Gradient estimates for degenerate quasi-linear parabolic equations

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Laplacian we obtain $L^q$-estimates for the gradients of solutions, and for the lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space variable

A method validation for simultaneous determination of phthalates and bisphenol A released from plastic water containers

Phthalates (or phthalate esters, PAEs) and bisphenol A (BPA) are widely used in various industries, particularly in the fields of cosmetics and packaging, and they increase the malleability and workability of materials. As a result of their use, some international health organizations have begun to study them. In this study, the authors developed a methodology for the simultaneous determination of dimethyl phthalate (DMP), diethyl phthalate (DEP), diisobutyl phthalate (DiBP); dibutyl phthalate (DBP), bis(2-ethylhexyl) phthalate (DEHP); di-n-octyl-phthalate (DnOP) and bisphenol A (BPA) from drinking and non-potable waters. The extraction of PAEs and BPA was performed using a solvent-based dispersive liquid-liquid microextraction (SB-DLLME) method. The analytical determination was performed using a gas chromatography-ion trap mass spectrometry (GC-IT/MS) analysis. The entire procedure was validated as recoveries were studied according to the volume and the extraction solvent used, pH, and ionic strength. Dynamic linearity ranges and linear equations of all the compounds were experimentally determined as well as the limit of detection (LOD) (1-8 ng mL-1) and the limit of quantification (LOQ) (5-14 ng mL-1), reproducibility, and sensitivity. The method was applied to 15 water samples (mineral water and tap water) for determining PAEs and BPA released from the plastic container. After the release simulation, four PAEs (i.e., DiBP, DBP, DHEP, and DnOP) were determined at very low concentrations (below 1.2 ng mL-1) in two water samples from (sport) bottles

Generation and detection of large and robust entanglement between two different mechanical resonators in cavity optomechanics

We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature.Comment: To appear in New J. Phys. Small extensions in response to the points raised by the referee and Refs adde

Why do These Match? Explaining the Behavior of Image Similarity Models

Explaining a deep learning model can help users understand its behavior and allow researchers to discern its shortcomings. Recent work has primarily focused on explaining models for tasks like image classification or visual question answering. In this paper, we introduce Salient Attributes for Network Explanation (SANE) to explain image similarity models, where a model's output is a score measuring the similarity of two inputs rather than a classification score. In this task, an explanation depends on both of the input images, so standard methods do not apply. Our SANE explanations pairs a saliency map identifying important image regions with an attribute that best explains the match. We find that our explanations provide additional information not typically captured by saliency maps alone, and can also improve performance on the classic task of attribute recognition. Our approach's ability to generalize is demonstrated on two datasets from diverse domains, Polyvore Outfits and Animals with Attributes 2. Code available at: https://github.com/VisionLearningGroup/SANEComment: Accepted at ECCV 202

Sensitivity-bandwidth limit in a multi-mode opto-electro-mechanical transducer

An opto--electro--mechanical system formed by a nanomembrane capacitively coupled to an LC resonator and to an optical interferometer has been recently employed for the high--sensitive optical readout of radio frequency (RF) signals [T. Bagci, \emph{et~al.}, Nature {\bf 507}, 81 (2013)]. Here we propose and experimentally demonstrate how the bandwidth of such kind of transducer can be increased by controlling the interference between two--electromechanical interaction pathways of a two--mode mechanical system. With a proof--of--principle device \new{operating at room temperature, we achieve a sensitivity of 300 nV/Hz^(1/2) over a bandwidth of 15 kHz in the presence of radiofrequency noise, and an optimal shot-noise limited sensitivity of 10 nV/Hz^(1/2) over a bandwidth of 5 kHz. We discuss strategies for improving the performance of the device, showing that, for the same given sensitivity, a mechanical multi--mode transducer can achieve a bandwidth} significantly larger than that of a single-mode one

High-Pressure Synthesis of a Pentazolate Salt

The pentazolates, the last all-nitrogen members of the azole series, have been notoriously elusive for the last hundred years despite enormous efforts to make these compounds in either gas or condensed phases. Here we report a successful synthesis of a solid state compound consisting of isolated pentazolate anions N5-, which is achieved by compressing and laser heating cesium azide (CsN3) mixed with N2 cryogenic liquid in a diamond anvil cell. The experiment was guided by theory, which predicted the transformation of the mixture at high pressures to a new compound, cesium pentazolate salt (CsN5). Electron transfer from Cs atoms to N5 rings enables both aromaticity in the pentazolates as well as ionic bonding in the CsN5 crystal. This work provides a critical insight into the role of extreme conditions in exploring unusual bonding routes that ultimately lead to the formation of novel high nitrogen content species

The role of the central limit theorem in the heterogeneous ensemble of Brownian particles approach

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid