The index of a plane curve and green’s formula

Rendiconti del Circolo Matematico di Palermo Series 2 - In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green’s formula...     

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.     

Removal of lead(II) and zinc(II) ions from aqueous solutions by adsorption onto activated carbon synthesized from watermelon shell and walnut shell

Activated carbons from watermelon shell (GACW) and walnut shell (GACN) were synthesized through chemical activation with phosphoric acid 40 % w/w, as an alternative low-cost adsorbent for the removal of lead(II) and zinc(II) ions from aqueous solutions. The yield of production was 85 and 80 % for GACW and GACN respectively. To compare the differences and similarities between the two activated carbons the following tests were performed: surface and pore width with SEM, nitrogen adsorption isotherms at ?196 °C (77 K), IR spectroscopy, TGA, point of zero charge (PZC) and Boehm titration. The GACN has 10 % more surface area (789 m² g^?1 for GACN and 710 m² g^?1 for GACW) and 13 % more pore volume than GACW. Also, GACN has a better resistance to high temperatures than GACW (the loss of mass at 900 °C was 20 % for GACN, while for GACW was 31 %). The effect of the initial concentration of lead(II) and zinc(II) ions on the adsorption process was studied in a batch process mode. To quantify the adsorption of lead and zinc adsorption isotherms of both metals in aqueous solution were performed for each carbon using analytic technique of atomic absorption. The adsorption isotherm data were better fitted by Langmuir model. Experimental results suggests that one gram of GACW adsorbs more milligrams of lead(II) and zinc(II) than one gram of GACN; it is suggest that the pore distribution is a significant variable in the adsorption process because GACW present mesopores and micropores, while GACN has only micropores. Also, the surface chemistry is an important variable in the adsorption process because GACW presents a lower pH_PZC than GACN (3.05 for GACW and 4.5 for GACN) and the solution’s pH of each metal was adjusted in 4.5, for that it could be suggested that the electrostatic interactions were increased between the ion and the carbon surface.     

Solving a problem proposed by T. Ogawa

This paper ascertains the sharp behavior of the first zero of the radially symmetric solution of a superlinear elliptic three-dimensional equation as a function of its value at the origin, and it establishes the strict monotonicity and asymptotic finitude of the underlying associated mass.     

A formal,stereoselective synthesis of the natural tetrahydropyran derivative ophiocerin D

A short, formal stereoselective synthesis of the naturally occurring tetrahydropyran derivative ophiocerin D is reported. The four stereocenters of the molecule were created with the aid of two Sharpless asymmetric dihydroxylations.     

Synthesis and photophysical properties of cyclometalated platinum(II) 1,2-benzenedithiolate complexes and heterometallic derivatives obtained from the addition of [Au(PCy3)]+ units

The cyclometalated compounds [Pt(C^N)(HC^N)Cl] [HC^N = 2-phenylpyridine (Hppy; 1a), 1-(4-tert-butylphenyl)isoquinoline (Htbpiq; 1b)] react with 1,2-benzenedithiol, t-BuOK, and Bu(4)NCl in a 1:1:2:1 molar ratio in CH(2)Cl(2)/MeOH to give the complexes Bu(4)N[Pt(C^N)(bdt)] [bdt = 1,2-benzenedithiolate; C^N = ppy (Bu(4)N2a), tbpiq (Bu(4)N2b)]. In the absence of Bu(4)NCl, the same reactions afford solutions of K2a and K2b, which react with [AuCl(PCy(3))] to give the neutral heterometallic derivatives [Pt(C^N)(bdt){Au(PCy(3))}] [C^N = ppy (3a), tbpiq (3b)]. The cationic derivatives [Pt(C^N)(bdt){Au(PCy(3))}(2)]ClO(4) [C^N = ppy (4a), tbpiq (4b)] are obtained by reacting 3a and 3b with acetone solutions of [Au(OClO(3))(PCy(3))]. The crystal structures of 3b and 4b reveal the formation of short Pt···Au metallophilic contacts in the range 2.929-3.149 ?. Complexes 3b, 4a, and 4b undergo dynamic processes in solution that involve the migration of the [Au(PCy(3))](+) units between the S atoms of the dithiolate. Complexes Bu(4)N2a and 2b display a moderately solvatochromic band in their electronic absorption spectra that can be ascribed to a transition of mixed ML'CT/LL'CT character (M= metal; L = bdt; L' = C^N; CT = charge transfer), while their emissions are assignable to transitions of the same orbital parentage but from triplet excited states. The successive addition of [Au(PCy(3))](+) units to the anions 2a and 2b results in an increase in the absorption and emission energies attributable to lower highest occupied molecular orbital energies. Additionally, the characteristics of the absorption and emission spectra of the heterometallic derivatives indicate a gradual loss of LL'CT character in the involved electronic transitions, with a concomitant increase of the L'C and ML'CT contributions.     

Alkylsulfate-based ionic liquids in the liquid–liquid extraction of aromatic hydrocarbons

The (liquid + liquid) equilibrium data (LLE) for the extraction of toluene from heptane with different ionic liquids (ILs) based on the alkylsulfate anion (R-SO₄) was determined at T = 313.2 K and atmospheric pressure. The effect of more complex R-SO₄ anions on capacity of extraction and selectivity in the liquid–liquid extraction of toluene from heptane was studied. The ternary systems were formed by {heptane + toluene + 1,3-dimethylimidazolium methylsulfate ([mmim][CH₃SO₄]), 1-ethyl-3-methylimidazolium hydrogensulfate ([emim][HSO₄]), 1-ethyl-3-methylimidazolium methylsulfate ([emim][CH₃SO₄]), or 1-ethyl-3-methylimidazolium ethylsulfate ([emim][C₂H₅SO₄])}. The degree of quality of the experimental LLE data was ascertained by applying the Othmer–Tobias correlation. The phase diagrams for the ternary systems were plotted, and the tie lines correlated with the NRTL model compare satisfactorily with the experimental data.