Invertibility of a linear combination of two matrices and partial orderings

In this paper, we present some results relating different matrix partial orderings and the invertibility of a linear combination of EP matrices.     

Dynamical versus variational symmetries: understanding Noether's first theorem

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Special attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.     

Photoinduced dynamics of a cyanine dye: parallel pathways of non-radiative deactivation involving multiple excited-state twisted transients

Cyanine dyes are broadly used for fluorescence imaging and other photonic applications. 3,3′-Diethylthiacyanine (THIA) is a cyanine dye composed of two identical aromatic heterocyclic moieties linked with a single methine, –CH. The torsional degrees of freedom around the methine bonds provide routes for non-radiative decay, responsible for the inherently low fluorescence quantum yields. Using transient absorption spectroscopy, we determined that upon photoexcitation, the excited state relaxes along two parallel pathways producing three excited-state transients that undergo internal conversion to the ground state. The media viscosity impedes the molecular modes of ring rotation and preferentially affects one of the pathways of non-radiative decay, exerting a dominant effect on the emission properties of THIA. Concurrently, the polarity affects the energy of the transients involved in the decay pathways and further modulates the kinetics of non-radiative deactivation.     

Volatiles,color characteristics and other physico–chemical parameters of commercial Moroccan honeys

Seven commercial Moroccan honeys were considered for chemical characterisation. Volatile fraction, total polyphenols content, antioxidant and antiradical activities were evaluated by employing different analytical methodologies. Several physical parameters such as refractive index, pH, water content, solids content and colour were measured. Volatile fraction revealed an abundant presence of cis- and trans-linalool oxide in the seven studied samples. The presence of high levels of compounds related to the Maillard reaction, like furfural and hydroxymethylfurfural, could be the result of thermal treatments used to liquefy commercial honeys or of long storage times. The CIE L^*a^*b^*C_ab^*h_ab° chromatic coordinates confirmed the advanced stage of the Maillard reaction, showing L^* values lower than the common values found for honey of similar typologies.     

Development of a Novel Microwave Distillation Technique for the Isolation of Cannabis sativa L. Essential Oil and Gas Chromatography Analyses for the Comprehensive Characterization of Terpenes and Terpenoids,Including Their Enantio-Distribution

A microwave distillation method was optimized for the extraction and isolation of cannabis essential oil from fresh and dried hemp inflorescences. The developed method enabled us to obtain a distilled product rich in terpenes and terpenoid compounds, responsible of the typical and unique smell of the cannabis plant. The distillate from different hemp cultivars, including Kompolti, Futura 75, Carmagnola, Felina 32 and Finola were characterized by using a gas chromatograph equipped with both mass spectrometer and flame ionization detectors. In a single chromatographic run, the identity and absolute amounts of distilled compounds were determined. Peak assignment was established using a reliable approach based on the usage of two identification parameters, named reverse match, and linear retention index filter. Absolute quantification (mg g⁻¹) of the analytes was performed using an internal standard method applying the flame ionization detector (FID) response factors according to each chemical family. An enantio-GC-MS method was also developed in order to evaluate the enantiomeric distribution of chiral compounds, an analytical approach commonly utilized for establishing the authenticity of suspicious samples.     

BMO‐Type Norms Related to the Perimeter of Sets

In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc.