Mathematical Analysis of Inertial Waves in Rectangular Basins with One Sloping Boundary

We consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two‐dimensional Poincaré–Sobolev equation in a class of domains including trapezoid are found in an explicit form and their main properties are described. These solutions correspond to the absolutely continuous spectrum of a linear operator that is associated with this system of equations. For specialists in Astrophysics and Geophysics, the existence of these solutions signifies the existence of some previously unknown type of inertial waves corresponding to the continuous spectrum of inertial oscillations. A fundamental distinction between monochromatic inertial waves and waves of the new type is shown: usual characteristics (frequency, amplitude, wave vector, dispersion relation, direction of energy propagation, and so on) are not applicable to the last. Main properties of these waves are described. In particular, it is proved that they are progressive. Main features of their energy transfer are described.     

Polymerization of ethylene oxide with a calixarene‐based precursor: Synthesis of eight‐arm poly(ethylene oxide) stars by the core‐first methodology

Eight‐arm poly(ethylene oxide) (PEO) stars were prepared by the core‐first method with a newly designed octahydroxylated precursor. This compound was readily obtained in two steps from commercially available tert‐butylcalix[8]arene. The choice of the proper solvent of polymerization proved crucial to obtain PEO star materials with a narrow distribution of molar masses. For instance, the use of dimethyl sulfoxide (DMSO) resulted in PEO samples of rather large polydispersities (PDI: 1.3–1.5). In this solvent, the calixarene‐based precursor was only sparingly soluble, and an attempt to metalate its eight hydroxyl groups produced insoluble alkoxides. In addition, the presence of a side population of low‐molar‐mass species attributable to linear chains was detected because of the chain transfer of propagating alkoxides to DMSO. Polymerization experiments carried out in tetrahydrofuran (THF) as solvent afforded better control over the molar masses and PDIs. This was related to the better solubility of the octafunctional calixarene‐based precursor in THF and to the small tendency of the alkoxides formed to aggregate in that solvent. Under such conditions, all eight hydroxyl functions efficiently initiated the polymerization of ethylene oxide. In this way, well‐defined PEO stars (PDI < 1.2) of tunable molar masses incorporating a calixarene‐based core could be obtained, as it was supported by the characterization of the samples by size exclusion chromatography, NMR, and viscometry. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1669–1676, 2003     

Polyelectrolyte-surfactant association—from fundamentals to applications

Mixed polymer-surfactant systems have broad applications, ranging from detergents, paints, pharmaceutical, and cosmetic to biotechnological. A review of the underlying polymer-surfactant association in bulk is given. While ionic surfactants bind broadly to polymers, nonionics only do so if the polymer has a lower polarity and can interact by hydrophobic interactions. Water-soluble polymers, which have hydrophobic groups, form physical cross-links, hence they may be used as thickeners. The rheological behaviour is strongly influenced by various cosolutes; especially strong effects are due to surfactants and both a decrease and an increase in viscosity can occur. When the polymer-surfactant interactions are particularly strong, an associative phase separation can occur, like in the case where there is electrostatic attraction as well as hydrophobic; this and other types of phase separation phenomena are described. Except for linear ionic and nonionic polymers, the interactions between surfactants and cross-linked polymers, microgel particles and covalent macroscopic gels are analyzed, as well as the possibility of forming gel particles of interest for encapsulation purposes. Furthermore, the behavior of these mixed systems on surfaces is discussed. In particular, we consider the adsorption of mixtures of ionic polymers and oppositely charged surfactants on polar and nonpolar surfaces. Depending on concentration, an ionic surfactant can either induce additional polyion adsorption or induce desorption. Kinetic control of adsorption and, in particular, desorption is typical. Important consequences of this include an increased adsorption on rinsing and path dependent adsorbed layers. Recently, considerable attention has been given to the interaction between DNA and cationic surfactant, both as a means to understand the behaviour of DNA in biological systems and to develop novel formulations, for example for gene therapy. Here we review aspects such as DNA compaction, DNA covalent gels and DNA soft nanoparticles.     

Polyelectrolyte/surfactant mixtures in the bulk and at water/oil interfaces

Stabilization of emulsions by mixed polyelectrolyte/surfactant systems is a prominent example for the application in modern technologies. The formation of complexes between the polymers and the surfactants depends on the type of surfactant (ionic, non-ionic) and the mixing ratio. The surface activity (hydrophilic–lipophilic balance) of the resulting complexes is an important quantity for its efficiency in stabilizing emulsions. The interfacial adsorption properties observed at liquid/oil interfaces are more or less equivalent to those observed at the aqueous solution/air interface, however, the corresponding interfacial dilational and shear rheology parameters differ quite significantly. The interfacial properties are directly linked to bulk properties, which support the picture for the complex formation of polyelectrolyte/surfactant mixtures, which is the result of electrostatic and hydrophobic interactions. For long alkyl chain surfactants the interfacial behavior is strongly influenced by hydrophobic interactions while the complex formation with short chain surfactants is mainly governed by electrostatic interactions.     

Innate Immunomodulatory Activity of Cedrol,a Component of Essential Oils Isolated from Juniperus Species

Little is known about the immunomodulatory activity of essential oils isolated from Juniperus species. Thus, we isolated essential oils from the cones and leaves of eight juniper species found in Montana and in Kazakhstan, including J. horizontalis, J. scopolorum, J. communis, J. seravschanica, J. sabina, J. pseudosabina, J. pseudosabina subsp. turkestanica, and J. sibirica. We report here the chemical composition and innate immunomodulatory activity of these essential oils. Compositional analysis of the 16 samples of Juniper essential oils revealed similarities and differences between our analyses and those previously reported for essential oils from this species. Our studies represent the first analysis of essential oils isolated from the cones of four of these Juniper species. Several essential oil samples contained high levels of cedrol, which was fairly unique to three Juniper species from Kazakhstan. We found that these essential oils and pure (+)-cedrol induced intracellular Ca²⁺ mobilization in human neutrophils. Furthermore, pretreatment of human neutrophils and N-formyl peptide receptor 1 and 2 (FPR1 and FPR2) transfected HL60 cells with these essential oils or (+)-cedrol inhibited agonist-induced Ca²⁺ mobilization, suggesting these responses were desensitized by this pretreatment. In support of this conclusion, pretreatment with essential oils from J. seravschanica cones (containing 16.8% cedrol) or pure (+)-cedrol inhibited human neutrophil chemotaxis to N-formyl peptide. Finally, reverse pharmacophore mapping predicted several potential kinase targets for cedrol. Thus, our studies have identified cedrol as a novel neutrophil agonist that can desensitize cells to subsequent stimulation by N-formyl peptide.