On a Hele-Shaw Flow Problem with Free and Solid Boundary Components

The purpose of this work is to study a one phase Hele-Shaw fluid flow occupying a time variable domain \(\Omega (t)\), due to the injection of the fluid with a constant rate at a single point of the initial domain \(\Omega (0)\), and in the presence of a fixed solid body \(\Omega _0\). We show the short time existence and uniqueness of the solution for the corresponding boundary value problem in the three dimensional case and in the absence of surface tension.     

On the mixed problem for the semilinear Darcy‐Forchheimer‐Brinkman PDE system in Besov spaces on creased Lipschitz domains

The purpose of this paper is to study the mixed Dirichlet‐Neumann boundary value problem for the semilinear Darcy‐Forchheimer‐Brinkman system in L _p ‐based Besov spaces on a bounded Lipschitz domain in ${\mathbb{R}}^3$, with p in a neighborhood of 2. This system is obtained by adding the semilinear term | u | u to the linear Brinkman equation. First, we provide some results about equivalence between the Gagliardo and nontangential traces, as well as between the weak canonical conormal derivatives and the nontangential conormal derivatives. Various mapping and invertibility properties of some integral operators of potential theory for the linear Brinkman system, and well‐posedness results for the Dirichlet and Neumann problems in L _p ‐based Besov spaces on bounded Lipschitz domains in ${\mathbb{R}}^n$(n ≥3) are also presented. Then, using integral potential operators, we show the well‐posedness in L ₂‐based Sobolev spaces for the mixed problem of Dirichlet‐Neumann type for the linear Brinkman system on a bounded Lipschitz domain in ${\mathbb{R}}^n$(n ≥3). Further, by using some stability results of Fredholm and invertibility properties and exploring invertibility of the associated Neumann‐to‐Dirichlet operator, we extend the well‐posedness property to some L _p ‐based Sobolev spaces. Next, we use the well‐posedness result in the linear case combined with a fixed point theorem to show the existence and uniqueness for a mixed boundary value problem of Dirichlet and Neumann type for the semilinear Darcy‐Forchheimer‐Brinkman system in L _p ‐based Besov spaces, with p ∈(2?ε ,2+ε ) and some parameter ε >0.     

On the Oseen–Brinkman flow around an $$$$-dimensional solid obstacle

The purpose of this paper is to develop a layer potential analysis in order to show the well-posedness result of a transmission problem for the Oseen and Brinkman systems in open sets in \({\mathbb R}^m\) (\(m\in \{2,3\}\)) with compact Lipschitz boundaries and around a lower dimensional solid obstacle, when the boundary data belong to some \(L^q\)-spaces. If \(m=3\) or if the Brinkman system is given on bounded open set then there exists a solution of the transmission problem for arbitrary data. If \(m=2\) and the Brinkman system is given on exterior open set then necessary and sufficient conditions for the existence of a solution of the transmission problem are stated. A solution of the transmission problem is not unique. All solutions of the problem are found.     

Stability,periodicity, and symmetries of certain second‐order fractional difference equation with quadratic terms via KAM theory

By using the Kolmogorov–Arnold–Moser theory, we investigate the stability of the equilibrium solution of the difference equation where A ,B ,D > 0,u _?1,u ₀>0. We also use the symmetries to find effectively the periodic solutions with feasible periods. Copyright © 2016 John Wiley & Sons, Ltd.     

Simple method for the determination of Cu and Fe by electrothermal atomic absorption spectrometry in biodiesel treated with tetramethylammonium hydroxide

A simple analytical procedure for the determination of Cu and Fe in biodiesel samples by electrothermal atomic absorption spectrometry is proposed. An aliquot of the sample is simply mixed with tetramethylammonium hydroxide (TMAH) and heated to 90 °C for 5 min. Pyrolysis and atomization temperatures were optimized through pyrolysis and atomization curves. The high pyrolysis temperature adopted, of 1000 °C, certainly helped minimizing potential interferences. Even though, calibration should be carried out with aqueous standard solutions in the presence of the TMAH. The detection limits (3 s, n = 10), in the sample, were quite low 15 ng g⁻¹ and 24 ng g⁻¹ for Cu and Fe, respectively. Seven biodiesel samples, produced from different raw materials, including vegetable seed, frying oil and animal fat were analyzed. Accuracy was validated by applying the recovery test to two samples, enriching the samples with two concentration levels (recoveries from 105% to 120%). The precision, expressed by the relative standard deviation was less than 3% for Cu and less than 7% for Fe. Copper could be quantified in two and Fe in three of the seven samples. The biodiesel sample from fodder turnip was especially rich in the analytes in comparison to the other samples.     

Distributed computation of virtual coordinates for greedy routing in sensor networks

Sensor networks are emerging as a paradigm for future computing, but pose a number of challenges in the fields of networking and distributed computation. One challenge is to devise a greedy routing protocol—one that routes messages through the network using only information available at a node or its neighbors. Modeling the connectivity graph of a sensor network as a 3-connected planar graph, we describe how to compute on the network in a distributed and local manner a special geometric embedding of the graph. This embedding supports a geometric routing protocol called “greedy routing” based on the “virtual” coordinates of the nodes derived from the embedding.     

Quercetin-PVP K25 solid dispersions

Quercetin is a flavonoid very well studied and has already entered clinical trials emerging as prospective anticancer drug candidate. In addition, quercetin has being reported to its free-radical scavenging activity and suggests potential uses for the prevention and treatment of pathologies as atherosclerosis, chronic inflammation, and others. However, quercetin is sparingly soluble in water, which may be responsible for its limited absorption upon oral administration. The solid dispersion of quercetin with polyvinylpyrrolidone Kollidon^® 25 (PVP K25) suggests an interesting way to increase quercetin solubility, antioxidant activity, and consequently bioavailability. Then, the purpose of this study was to prepare solid dispersions of quercetin with PVP K25 and evaluate their thermal characterization, antioxidant activity and quercetin improvement solubility. For this purpose, quercetin-PVP K25 solutions were dried and quercetin-PVP K25 solids were obtained. The formation of quercetin-PVP K25 solid dispersion was evaluated by solubility studies, powder X-ray diffraction (XRD), fourier transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), thermogravimetry (TG), and antioxidant activity. It was observed that PVP K25 was able to provide quercetin clear aqueous solutions and that quercetin solubility was increased in a PVP K25 concentration dependent manner, improving solubility even 436-fold the pure quercetin. The results obtained with XRD, FT-IR, DSC, and TG demonstrated possible quercetin-PVP K25 solid dispersion formation. Besides, the antioxidant activity of the quercetin-PVP K25 solid dispersions dissolved in aqueous solution and pure quercetin dissolved in methanol showed IC₅₀ value of 0.61 ± 0.03 and 1.00 ± 0.02 μg/mL, respectively, demonstrating that the solid dispersions presented a significant increase in antioxidant activity (P < 0.05). Putting results together, it was possible to conclude there was the formation of quercetin-PVP K25 solid dispersion.     

High‐pressure studies of the micro‐Raman spectra of iron cyanide complexes: Prussian blue (Fe4[Fe(CN)6]3), potassium ferricyanide (K3[Fe(CN)6]), and sodium nitroprusside (Na2[Fe(CN)5(NO)]·2H2O)

The pressure dependences of the peaks observed in the micro‐Raman spectra of Prussian blue (Fe₄[Fe(CN)₆]₃), potassium ferricyanide (K₃[Fe(CN)₆]), and sodium nitroprusside (Na₂[Fe(CN)₅(NO)]·2H₂O) have been measured up to 5.0 GPa. The vibrational modes of Prussian blue appearing at 201 and 365 cm⁻¹ show negative dν/dP values and Grüneisen parameters and are assigned to the transverse bending modes of the Fe C N Fe linkage which can contribute to a negative thermal expansion behavior. A phase transition occurring between 2.0 and 2.8 GPa in potassium ferricyanide is shown by changes in the spectral region 150–700 cm⁻¹. In the spectra of the nitroprusside ion, there are strong interactions between the FeN stretching mode and the FeNO bending and the axial CN stretching modes. The pressure dependence of the NO stretching vibration is positive, 5.6 cm⁻¹ GPa⁻¹, in contrast to the negative behavior in the iron(II)‐meso‐tetraphenyl porphyrinate complex. Copyright © 2011 John Wiley & Sons, Ltd.