Higher Loop Corrections to a Schwinger–Dyson Equation

We consider the effects of higher loop corrections to a Schwinger–Dyson equation for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess–Zumino model as a laboratory. We obtain the dominant contributions of the three and four-loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.     

Multiaxial mechanical behavior of aramid fibers and identification of skin/core structure from single fiber transverse compression testing

The transverse and longitudinal mechanical properties of aramid fibers like Kevlar? 29 (K29) fibers are strongly linked to their highly oriented structure. Mechanical characterization at the single fiber scale is challenging especially when the diameter is as small as 15 µm. Longitudinal tensile tests on single K29 fibers and single fiber transverse compression test (SFTCT) have been developed. Our approach consists of coupling morphological observations and mechanical experiments with SFTCT analysis by comparing analytical solutions and finite element modeling. New insights on the analysis of the transverse direction response are highlighted. Systematic loading/unloading compression tests enable to experimentally determine a transverse elastic limit. Taking account of the strong anisotropy of the fiber, the transverse mechanical response sheds light on a skin/core architecture. More importantly, results suggest that the skin of the fiber, typically representing a shell of one micrometer in thickness, has a transverse apparent modulus of 0.2 GPa. That is around more than fifteen times lower than the transverse modulus of 3.0 GPa in the core. By comparison, the measured longitudinal modulus is about 84 GPa. The stress distribution in the fiber is explored and the critical areas for damage initiation are discussed. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 374–384     

Comparison between preparative methodologies of nanostructured carbon nitride and their use as selective photocatalysts in water suspension

Carbon nitride photocatalysts have been prepared by different methodologies, such as chemical ultrasonic irradiation (sonochemical treatment), hydrothermal and ball milling and thermoexfoliation, and have been used for the selective oxidation of 5-hydroxymethyl-2-furaldehyde (HMF) to form 2,5-furandicarboxyaldehyde (FDC) in water suspension both under UV and natural solar irradiation. The physico-chemical features of the photocatalysts have been studied by X-ray diffraction, infrared spectroscopy, UV–Vis diffuse reflectance spectroscopy, photoluminescence spectroscopy, scanning electron microscopy, and specific surface area measurements. The results indicate that exfoliation of carbon nitrides can increase the conversion of HMF and the selectivity to FDC. In particular, samples exfoliated by both thermal and acidic ultrasonic irradiation treatments showed the best photocatalytic performance.     

H?lder metric regularity of set-valued maps

This paper is devoted to metric regularity of set-valued maps from a complete metric space to a Banach space. In particular we extend a known characterization of the regularity modulus to maps defined on reflexive spaces. The higher order metric regularity, i.e. an extension of metric regularity to H?lder context, is also investigated using high order variations of set-valued maps and results of similar nature are obtained for conical metric regularity.     

Discovering patterns in time-varying graphs: a triclustering approach

This paper introduces a novel technique to track structures in time varying graphs. The method uses a maximum a posteriori approach for adjusting a three-dimensional co-clustering of the source vertices, the destination vertices and the time, to the data under study, in a way that does not require any hyper-parameter tuning. The three dimensions are simultaneously segmented in order to build clusters of source vertices, destination vertices and time segments where the edge distributions across clusters of vertices follow the same evolution over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make any a priori quantization. Experiments conducted on artificial data illustrate the good behavior of the technique, and a study of a real-life data set shows the potential of the proposed approach for exploratory data analysis.     

Hexasulfanyl analogues of cyclotriveratrylene

The synthesis of four 3,4-di(alkylsulfanyl)benzyl alcohol derivatives is described, in five steps from methyl 3,4-di(hydroxy)benzoate via a Newman–Kwart rearrangement. Incubation of these derivatives in formic acid affords 2,3,7,8,12,13-hexakis(alkylsulfanyl)-10,15-dihydro-5H-tribenzo[a,d,g]cyclononene products, which are hexa-sulfanyl analogues of the well-known supramolecular cavitand host, cyclotriveratrylene (CTV). The yield of this cyclization depends strongly on the alkylsulfanyl substituents present, in the order SMe > SEt ≈ SiPr ? SBn. A crystal structure determination of one of the cyclotrimers shows a mode of self-association that is commonly exhibited by CTV itself.