Interface boundary value problems of Robin‐transmission type for the Stokes and Brinkman systems on n‐dimensional Lipschitz domains: applications

In this paper, we describe a layer potential analysis in order to show an existence result for an interface boundary value problem of Robin‐transmission type for the Stokes and Brinkman systems on Lipschitz domains in Euclidean setting, when the given boundary data belong to some L^p or Sobolev spaces associated to such domains. Applications related to an exterior three‐dimensional Stokes flow past two concentric porous spheres with stress jump conditions on the fluid‐porous interface are also considered. Copyright © 2013 John Wiley & Sons, Ltd.     

Establishing strong connectivity using optimal radius half-disk antennas

Given a set S of points in the plane representing wireless devices, each point equipped with a directional antenna of radius r and aperture angle $\alpha ?180\mathrm{°}$, our goal is to find orientations and a minimum r for these antennas such that the induced communication graph is strongly connected. We show that $r=\sqrt{3}$ if $\alpha \in [180\mathrm{°},240\mathrm{°})$, $r=\sqrt{2}$ if $\alpha \in [240\mathrm{°},270\mathrm{°})$, $r=2\sin (36\mathrm{°})$ if $\alpha \in [270\mathrm{°},288\mathrm{°})$, and $r=1$ if $\alpha ?288\mathrm{°}$ suffices to establish strong connectivity, assuming that the longest edge in the Euclidean minimum spanning tree of S is 1. These results are worst-case optimal and match the lower bounds presented in [I. Caragiannis, C. Kaklamanis, E. Kranakis, D. Krizanc, A. Wiese, Communication in wireless networks with directional antennae, in: Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, 2008, pp. 344–351]. In contrast, $r=2$ is sometimes necessary when $\alpha <180\mathrm{°}$.     

Efficient reconfiguration of lattice-based modular robots

Modular robots consist of many identical units (or atoms) that can attach together and perform local motions. By combining such motions, one can achieve a reconfiguration of the global shape of a robot. The term modular comes from the idea of grouping together a fixed number of atoms into a metamodule, which behaves as a larger individual component. Recently, a fair amount of research has focused on algorithms for universal reconfiguration using Crystalline and Telecube metamodules, which use expanding/contracting cubical atoms.From an algorithmic perspective, this work has achieved some of the best asymptotic reconfiguration times under a variety of different physical models. In this paper we show that these results extend to other types of modular robots, thus establishing improved upper bounds on their reconfiguration times. We describe a generic class of modular robots, and we prove that any robot meeting the generic class requirements can simulate the operation of a Crystalline atom by forming a six-arm structure. Previous reconfiguration bounds thus transfer automatically by substituting the six-arm structures for the Crystalline atoms. We also discuss four prototyped robots that satisfy the generic class requirements: M-TRAN, SuperBot, Molecube, and RoomBot.     

Variational approach for the Stokes and Navier–Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds

The purpose of this paper is to show well-posedness results for Dirichlet problems for the Stokes and Navier–Stokes systems with \(L^{\infty }\)-variable coefficients in \(L^2\)-based Sobolev spaces in Lipschitz domains on compact Riemannian manifolds. First, we refer to the Dirichlet problem for the nonsmooth coefficient Stokes system on Lipschitz domains in compact Riemannian manifolds and show its well-posedness by employing a variational approach that reduces the boundary value problem of Dirichlet type to a variational problem defined in terms of two bilinear continuous forms, one of them satisfying a coercivity condition and another one the inf-sup condition. We show also the equivalence between some transmission problems for the nonsmooth coefficient Stokes system in complementary Lipschitz domains on compact Riemannian manifolds and their mixed variational counterparts, and then their well-posedness in \(L^2\)-based Sobolev spaces by using the remarkable Nec?as–Babus?ka–Brezzi technique (see Babus?ka in Numer Math 20:179–192, 1973; Brezzi in RAIRO Anal Numer R2:129–151, 1974; Nec?as in Rev Roum Math Pures Appl 9:47–69, 1964). As a consequence of these well-posedness results we define the layer potential operators for the nonsmooth coefficient Stokes system on Lipschitz surfaces in compact Riemannian manifolds, and provide their main mapping properties. These properties are used to construct explicitly the solution of the Dirichlet problem for the Stokes system. Further, we combine the well-posedness of the Dirichlet problem for the nonsmooth coefficient Stokes system with a fixed point theorem to show the existence of a weak solution to the Dirichlet problem for the nonsmooth variable coefficient Navier–Stokes system in \(L^2\)-based Sobolev spaces in Lipschitz domains on compact Riemannian manifolds. The well developed potential theory for the smooth coefficient Stokes system on compact Riemannian manifolds (cf. Dindos? and Mitrea in Arch Ration Mech Anal 174:1–47, 2004; Mitrea and Taylor in Math Ann 321:955–987, 2001) is also discussed in the context of the potential theory developed in this paper.     

Eco-friendly synthesis,in vitro anti-proliferative evaluation,and 3D-QSAR analysis of a novel series of monocationic 2-aryl/heteroaryl-substituted 6-(2-imidazolinyl)benzothiazole mesylates

Abstract

Herein, we describe the synthesis of twenty-one novel water-soluble monocationic 2-aryl/heteroaryl-substituted 6-(2-imidazolinyl)benzothiazole mesylates 3a–3u and present the results of their anti-proliferative assays. Efficient syntheses were achieved by three complementary simple two-step synthetic protocols based on the condensation reaction of aryl/heteroaryl carbaldehydes or carboxylic acid. We developed an eco-friendly synthetic protocol using glycerol as green solvent, particularly appropriate for the condensation of thermally and acid-sensitive heterocycles such as furan, benzofuran, pyrrole, and indole. Screening of anti-proliferative activity was performed on four human tumour cell lines in vitro including pancreatic cancer (CFPAC-1), metastatic colon cancer (SW620), hepatocellular carcinoma (HepG2), and cervical cancer (HeLa), as well as in normal human fibroblast cell lines. All tested compounds showed strong to moderate anti-proliferative activity on tested cell lines depending on the structure containing aryl/heteroaryl moiety coupled to 6-(2-imidazolinyl)benzothiazole moiety. The most potent cytostatic effects on all tested cell lines with \(\hbox {IC}_{50}\) values ranging from 0.1 to 3.70 \(\upmu \hbox {M}\) were observed for benzothiazoles substituted with naphthalene-2-yl 3c, benzofuran-2-yl 3e, indole-3-yl 3j, indole-2-yl 3k, quinoline-2-yl 3s, and quinoline-3-yl 3t and derivatives substituted with phenyl 3a, naphthalene-1-yl 3b, benzothiazole-2-yl 3g, benzothiazole-6-yl 3h, N-methylindole-3-yl 3l, benzimidazole-2-yl 3n, benzimidazole-5(6)-yl 3o, and quinolone-4-yl 3u with \(\hbox {IC}_{50}\) values ranging from 1.1 to 29.1 \(\upmu \hbox {M}\). Based on obtained anti-proliferative activities, 3D-QSAR models for five cell lines were derived. Molecular volume, molecular surface, the sum of hydrophobic surface areas, molecular mass, and possibility of making dispersion forces were identified by QSAR analyses as molecular properties that are positively correlated with anti-proliferative activity, while compound’s capability to accept H-bond was identified as a negatively correlated property. Comparison of molecular properties identified for different cell lines enabled assumptions about similarity of mode of action through which anti-proliferative activities against different cell lines are accomplished. Novel compounds that are predicted to have enhanced activities in comparison with herein presented ones were designed using 3D-QSAR analysis as guideline.

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Recovery of Phenolic Acid and Enzyme Production from Corn Silage Biologically Treated by <Emphasis Type="Italic">Trametes versicolor</Emphasis>

Corn silage is used as high-energy forage for dairy cows and more recently for biogas production in a process of anaerobic co-digestion with cow manure. In this work, fresh corn silage after the harvest was used as a substrate in solid-state fermentations with T. versicolor with the aim of phenolic acid recovery and enzyme (laccase and manganese peroxidase) production. During 20 days of fermentation, 10.4-, 3.4-, 3.0-, and 1.8-fold increments in extraction yield of syringic acid, vanillic acid, p-hydroxybenzoic acid, and caffeic acid, respectively, were reached when compared to biologically untreated corn silage. Maximal laccase activity was gained on the 4th day of fermentation (V.A. = 180.2 U/dm³), and manganese peroxidase activity was obtained after the 3rd day of fermentation (V.A. = 30.1 U/dm³). The addition of copper(II) sulfate as inducer during solid state fermentation resulted in 8.5- and 7-fold enhancement of laccase and manganese peroxidase activities, respectively. Furthermore, the influence of pH and temperature on enzyme activities was investigated. Maximal activity of laccase was obtained at T = 50 °C and pH = 3.0, while manganese peroxidase is active at temperature range T = 45–70 °C with the maximal activity at pH = 4.5.     

Implementation of an Analytical Method for Spectrophotometric Evaluation of Total Phenolic Content in Essential Oils

Over the past decade, there has been growing interest in polyphenols’ research since these compounds, as antioxidants, have several health benefits, such as preventing neurodegenerative diseases, inflammation, cancer, cardiovascular diseases, and type 2 diabetes. This study implements an analytical method to assess the total phenolic content (TPC) in essential oils using Folin–Ciocalteu’s phenol reagent and quantifies the individual phenolic compounds by liquid chromatography. Thus, the research design and methodology included: (1) extraction of essential oil from dried thyme leaves by hydrodistillation; (2) spectrophotometric measurement of TPC by Folin–Ciocalteu method; and (3) identification and quantification of individual phenolic compounds by high-performance liquid chromatography-diode array detection/electrospray ionization mass spectrometry (HPLC-DAD-ESI-MS). Results revealed a TPC of 22.62 ± 0.482 mg GAE/100 µL and a polyphenolic profile characterized by phenolic acids (52.1%), flavonoids (16.1%), and other polyphenols (31.8%). Thymol, salvianolic acid A, and rosmarinic acid were the major compounds of thyme essential oil. The proposed analytical procedure has an acceptable level of repeatability, reproducibility, linearity, LOD (limit of detection), and LOQ (limit of quantification).     

Polyphenols and Antioxidant Activity of Citrus Fiber/Blackberry Juice Complexes

The objective of this study was to investigate the use of citrus fiber as a carrier of blackberry juice polyphenols. For that purpose, freeze-dried complexes with blackberry juice and different amounts of citrus fiber (1%, 2% and 4%) were prepared. Complexes were evaluated spectrophotometrically for total polyphenols, proanthocyanidins and antioxidant activity. Analyses of individual polyphenols were performed using high-performance liquid chromatography. IR spectra were recorded to confirm encapsulation. All analyses were performed after preparation and after eight months of storage, in order to examine the stability of formed complexes. The obtained results indicated that increasing the amount of fiber led to a decrease in the concentration of polyphenols and the antioxidant activity of complexes. Cyanidin 3-glucoside was the prevalent anthocyanin in complexes (138.32–246.45 mg/100 g), while cyanidin 3-dioxalylglucoside was present at lower concentrations (22.19–31.45 mg/100 g). The other identified and quantified polyphenols were hesperidin (from citrus fiber), ellagic acid and quercetin (1317.59–1571.65 mg/100 g, 31.94–50.11 mg/100 g and 20.11–33.77 mg/100 g, respectively). Degradation of polyphenols occurred during storage. Results obtained in this study confirmed that citrus fiber could be used for the formulation of novel bioactive additives. Such additives could enhance the antioxidant potential of products to which they are added, such as baked goods, dairy, or fruit products.     

Expansions at small Reynolds numbers for the flow past a porous circular cylinder

The purpose of this article is to use the method of matched asymptotic expansions (MMAE) in order to study the two-dimensional steady low Reynolds number flow of a viscous incompressible fluid past a porous circular cylinder. We assume that the flow inside the porous body is described by the continuity and Brinkman equations, and the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. Formal expansions for the corresponding stream functions are used. We show that the force exerted by the exterior flow on the porous cylinder admits an asymptotic expansion with respect to low Reynolds numbers, whose terms depend on the characteristics of the porous cylinder. In addition, by considering Darcy's law for the flow inside the porous circular cylinder, an asymptotic formula for the force on the cylinder is obtained. Also, a porous circular cylinder with a rigid core inside is considered with Brinkman equation inside the porous region. Stress jump condition is used at the porous–liquid interface together with the continuity of velocity components and continuity of normal stress. Some particular cases, which refer to the low Reynolds number flow past a solid circular cylinder, have also been investigated.