Small ball probability for the condition number of random matrices

Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb P}\big\{s_{\max}(A)/s_{\min}(A)\leq n/t\big\}\leq 2\exp(-c t^2),\quad t\geq 1,$$ where $c>0$ may only depend on the subgaussian moment. Although the estimate can be obtained as a combination of known results and techniques, it was not noticed in the literature before. As a key step of the proof, we apply estimates for the singular values of $A$, ${\mathbb P}\big\{s_{n-k+1}(A)\leq ck/\sqrt{n}\big\}\leq 2 \exp(-c k^2), \quad 1\leq k\leq n,$ obtained (under some additional assumptions) by Nguyen.Comment: Some changes according to the Referee's comment

LpL_p-Steiner quermassintegrals

Inspired by an $L_p$ Steiner formula for the $L_p$ affine surface area proved by Tatarko and Werner, we define, in analogy to the classical Steiner formula, $L_p$-Steiner quermassintegrals. Special cases include the classical mixed volumes, the dual mixed volumes, the $L_p$ affine surface areas and the mixed $L_p$ affine surface areas. We investigate the properties of the $L_p$-Steiner quermassintegrals. In particular, we show that they are rotation and reflection invariant valuations on the set of convex bodies with a certain degree of homogeneity. Such valuations seem new and not have been observed before

Predicting soil wind erosion potential under different corn residue management scenarios in the central Great Plains

Various models and simplified equations are available to predict wind erosion potential. However, their performance can be often site-specific, depending on soil characteristics and agronomic practices, warranting sitespecific model validations. Thus, in this study, we 1) validated the wind erodible fraction (WEF) predictive equations by Fryrear et al. (1994) and López et al. (2007) and 2) estimated the total soil loss with the Singleevent Wind Erosion Evaluation Program (SWEEP) using 3-yr measured data from six experiments located across a precipitation gradient in the central Great Plains. Each site had three corn (Zea mays L.) residue removal treatments: control (no removal), grazed, and baled. The measured and predicted WEF were significantly correlated. While the Fryrear et al. (1994) equation performed better than the López et al. (2007) equation, it underestimated WEF with 59% uncertainty across site-years. To reduce this underestimation and uncertainty, we developed a new statistical equation (WEF%=84.3+2.64×% silt-0.30×% clay-7.43×% organic matter- 0.15×% residue cover; r2=0.56). The predictive ability of the new equation was, however, no better than that of the existing predictive equations, suggesting the need for further refinement of WEF equations for the region. Simulated total soil loss by wind using the SWEEP model indicated that corn residue baling may increase soil loss if residue cover drops below 20% in the study region. Overall, the existing WEF equations could under- or overestimate WEF based on site-specific residue management, warranting further model refinement and site-specific validation, whereas the SWEEP estimated soil loss corroborates the critical importance of maintaining sufficient residue cover (\u3e 20%) to reduce wind erosion

Ytterbium disilicate-based glass-ceramic as joining material for ceramic matrix composites

A key aspect of ceramic matrix composites integration is related to a reliable joining technique. An ytterbium disilicate based glass-ceramic material is processed by reactive viscous flow sintering between a barium aluminium borosilicate glass and ytterbium oxide and it is used to join SiC/SiC and C/SiC composites. The joining temperature and the in situ formation of the Yb2Si2O7 is optimised at 1200°C without pressure, on the basis of the sintering and crystallisation mechanisms. The mechanical characterization of SiC/SiC and C/SiC joined with the ytterbium disilicate-based glass-ceramic, tested by single-lap offset at RT, exhibits an apparent shear strength of 35 MPa, similar to their interlaminar shear strength. The proposed system displays self-healing behaviour at 1000 °C and 1150 °C, as demonstrated by the partial and complete sealing of induced cracks by Vickers indentation on its surface at different loads, thus suggesting that it can effectively be used as promising joining material for CMCs

Optimization of cytochrome c detection by acoustic and electrochemical methods based on aptamer sensors

© 2016 Elsevier B.V.We report the effect of various factors such as oligonucleotide sequence, buffer composition, ionic strength for optimal determination of cytochrome c (cyt c) by DNA aptamer sensors using thickness shear mode acoustics (TSM) and electrochemical methods. Up to now, several DNA aptamers specific to cyt c have been selected and used in various sensing approaches including optical, electrochemical and mass sensitive transducers. We have analyzed the response of three different aptamers immobilized via biotin-neutravidin method on a gold support by TSM technique. Using this approach we have shown that only 76-length base sequence (apt 76) exhibited specific binding to cyt c with detection limit of 0.50 ± 0.05 nM. This aptamer was then studied under different ionic conditions showing an optimal response for HEPES buffer. Apt 76 based sensor has been also examined by electrochemical methods. However due to the electroactive nature of cyt c, the response of this aptamer was less favorable in comparison with TSM. The apt 76 based sensor was tested also in spiked samples of human plasma by TSM achieving a recovery of 92 ± 6.6% for 1 nM cyt c

Design, Realization, and Characterization of Advanced Adhesives for Joining Ultra-Stable C/C Based Components

The aim of this work is to develop high-performance adhesives to join carbon fiber reinforced composites (C/C) for use in aerospace applications; in order to guarantee sound mechanical strength, a low coefficient of thermal expansion, and ease of application on large components. Several different adhesive formulations, based on phenolic or cyanate-ester resins (charged with the maximum experimentally feasible amount of carbon-based fillers), are developed and tested. The measurements of the lap shear strength at room temperature of the C/C joined by means of one phenolic and one cyanate ester-based resin demonstrates that these formulations are the most suitable for the given application. A complete characterization, by means of viscosimetry, dilatometry, and thermal gravimetric analysis, coupled with gas analysis by means of mass spectroscopy, confirms that the phenolic-based formulation is the most promising joining material. A nano-indenter is used to obtain its Young modulus and hardness, both inside the joint and as a bulk cured adhesive

Enhancing wind erosion monitoring and assessment for U.S. rangelands

Wind erosion is a major resource concern for rangeland managers because it can impact soil health, ecosystem structure and function, hydrologic processes, agricultural production, and air quality. Despite its significance, little is known about which landscapes are eroding, by how much, and when. The National Wind Erosion Research Network was established in 2014 to develop tools for monitoring and assessing wind erosion and dust emissions across the United States. The Network, currently consisting of 13 sites, creates opportunities to enhance existing rangeland soil, vegetation, and air quality monitoring programs. Decision-support tools developed by the Network will improve the prediction and management of wind erosion across rangeland ecosystems. © 2017 The Author(s)The Rangelands archives are made available by the Society for Range Management and the University of Arizona Libraries. Contact [email protected] for further information