Linear stability analysis of a non-slipping mean flow in a 2D-straight lined duct with respect to modes type initial (instantaneous) perturbations

In this paper a necessary and sufficient condition is found for the existence of non-zero modes, which satisfy the Pridmore–Brown equation and the mass-spring-damper impedance boundary condition. The flowing fluid is assumed to be inviscid, non-slipping and compressible. The mean flow velocity profile in the equation is assumed to be function of y only. The condition which is found defines in fact a dispersion relation, which has to be used in the linear stability analysis of the flow also by Briggs–Bers method. As far as we know, the dispersion relation reported in the present paper is new and it is not an obvious consequence of other results already reported in the literature. The numerical illustration shows that the dispersion-relation is effective and for the considered numerical data reveals the existence of mode type initial perturbations whose amplitude increase exponentially in time showing linear instability. In the same time the numerical illustration reveals the existence of mode type initial perturbations whose amplitude decrease exponentially tending to zero for t tending to plus infinity.     

Encapsulation of Fruit Flavor Compounds through Interaction with Polysaccharides

Production and storage, the influence of packaging materials and the presence of other ingredients in fruit products can cause changes in flavor compounds or even their loss. Due to these issues, there is a need to encapsulate flavor compounds, and polysaccharides are often used as efficient carriers. In order to achieve effective encapsulation, satisfactory retention and/or controlled release of flavor compounds, it is necessary to understand the nature of the coated and coating materials. Interactions that occur between these compounds are mostly non-covalent interactions (hydrogen bonds, hydrophobic interactions and van der Waals forces); additionally, the formation of the inclusion complexes of flavor compounds and polysaccharides can also occur. This review provides insight into studies about the encapsulation of flavor compounds, as well as basic characteristics of encapsulation such as the choice of coating material, the effect of various factors on the encapsulation efficiency and an explanation of the nature of binding.     

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.

Graphical abstract

Open image in new window

     

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).     

Identification and Structural Characterization of Novel Chondroitin/Dermatan Sulfate Hexassacharide Domains in Human Decorin by Ion Mobility Tandem Mass Spectrometry

Chondroitin sulfate (CS) and dermatan sulfate (DS) are found in nature linked to proteoglycans, most often as hybrid CS/DS chains. In the extracellular matrix, where they are highly expressed, CS/DS are involved in fundamental processes and various pathologies. The structural diversity of CS/DS domains gave rise to efforts for the development of efficient analytical methods, among which is mass spectrometry (MS), one of the most resourceful techniques for the identification of novel species and their structure elucidation. In this context, we report here on the introduction of a fast, sensitive, and reliable approach based on ion mobility separation (IMS) MS and MS/MS by collision-induced dissociation (CID), for the profiling and structural analysis of CS/DS hexasaccharide domains in human embryonic kidney HEK293 cells decorin (DCN), obtained after CS/DS chain releasing by β-elimination, depolymerization using chondroitin AC I lyase, and fractionation by size-exclusion chromatography. By IMS MS, we were able to find novel CS/DS species, i.e., under- and oversulfated hexasaccharide domains in the released CS/DS chain. In the last stage of analysis, the optimized IMS CID MS/MS provided a series of diagnostic fragment ions crucial for the characterization of the misregulations, which occurred in the sulfation code of the trisulfated-4,5-Δ-GlcAGalNAc[IdoAGalNAc]₂ sequence, due to the unusual sulfation sites.     

Efficient palladium-mediated or base-induced 5-endo-dig cyclisation of C5-alkynylated pyrimidine derivatives: conventional and microwave-assisted synthesis of novel furo[2,3-d]pyrimidines

A series of the novel 5-alkynyl- and furo[2,3-d]pyrimidine derivatives in which the sugar moiety is replaced by a methoxymethyl (MOM) group is synthesised using the Sonogashira cross-coupling reaction under both conventional and microwave conditions, in good to excellent yields. The 5-endo-dig cyclisation of 5-alkynylpyrimidine derivatives promoted by a Pd-catalyst or base gives the corresponding furo[2,3-d]pyrimidines in good yields.