Weighted a priori estimates for solution of (−Δ)<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript><Emphasis Type="Italic">u</Emphasis> = <Emphasis Type="Italic">f</Emphasis> with homogeneous dirichlet conditions

Let u be a weak solution of (-△)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω  Rn. Then, the main goal of this paper is to prove the following a priori estimate:‖u‖ Wω2 m,p(Ω) ≤ C ‖f‖ Lωp (Ω),where ω is a weight in the Muckenhoupt class Ap.     

On minimal forbidden subgraph characterizations of balanced graphs

A graph is balanced if its clique-matrix contains no edge–vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work, we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to graphs that belong to one of the following graph classes: complements of bipartite graphs, line graphs of multigraphs, and complements of line graphs of multigraphs. These characterizations lead to linear-time recognition algorithms for balanced graphs within the same three graph classes.     

Solid-phase extraction method for determination of volatile compounds in traditional balsamic vinegar

A solid-phase extraction method for the determination of volatile compounds in traditional balsamic vinegar (TBV) has been developed. The optimisation has been carried out using a two-level factorial design expanded further to a central composite design. LiChrolut-EN SPE cartridges were used and the optimised analytical conditions were: 7 g of TBV diluted 1:4, 5 mL of washing water, and elution with 10 mL of dichloromethane. The linear ranges and detection and quantitation limits were adequate for the analysis of the studied compounds in TBV. The accuracy of the method was also studied: recoveries up to 80% and repeatability values lower than 15% were obtained for the majority of the studied compounds. Two TBVs of different age were analysed by the optimised method.     

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ _c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ _c . This algorithm is employed for finding the minimum cardinality clique-transversal of [`(3K₂)]\overline{3K_{2}} -free circular-arc graphs in O(n ⁴) time. Further we describe an algorithm for determining τ _c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n ²) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n ²) time.     

Spectrofluorimetric determination of irinotecan in the presence of oxidant agents and metal ions

In this work four spectrofluorimetric methods for the determination of irinotecan (CPT-11) in human urine and pharmaceuticals have been developed. Initially, the fluorescent characteristics of irinotecan (CPT-11) have been studied in both acidic and basic media. Later, the fluorescence emission generated by the oxidation of CPT-11 with several agents was studied. A quenching of fluorescence could be observed in the presence of Ce(IV) and I₂/I⁻. Also, the reaction between several divalent and trivalent metal ions with CPT-11 was studied, and one method in presence of Fe³⁺ was developed since it was the only metal ion that changes the fluorescence of the analyte. The proposed methods present limit of detection comprises between 0.46 and 2.57 ng mL⁻¹. The spectrofluorimetric methods were applied to human urine. No pre-treatment of the sample was necessary, only a dilution 1:20 with water was made. No interference of the matrix was observed in the conditions used. Recoveries were comprises between 100.0 and 104.3%. Also, pharmaceuticals preparations were analyzed with recoveries between 106.7 and 119.7%. The proposed spectrofluorimetric methods were validated by RP-HPLC, obtaining that the oxidation with iodine is the best method to analyze urine samples, while than, the fluorimetric method developed at acidic pH value is the best for the analysis of pharmaceuticals.     

Study of the magnetorheological response of aqueous magnetite suspensions stabilized by acrylic acid polymers

In this paper we describe the magnetorheological (MR) behavior of aqueous suspensions consisting of magnetite particles stabilized by poly(acrylic acid) polymers (PAA). A previous work on the colloidal stability of the same systems for different pH values and polymer concentrations demonstrated that the addition of PAA polymers has a very significant effect on the stability. In the present contribution, we study the MR effect of the suspensions stabilized by two different commercial polymers, as a function of pH, magnetic field strength and magnetite volume fraction. All the results are discussed in terms of the interfacial properties of the systems. It is demonstrated that for a given concentration of micrometer particles, the rheological response strongly depends on pH, on the volume fraction of magnetite particles, on the type of polymer added for increasing the stability and on the magnetic field strength. Changing the polymer used provokes clear rheological differences for the same sample conditions (field strength, volume fraction and pH). This is suggested to be due to the hydrophobic/hydrophilic balance of the polymer affecting the magnetic field ability to form magnetic structures by aggregation of the magnetized particles. The results are compared to the predictions of the so-called standard chain model, based on the assumption that the MR effect is the result of the balance between the magnetic interactions (tending to establish some degree of order in the suspension by formation of particle chains in the direction of the field) and hydrodynamic ones (tending to destroy the formed structures by viscous stress on the chains). It is found that the behavior of the yield stress does not agree well with the predictions of the model when the relative proportion of both particle and polymer confers optimum stability to the dispersions. This is likely due to the fact that the presence of the stabilizing polyelectrolyte provokes that the magnetic field is not as effective in structuring the suspension as deduced from the chain model.     

Anthracene-Fused Oligo-BODIPYs: A New Class of π-Extended NIR-Absorbing Materials

Large π-conjugated systems are key in the area of molecular materials. Herein, we prepare via Au^I-catalyzed cyclization a series of fully π-conjugated anthracene-fused oligo-BODIPYs. Their structural and optoelectronic properties were studied by several techniques, ranging from X-ray, UV/Vis, and cyclic voltammetry to transient absorption spectroscopy. As a complement, their electronic structures were explored by means of Density Functional Theory (DFT) calculations. Depending on the size and shape of the π-conjugated skeleton, unique features—such as face-to-face supramolecular organization, NIR absorption and fluorescence as well as strong electron accepting character—were noted. All in all, the aforementioned features render them valuable for technological applications.     

Study of the colloidal stability of concentrated bimodal magnetic fluids

In this paper, we describe an investigation of the stability and sedimentation behavior of moderately concentrated suspensions of extremely bimodal magnetite particles, including micro- (diameter 1450 nm) and nano- (diameter 8 nm) units. An original method is used, based on the determination of the time dependence of the inductance of a coil surrounding the suspensions. The method proves to be very useful for the determination of the volume fraction of magnetic material in the sensed volume. The observed changes in the resonant frequency of a parallel LC circuit demonstrate that the addition of the magnetite nanoparticles improves the stability and slows down the settling rate of the mixed suspensions. It is proposed that the observed behavior is the result of competition between two processes. One is the formation of a cloud of nanoparticles around the large magnetite units, by virtue of which the latter are maintained at distances beyond the range of DLVO and magnetic attractive interactions. At long times, these composite units will eventually sediment when some critical size is reached, as the small particles are progressively associated with the large ones. The second mechanism is mainly predominant at short times and is related to the higher viscosity of the dispersion medium (the nanoparticles dispersed in the base fluid) for higher nanoparticle concentrations. The stability of the suspensions is discussed in terms of the competition between the two mechanisms.     

Preferential orientation of modified SrBi2Nb2O9 ferroelectric thin films prepared by pulsed laser deposition

We report on the deposition of SrBi₂Nb₂O₉ and Sr_1-xNa_xBi_2-xTe_xNb₂O₉ ferroelectric thin films on Pt/TiO₂/SiO₂/(100)Si substrates using the pulsed laser deposition technique. Deposition on substrates heated to 600-700 °C produces {11l} film texture and dense films with grain sizes up to about 500 nm. The recrystallization at 700 °C of amorphous films deposited at lower temperatures enhances the contribution of the {100} and {010} orientations. These films show smaller grain size, namely 50-100 nm. {11l}-oriented Sr_1-xNa_xBi_2-xTe_xNb₂O₉ films have remnant polarization P_rۆ 7C/cm², a coercive field E_c䏐 kV/cm and dielectric constant, )𪓴. The low value of P_r is probably related to the low fraction of grains with the ferroelectric axis in the direction of the applied field, E. The recrystallized films have more grains with the ferroelectric axis parallel to E; however, they have a low resistivity which so far has prevented electrical characterization.