 12 months period with an effect size of 1.04 from baseline to 12 months post-injury.  Conclusions: The NPI Score is a valid tool to assess patellar instability symptoms in people conservatively managed following FTPD.  Level of evidence: Level I

    Modulating proton conductivity through crystal structure tuning in arenedisulfonate coordination polymers

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    The functional group-directed structures of coordination polymers (CPs) and metal–organic frameworks (MOFs) have made them key candidates for proton exchange membranes in fuel cell technologies. Sulfonate group chemistry is well established in proton conducting polymers but has seen less exploration in CPs. Here, we report solvent-directed crystal structures of Cu²⁺ and Ca²⁺ CPs constructed with naphthalenedisulfonate (NDS) and anthraquinone-1,5-disulfonate (ADS) ligands, and we correlate single crystal structures across this set with proton conductivities determined by electrochemical impedance spectroscopy. Starting from the Cu²⁺-based NDS and aminotriazolate MOF designated Cu-SAT and the aqueous synthesis of the known Ca²⁺-NDS structure incorporating water ligands, we now report a further five sulfonate CP structures. These syntheses include a direct synthesis of the primary degradation product of Cu-SAT in water, solvent-substituted Ca-NDS structures prepared using dimethylformamide and dimethylsulfoxide solvents, and ADS variants of Cu-SAT and Ca-NDS. We demonstrate a consistent 2D layer motif in the NDS CPs, while structural modifications introduced by the ADS ligand result in a 2D hydrogen bonding network with Cu²⁺ and aminotriazolate ligands and a 1D CP with Ca²⁺ in water. Proton conductivities across the set span 10ˉ⁴ to >10ˉ³ S cmˉ¹ at 80 °C and 95% RH. These findings reveal an experimental structure–function relationship between proton conductivity and the tortuosity of the hydrogen bonding network and establish a general, cross-structure descriptor for tuning the sulfonate CP unit cell to systematically modulate proton conductivity

    Long-term aircraft noise exposure and risk of hypertension in postmenopausal women

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    Background: Studies of the association between aircraft noise and hypertension are complicated by inadequate control for potential confounders and a lack of longitudinal assessments, and existing evidence is inconclusive. Objectives: We evaluated the association between long-term aircraft noise exposure and risk of hypertension among post-menopausal women in the Women's Health Initiative Clinical Trials, an ongoing prospective U.S. cohort. Methods: Day-night average (DNL) and night equivalent sound levels (Lnight) were modeled for 90 U.S. airports from 1995 to 2010 in 5-year intervals using the Aviation Environmental Design Tool and linked to participant geocoded addresses from 1993 to 2010. Participants with modeled exposures ≥45 A-weighted decibels (dB [A]) were considered exposed, and those outside of 45 dB(A) who also did not live in close proximity to unmodeled airports were considered unexposed. Hypertension was defined as systolic/diastolic blood pressure ≥140/90 mmHg or inventoried/self-reported antihypertensive medication use. Using time-varying Cox proportional hazards models, we estimated hazard ratios (HRs) for incident hypertension when exposed to DNL or Lnight ≥45 versus &lt;45 dB(A), controlling for sociodemographic, behavioral, and environmental/contextual factors. Results/discussion: There were 18,783 participants with non-missing DNL exposure and 14,443 with non-missing Lnight exposure at risk of hypertension. In adjusted models, DNL and Lnight ≥45 db(A) were associated with HRs of 1.00 (95% confidence interval [CI]: 0.93, 1.08) and 1.06 (95%CI: 0.91, 1.24), respectively. There was no evidence supporting a positive exposure-response relationship, and findings were robust in sensitivity analyses. Indications of elevated risk were seen among certain subgroups, such as those living in areas with lower population density (HRinteraction: 0.84; 95%CI: 0.72, 0.98) or nitrogen dioxide concentrations (HRinteraction: 0.82; 95%CI: 0.71, 0.95), which may indicate lower ambient/road traffic noise. Our findings do not suggest a relationship between aircraft noise and incident hypertension among older women in the U.S., though associations in lower ambient noise settings merit further investigation

    The Structure of Jupiter, Saturn, and Exoplanets: Key Questions for High-Pressure Experiments

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    We give an overview of our current understanding of the structure of gas giant planets, from Jupiter and Saturn to extrasolar giant planets. We focus on addressing what high-pressure laboratory experiments on hydrogen and helium can help to elucidate about the structure of these planets.Comment: Invited contribution to proceedings of High Energy Density Laboratory Astrophysics, 6. Accepted to Astrophysics & Space Science. 12 page

    Effective Suppressing Phase Segregation of Mixed-Halide Perovskite by Glassy Metal-Organic Frameworks.

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    Lead mixed-halide perovskites offer tunable bandgaps for optoelectronic applications, but illumination-induced phase segregation can quickly lead to changes in their crystal structure, bandgaps, and optoelectronic properties, especially for the Br–I mixed system because CsPbI3 tends to form a non-perovskite phase under ambient conditions. These behaviors can impact their performance in practical applications. By embedding such mixed-halide perovskites in a glassy metal-organic framework, a family of stable nanocomposites with tunable emission is created. Combining cathodoluminescence with elemental mapping under a transmission electron microscope, this research identifies a direct relationship between the halide composition and emission energy at the nanoscale. The composite effectively inhibits halide ion migration, and consequently, phase segregation even under high-energy illumination. The detailed mechanism, studied using a combination of spectroscopic characterizations and theoretical modeling, shows that the interfacial binding, instead of the nanoconfinement effect, is the main contributor to the inhibition of phase segregation. These findings pave the way to suppress the phase segregation in mixed-halide perovskites toward stable and high-performance optoelectronics
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