Asymptotics of Higher Order Ospt-Functions for Overpartitions

In this paper we obtain asymptotic formulas for positive crank and rank moments for overpartitions. Moreover, we show that crank and rank moments are asymptotically equal while the difference is asymptotically positive. This indicates that there exist analogous higher ospt-functions for overpartitions, which we define.     

Monitoring and Evolution of the Pollution by Volatile Organic Compounds (Vocs) in the Groundwaters of The Najerilla River Basin (Spain)

VOCs were detected and identified in the water of several wells in the area of Nájera (La Rioja). The past uncontrolled spills from an important painting and varnishing industry and from other smaller ones devoted to the manufacture of furniture and varnishing activities were the sources of the VOCs plume detected in this aquifer. This article shows the results obtained in the monitoring and assessment of the pollution at 18 sampling points for more than a year. It has allowed us to study the evolution of the different pollutants and the influence of a remediation process applied by the company in the main pollution source. The analytical method is based on headspace-solid-phase microextraction (SPME) using a 75-μm carboxen-polydimethylsiloxane fibre. Quantification was carried out by gas chromatography with flame ionization detection. This method has allowed us to determine the 13 VOCs identified in the polluted underground samples providing good sensitivity (LOD between 0.1 and 6.0 ng/mL) and reproducibility (r.s.d. less than 10%).     

Implicit–explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension

Nonlinear convection–diffusion equations with nonlocal flux and possibly degenerate diffusion arise in various contexts including interacting gases, porous media flows, and collective behavior in biology. Their numerical solution by an explicit finite difference method is costly due to the necessity of discretizing a local spatial convolution for each evaluation of the convective numerical flux, and due to the disadvantageous Courant–Friedrichs–Lewy (CFL) condition incurred by the diffusion term. Based on explicit schemes for such models devised in the study of Carrillo et al. a second‐order implicit–explicit Runge–Kutta (IMEX‐RK) method can be formulated. This method avoids the restrictive time step limitation of explicit schemes since the diffusion term is handled implicitly, but entails the necessity to solve nonlinear algebraic systems in every time step. It is proven that this method is well defined. Numerical experiments illustrate that for fine discretizations it is more efficient in terms of reduction of error versus central processing unit time than the original explicit method. One of the test cases is given by a strongly degenerate parabolic, nonlocal equation modeling aggregation in study of Betancourt et al. This model can be transformed to a local partial differential equation that can be solved numerically easily to generate a reference solution for the IMEX‐RK method, but is limited to one space dimension.     

Synthesis of Pure Silica MWW Zeolite in Fluoride Medium by Using an Imidazolium-Based Long Dication

As the spacer length in 1,2-dimethylimidazolium-based dications increases beyond a specific point (six methylene units), they fail in structure-directing towards STW zeolites in any synthetic conditions. These dications can instead produce, under fluoride concentrated conditions, either *BEA [in the case of the eight-methylene-unit structure-directing agent (SDA)] or MWW (ten methylene units) zeolites. For any length of the dication, the default zeolite (MTW) is a relatively dense zeolite containing a unidimensional channel, whereas the zeolite demanding most specificity (STW, *BEA or MWW) is more porous, affording a larger concentration of the dication to be occluded. This work provides the first reported fluoride synthesis of pure silica MWW zeolites. Charge balance of the organic dications in this zeolite was achieved by combining “structural” silanolates, regular “connectivity defects” and occluded fluoride. Molecular mechanics calculations showed a perfect fit of the decamethylenebis(dimethylimidazolium) dication in the sinusoidal intralayer pore system of MWW. The calculations showed also that the dication is able to stabilize the interlayer space without disturbing the hydrogen-bonding system that holds the layers together in the as-made material. The ¹⁹F magic-angle spinning (MAS) NMR presented two distinct resonances at −71 and −83 ppm, which, on the basis of DFT calculations, we tentatively assigned to fluoride occluded in [4⁶6²] and [4¹5²6²] cages of the MWW structure, respectively. The same DFT study determines a different chemical shift of one methyl ¹³C nuclear magnetic resonance according to the imidazolium ring residing in the sinusoidal channels or in the large cup cavities, thus explaining an experimentally observed splitting of that resonance.     

Two Types of σ-Allenyl Complexes from Reactions of Silylenes and Germylenes with Chromium Fischer Alkynyl(alkoxy)carbenes

The reactivity of amidinatotetrylenes of the type E(tBu₂bzm)R¹ (E=Si, Ge; tBu₂bzm=N,N′-bis(tertbutyl)benzamidinate; R¹=alkyl or aryl) with the chromium Fischer alkynylcarbene complexes [Cr{C(OEt)C₂R²}(CO)₅] (R²=Ph; ferrocenyl, Fc) has been studied. At room temperature, two different reaction pathways have been identified: (a) attack of the amidinatotetrylene to the alkynyl C² atom (γ-attack), which leads to σ-allenyl complexes in which the original C_carbene atom maintains its attachment to the Cr(CO)₅ and OEt groups (compounds 3 ), and (b) attack of the amidinatotetrylene to the C_carbene atom (α-attack), which ends in σ-allenyl complexes in which the original C_carbene atom is not attached to the metal atom and has been inserted into an E−N bond of the amidinatotetrylene forming an E-C-N-C-N five-membered ring (compounds 4 ). It has been found that compounds 3 are thermodynamically less stable than their corresponding 4 isomers and that some of the former (E=Ge; R¹=CH₂SiMe₃) can be transformed into the latter upon heating. At high temperatures (>70 °C) the reactions involving bulky amidinatotetrylenes (R¹=Mes, tBu) end in the carbene-substitution products [Cr{E(tBu₂bzm)R¹}(CO)₅].     

Preface to the Special Issue: Nonlinear systems theory and applications in engineering,control and life sciences

Nonlinear Dynamics -     

Synthesis and characterization of cellulose acetate from cellophane industry residues. Application as acetaminophen controlled-release membranes

Journal of Thermal Analysis and Calorimetry - Cellophane film production generates cellulosic residues from scraps, edges, and low-quality films. In this work, cellophane was used as a raw material...     

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical,Photophysical and Electrochemical Evaluation

A series of new symmetrical highly substituted BODIPYs 6 a – l was synthesized through a prefunctionalization approach in 35 %–89 % yields from the pyrrole core. This strategy allowed modulation of the substituents at the different positions based on the choice of Fischer's alkynyl carbenes, oxazolones and aldehydes used as precursors. The substituent variation at positions 2, 6, 3 and 5 had the greatest effect on the modulation of their photophysical properties such as absorption (λ_abs) and emission (λ_em) wavelengths, extinction coefficient (ϵ), quantum yields (ϕ), Stokes shifts (Δν), fluorescence decay, radiative (k_rad) and non-radiative (k_nr) constants and the CIE 1931 coordinates. Theoretical calculations allowed to corroborate the effect of the substituents of meso-position on the modification of the dihedral angles. Cyclic voltammetry studies revealed that the BODIPY series presents similar redox potential behavior, being electrochemically active even in successive cycles, which suggests that transport by diffusion is the dominant process.