A note on embedding into product spaces

Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of E, thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.     

Stability of liquid crystal micro-droplets based optical microresonators

Liquid crystal (LC) based tuneable optical microresonators are potential for being used as crucial components in photonic devices. In this article, we report experimental studies on LC micro-droplets dispersed in several dispersing media. We find that the size of the micro-droplets formed in a low refractive index and optically transparent perfluoropolymer are most stable with time than commonly used dispersing media. Using a negative dielectric anisotropy nematic liquid crystal, we show that the whispering gallery mode optical resonance properties such as the quality factor and the free spectral range of stable micro-droplets are independent of the strength of the applied electric field. The optical resonance properties under applied field are significantly different than that of the liquid crystals with positive dielectric anisotropy and are explained based on the elastic deformation of the micro-droplets.     

Nonlocal integral elasticity: 2D finite element based solutions

A finite element based method, theorized in the context of nonlocal integral elasticity and founded on a nonlocal total potential energy principle, is numerically implemented for solving 2D nonlocal elastic problems. The key idea of the method, known as nonlocal finite element method (NL-FEM), relies on the assumption that the postulated nonlocal elastic behaviour of the material is captured by a finite element endowed with a set of (cross-stiffness) element’s matrices able to interpret the (nonlocality) effects induced in the element itself by the other elements in the mesh. An Eringen-type nonlocal elastic model is assumed with a constitutive stress–strain law of convolutive-type which governs the nonlocal material behaviour. Computational issues, as the construction of the nonlocal element and global stiffness matrices, are treated in detail. Few examples are presented and the relevant numerical findings discussed both to verify the reliability of the method and to prove its effectiveness.     

Finite element solutions for nonhomogeneous nonlocal elastic problems

A finite element procedure for analysing nonhomogeneous nonlocal elastic 2D problems is presented and discussed. The procedure grounds on a variationally consistent approach known, in the relevant literature, as Nonlocal Finite Element Method. The latter is recast making use of a recently theorized phenomenological strain-difference-based nonhomogeneous nonlocal elastic model. The peculiarities of the numerical procedure together with the pertinent nonlocal operators are expounded and discussed. Two simple numerical 2D examples close the paper.     

Mn(II) and Cu(II) complexes of a dithiadiazolyl radical ligand: monomer/dimer equilibria in solution

Complexes of the 4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl radical bidentate ligand with bis(hexafluoroacetylacetonato)manganese(II) and with bis(hexafluoroacetylacetonato)copper(II) have been prepared. Unlike the previously reported cobalt(II) complex, these complexes form dimers via intermolecular S...S contacts in the solid state. The spectroscopic and magnetic properties of these species in the solid state and in solution are reported and compared to the previously reported Co(II) complex, with emphasis on the elucidation of the a monomer/dimer equilibrium in the solution. The electrochemical properties of these species in solution are also presented and discussed.     

Heavy quark systems and hadron mass spectra

The influence of chromomagnetic hyperfine interaction onB andT hadrons is studied. The colour magnetic moments are related to the hyperfine splittings of hadrons.     

Interplay between Lignans and Gut Microbiota: Nutritional,Functional and Methodological Aspects

Lignans are non-flavonoid polyphenols present in a wide range of foods frequently consumed in the Western world, such as seeds, vegetables and fruits, and beverages such as coffee, tea and wine. In particular, the human gut microbiota (GM) can convert dietary lignans into biologically active compounds, especially enterolignans (i.e., enterolactone and enterodiol), which play anti-inflammatory and anti-oxidant roles, act as estrogen receptor activators and modulate gene expression and/or enzyme activity. Interestingly, recent evidence documenting those dietary interventions involving foods enriched in lignans have shown beneficial and protective effects on various human pathologies, including colorectal and breast cancer and cardiovascular diseases. However, considering that more factors (e.g., diet, food transit time and intestinal redox state) can modulate the lignans bioactivation by GM, there are usually remarkable inter-individual differences in urine, fecal and blood concentrations of enterolignans; hence, precise and validated analytical methods, especially gas/liquid chromatography coupled to mass spectrometry, are needed for their accurate quantification. Therefore, this review aims to summarize the beneficial roles of enterolignans, their interaction with GM and the new methodological approaches developed for their evaluation in different biological samples, since they could be considered future promising nutraceuticals for the prevention of human chronic disorders.     

Design and synthesis of a 4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl cobalt complex

The 4-(2'-pyridyl)-1,2,3,5-dithiadiazolyl neutral radical 1 has been prepared for use as a spin-bearing bidentate ligand. The coordination of this ligand to bis(hexafluoroacetylacetonato)cobalt affords a thermally stable complex 2. Magnetic susceptibility measurements of the crystalline complex indicate ferromagnetic coupling between the ligand-centered spin and the unpaired electrons of the high-spin Co(II).