Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

Fundamental solution of the time‐fractional telegraph Dirac operator

In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems.     

A Molecular Secret Sharing Scheme

A method for implementing a secret sharing scheme at the molecular level is presented. By creating molecular code generators that are self‐assembled from several molecular components, we established a means for distributing distinct code‐activating elements among several participants. In this way, an authorization code can only be generated when all the participants are present, which ensures that highly secured systems cannot be operated by unauthorized individuals or disloyal users. Additional layers of protection result from the ability to program the security code by replacing one or several molecular components and by subjecting the system to distinct chemical inputs.     

Refratometric study of ternary mixtures formed by water,glucose and acetonitrile at temperatures ranging from 293 K to 333 K

The study of thermodynamic properties of solutions provides important information on existing molecular interactions between the components present in a solution. These studies are critical for testing, validation and development of theories and mathematical models. The refractometric study of a solution is a simple assessment that can contribute to the understanding of these interactions. In this context, the behaviour of the binary water and glucose mixture was studied as well as ternary mixtures of water, glucose and acetonitrile at five different temperatures in the range 293–333 K by the determination of the refractive index of the solution. Due to the weakening of the molecular interactions with the increasing of the temperature, a decreasing dependence of refractive index with temperature was observed. The addition of acetonitrile provides an increase in the refractive index indicating the formation of clusters in the solution.     

Chemical Approach to the Optimization of Conditions Using HS-SPME/GC–MS for Characterization of Volatile Compounds in Eugenia brasiliensis Fruit

Grumixama (Eugenia brasiliensis Lam.) is a native fruit of the Brazilian Atlantic Forest, belonging to the Myrtaceae family, which designatesthe most significant number of species with food potential. It stands out due to its phytochemical characteristics because of the presence of polyphenols and volatile organic compounds. Volatile compounds are substances released by foods that give off an aroma and influence flavor. Solid-phase microextraction is a technique that allows for low-cost, fast, and solvent-free extraction, has an affinity for numerous analytes, and is easily coupled to gas chromatography. The objectives of this work were to evaluate the efficiency of different fibers of SPME (solid-phase microextraction) in the extraction of volatile organic compounds from grumixama pulp; optimize a method for extraction time, temperature, and sample weight; and to determine the characteristic volatile profile of this fruit. For the extraction of volatile compounds, three fibers of different polarities were used: polar polyacrylate (PA) fibers, divinylbenzene/carboxyne/polydimethylsiloxane (DVB/CAR/PDMS) semipolar fibers, and polydimethylsiloxane/divinylbenzene (PDMS/DVB). Fourteen volatile organic compounds (VOCs) were identified by DVB/CAR/PDMS, six by PA, and seven by PDMS/DVB through solid-phase microextraction in the headspace mode (SPME-HS). Considering the total number of compounds identified, regardless of the fiber used, and the optimization of the method, Eugenia brasiliensis presented sesquiterpene fractions (85.7%, 83.3%, and 85.7% of total VOCs) higher than the monoterpene fractions (14.3%, 16.7%, and 14.3%) for DVB/CAR/PDMS, PA, and PDMS/DVB, respectively in its composition. In addition, it was possible to verify that the fiber DVB/CAR/PDMS presented a better efficiency due to the larger chromatographic area observed when the grumixama pulp was subjected to conditions of 75 °C, 2.0 g, and an adsorption time of 20 min.     

High-impact polystyrene/polyaniline membranes for acid solution treatment by electrodialysis: preparation, evaluation, and chemical calculation

In this study different membranes were produced, aiming to evaluate their use in electrodialysis. These membranes were produced using conventional polymer (high-impact polystyrene) and polyaniline. The membrane characterization was done by FTIR spectroscopy, scanning electron microscopy (SEM), and thermogravimetry (TGA). The studies of the zinc and proton extraction ionic transport through the membranes were evaluated using a three-compartment cell. The results obtained using the produced membranes were compared to the results obtained with the commercial membrane Nafion 450. It was found that a synthesized membrane can be used to recover zinc in acid media. In addition, a preliminary computational essay about the structures of PAni and CSA is presented.     

Magnetic properties of ferromagnetic quasi-1D copper-peptide compounds: exchange interactions and very low temperature phase transitions

The magnetic properties of the Cu(II)-peptide compounds (L-tyrosyl-L-leucinato)Cu(II) and (L-tryptophyl-glycinato)Cu(II), to be identified as Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively, have been investigated by specific heat (0.08 < T < 28 K), dc magnetization (2 < T < 80 K, with B(0) = mu(o)H < or = 9 T), and ac magnetic susceptibility (with B(0) = 0 for 0.03 < T < 3 K and B(0) up to 9 T for 2 < T < 80 K) measurements. Above approximately 1 K, the specific heat and magnetization of both compounds display a ferromagnetic (FM) spin chain behavior sustained by syn-anti carboxylate bridges connecting equatorially Cu(II) ions at about 5 A. To model this behavior, we calculated the eigenvalues of Heisenberg chains with up to 20 spins 1/2 and used the method of Bonner and Fisher. A global fit of the model to the specific heat and magnetization data gives 2J(0)/k(B) = 3.60(5) K and 2.59(5) K for the intrachain exchange interactions in Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively (H(ex)(i,j) = -2J(0) S(i).S(j)). These values of 2J(0) are discussed in terms of structural properties of the carboxylate bridges in the two compounds. Using the parameters obtained from the global fit, we calculated isothermal susceptibilities in agreement with the ac susceptibilities measured with small applied dc magnetic fields. However, the ac susceptibility measured with applied dc fields larger than 1 T lie between the values calculated for the isothermal and adiabatic susceptibilities. At 0.16 K for Cu(II)Tyr-Leu and 0.53 K for Cu(II)Trp-Gly, the observed specific heat and magnetic susceptibility display peaks associated to three-dimensional magnetic phase transitions. The interchain exchange couplings 2J(1) producing the 3D magnetic order are ferromagnetic and have magnitudes 2J(1)/k(B) approximately 0.015 and 0.073 K for Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively.     

Interaction of Tb(III) and hydrolyzed polyacrylamides in solution as a gel and in the solid state

Formation of the HPAM-Tb³ complex in solution was observed in the intensification of Tb(III) fluorescence, viscosity, and light scattering. The interaction is dependent on the degree of hydrolysis of the copolymer and the pH of the solution. As the pH value increases, an intensification of the interaction and formation of a gel is observed. The latter was associated with the appearance of crosslinks in which terbium, or one of its hydrolysis products, works as a binding agent between chains. After drying, the characterization of the residues of the gels was effected by analytical determination (C, H, N, Cl, Tb), fluorescence, and infrared spectrophotometry. The analysis and fluorescence revealed the existence of particles of terbium hydroxide; the infrared spectrophotometry showed the binding of terbium (III) to carboxylate of the copolymer.     

Antiproliferative activity, antioxidant capacity and tannin content in plants of semi-arid northeastern Brazil

The objective of this study was to evaluate antiproliferative activity, antioxidant capacity and tannin content in plants from semi-arid northeastern Brazil (Caatinga). For this study, we selected 14 species and we assayed the methanol extracts for antiproliferative activity against the HEp-2 (laryngeal cancer) and NCI-H292 (lung cancer) cell lines using the (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazole) (MTT) method. In addition, the antioxidant activity was evaluated with the DPPH (2,2-diphenyl-2-picrylhydrazyl) assay, and the tannin content was determined by the radial diffusion method. Plants with better antioxidant activity (expressed in a dose able to decrease the initial DPPH concentration by 50%, or IC50) and with higher levels of tannins were: Poincianella pyramidalis (42.95±1.77 μg/mL IC50 and 8.17±0.64 tannin content), Jatropha mollissima (54.09±4.36μg/mL IC50 and 2.35±0.08 tannin content) and Anadenanthera colubrina (73.24±1.47 μg/mL IC50 and 4.41±0.47 tannin content). Plants with enhanced antiproliferative activity (% living cells) were Annona muricata (24.94±0.74 in NCI-H292), Lantana camara (25.8±0.19 in NCI-H292), Handroanthus impetiginosus (41.8±0.47 in NCI-H292) and Mentzelia aspera (45.61±1.94 in HEp-2). For species with better antioxidant and antiproliferative activities, we suggest future in vitro and in vivo comparative studies with other pharmacological models, and to start a process of purification and identification of the possible molecule(s) responsible for the observed pharmacological activity. We believe that the flora of Brazilian semi-arid areas can be a valuable source of plants rich in tannins, cytotoxic compounds and antioxidant agents.