Oscillatory solutions of fractional integro-differential equations

We give necessary conditions to get oscillatory solutions of a class of fractional order neutral differential equations with continuously distributed delay by means of the fractional derivative with respect to a given function. In particular, oscillatory solutions of the considered fractional equations with Caputo and Hadamard type of fractional derivatives are established. Some explicit examples are given to illustrate the main results.     

Proportional counters for Mössbauer spectroscopy

The problem of ψ-ray detection by using proportional counters for Mössbauer effect spectroscopy has been studied. The investigations on the constructional solutions of proportional counters and filling gas mixtures have been worked out. Some measurement geometries using proportional counters have been proposed. The obtained results allow to improve signal to noise ratio as well as the detection stability.     

Topological study of the periodic system

We carried out a topological study of the Space of Chemical Elements, SCE, based on a clustering analysis of 72 elements, each one defined by a vector of 31 properties. We looked for neighborhoods, boundaries, and other topological properties of the SCE. Among the results one sees the well-known patterns of the Periodic Table and relationships such as the Singularity Principle and the Diagonal Relationship, but there appears also a robustness property of some of the better-known families of elements. Alkaline metals and Noble Gases are sets whose neighborhoods have no other elements besides themselves, whereas the topological boundary of the set of metals is formed by semimetallic elements.     

In Vitro and In Silico Anti-Arboviral Activities of Dihalogenated Phenolic Derivates of L-Tyrosine

Despite the serious public health problem represented by the diseases caused by dengue (DENV), Zika (ZIKV) and chikungunya (CHIKV) viruses, there are still no specific licensed antivirals available for their treatment. Here, we examined the potential anti-arbovirus activity of ten di-halogenated compounds derived from L-tyrosine with modifications in amine and carboxyl groups. The activity of compounds on VERO cell line infection and the possible mechanism of action of the most promising compounds were evaluated. Finally, molecular docking between the compounds and viral and cellular proteins was evaluated in silico with Autodock Vina^®, and the molecular dynamic with Gromacs^®. Only two compounds (TDC-2M-ME and TDB-2M-ME) inhibited both ZIKV and CHIKV. Within the possible mechanism, in CHIKV, the two compounds decreased the number of genome copies and in the pre-treatment strategy the infectious viral particles. In the ZIKV model, only TDB-2M-ME inhibited the viral protein and demonstrate a virucidal effect. Moreover, in the U937 cell line infected with CHIKV, both compounds inhibited the viral protein and TDB-2M-ME inhibited the viral genome too. Finally, the in silico results showed a favorable binding energy between the compounds and the helicases of both viral models, the NSP3 of CHIKV and cellular proteins DDC and β2 adrenoreceptor.     

Influence of nitrogen partial pressure on the microstructure and morphological properties of sputtered RuN coatings

In this work, the production of RuN thin films using the reactive direct current magnetron sputtering technique is presented. Samples were grown with varying Ar/N₂ ratio with values of 60/40, 80/20, 85/15, 90/10, 95/5, and 100/0. X‐ray photoelectron spectroscopy was employed to determine the presence of RuN before and after a sputtering etching process. According to the high‐resolution of N1s spectra, 3 peaks were identified at 397.4 ± 0.3 eV, 398.3 ± 0.3 eV, and 398.8 ± 0.3 eV binding energies, corresponding to hybridizations of nitrogen with transition metals, oxynitrides, and oxycarbides. X‐ray diffraction analyses were performed, showing the coexistence of the RuN face‐centered cubic and Ru hexagonal compact packed phases. After the etching process, the samples grown at nitrogen flow rates greater than 15% continued to show the RuN face‐centered cubic phase. Atomic force microscope analyses showed that as the nitrogen concentration increased, the grain size and roughness also tended to increase.     

Synthesis and Characterization of a Biocompatible Copolymer to be Used as Cell Culture Support

Summary: N-isopropylacrylamide (NIPAAm)/butylacrylate (BAc) copolymer was synthesized by emulsion polymerization in order to use it as a cell culture surface for corneal epithelium biosubstitutes. Results showed that the obtained polymers were thermosensitive hydrogels. The copolymer was characterized by Fourier transform infrared (FTIR), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and swelling degree. 3T3 Swiss cells were used as feeder layers and they were used to test the cytotoxic effect of the hydrogels. The conditions to isolate, cultivate, expand and cryo-preserve human oral mucosal cells were established and analysis of several morphological and immuno-histochemical characteristics of the cultivated oral mucous were made.     

To Be or Not To Be? that is the Entropic,Enthalpic, and Molecular Interaction Dilemma in the Formation of (Water)20 Clusters and Methane Clathrate

A detailed analysis under a comprehensive set of theoretical and computational tools of the thermodynamical factors and of the intermolecular interactions behind the stabilization of a well known set of (water)₂₀ cavities and of the methane clathrate is offered in this work. Beyond the available reports of experimental characterization at extreme conditions of most of the systems studied here, all clusters should be amenable to experimental detection at 1 atm and moderate temperatures since 280 K marks the boundary at which, ignoring reaction paths, formation of all clusters is no longer spontaneous from the 20H₂O→(H₂O)₂₀ and CH₄+20H₂O→CH₄@5¹² processes. As a function of temperature, a complex interplay leading to the free energy of formation occurs between the destabilizing entropic contributions, mostly due to cluster vibrations, and the stabilizing enthalpic contributions, due to intermolecular interactions and the PV term, is best illustrated by the highly symmetric 5¹² cage consistently showing signs of stronger intermolecular bonding despite having smaller binding energy than the other clusters. A fluxional wall of attractive non-covalent interactions, arising because of the cumulative effect of a large number of tiny individual charge transfers to the interstitial region, plays a pivotal role stabilizing the CH₄@5¹² clathrate.     

Holomorphic Hölder-type spaces and composition operators

We study boundedness and compactness of composition operators in the generalized Hölder-type space of holomorphic functions in the unit disc with prescribed modulus of continuity. We also devote a significant part of the article to outline some embeddings between such Hölder-type spaces, to discuss properties of modulus of continuity and to construct some useful examples.     

Improved mixing condition on the grid for counting and sampling independent sets

The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to λ^|I|, for a positive real parameter λ. For large λ, computing the partition function (namely, the normalizing constant which makes the weighting a probability distribution on a finite graph) on graphs of maximum degree Δ ≥ 3, is a well known computationally challenging problem. More concretely, let ${\lambda_c(\mathbb{T}_\Delta)}$ denote the critical value for the so-called uniqueness threshold of the hard-core model on the infinite Δ-regular tree; recent breakthrough results of Weitz (Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 140–149, 2006) and Sly (Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 287–296, 2010) have identified ${\lambda_c(\mathbb{T}_\Delta)}$ as a threshold where the hardness of estimating the above partition function undergoes a computational transition. We focus on the well-studied particular case of the square lattice ${\mathbb{Z}^2}$ , and provide a new lower bound for the uniqueness threshold, in particular taking it well above ${\lambda_c(\mathbb{T}_4)}$ . Our technique refines and builds on the tree of self-avoiding walks approach of Weitz, resulting in a new technical sufficient criterion (of wider applicability) for establishing strong spatial mixing (and hence uniqueness) for the hard-core model. Our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure, improving upon what can be achieved by just using the maximum degree. Applying our technique to ${\mathbb{Z}^2}$ we prove that strong spatial mixing holds for all λ < 2.3882, improving upon the work of Weitz that held for λ < 27/16 = 1.6875. Our results imply a fully-polynomial deterministic approximation algorithm for estimating the partition function, as well as rapid mixing of the associated Glauber dynamics to sample from the hard-core distribution.