Covering the alternating groups by products of cycle classes

Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99].     

Thermoelectric power and electrochemical studies on CdI<Subscript>2</Subscript>–Ag<Subscript>2</Subscript>O–V<Subscript>2</Subscript>O<Subscript>5</Subscript>–B<Subscript>2</Subscript>O<Subscript>3</Subscript> system

A quaternary super-ion-conducting system, 20CdI₂ − 80[xAg₂O − y(0.7V₂O₅ − 0.3B₂O₃)] where 1 ≤ x/y ≤ 3, has been prepared by melt quenching technique. The electrical conductivity measured was the order of 10⁻⁴  S/cm at room temperature. The values of silver-ion transport number obtained by electromotive force technique are nearly unity. The thermoelectric power and electrochemical studies were done on the CdI₂–Ag₂O–V₂O₅–B₂O₃ system. The discharge and polarization characteristics were examined for different cathodes to evaluate the utility of these cells as power sources for low energy applications.     

10a-(4-Biphenyl)-10b-methyl-10a,10b-dihydropyrene: a conformational study and ring current effect

A dithiacyclophane was employed as a precursor to the title compound. A conformational study of the dithiacyclophane revealed a unique phenomenon in its terphenyl unit: one ring is rigidly held, the other terminal ring undergoes free rotation and the central ring exhibits restricted mobility. The aromatic protons of the biphenyl unit are all shielded by the dihydropyrene unit and well resolved in the ¹H NMR spectrum, consistent with a ring current effect extended to eight conjugated carbon atoms away from the molecular plane of dihydropyrene.     

Accumulation and filtering of nanoparticles in microchannels using electrohydrodynamically induced vortical flows

We present an approach for the accumulation and filtering of nano- and microparticles in microfluidic devices that is based on the generation of electric traveling waves in the radio-frequency range. Upon application of the electric field via a microelectrode array, complex particle trajectories and particle accumulation are observed in well-defined regions in a microchannel. Through the quantitative mapping of the 3-D flow pattern using two-focus fluorescence cross-correlation spectroscopy, two vortices could be identified as one of the sources of the force field that induces the formation of particle clouds. Dielectrophoretic forces that directly act on the particles are the second source of the force field. A thorough 2-D finite element analysis identifies the electric traveling wave mechanism as the cause for the unexpected flow behavior observed. Based on these findings, strategies are discussed, first, for avoiding the vortices to optimize electrohydrodynamic micropumps and, secondly, for utilizing the vortices in the development of microdevices for efficient particle accumulation, separation, and filtering. Such devices may find numerous biomedical applications when highly diluted nano- and microsuspensions have to be processed.     

Application of high-speed counter-current chromatography for the isolation of antiviral eremophilenolides from Ligularia atroviolacea

Ligularia is mainly distributed in the western regions of China. Most of the species have been traditionally used in folk medicine for the treatment of hepatitis B, asthma, hemoptysis and pulmonary tuberculosis. In our continuation of research on antiviral components from traditional Chinese medicine, Ligularia atroviolacea was tested for inhibitory effects on hepatitis B virus (HBV). A bioassay-guided phytochemical examination of L. atroviolacea disclosed that its ethyl acetate extract, which was made up of two eremophilenolides, showed suppressive activity on the expression of HBV surface antigen (HBsAg) in the HepG2.2.15 cell line. Then a simple and effective preparative high-speed counter-current chromatography method was successfully developed for the isolation and purification of two main active metabolites, 8beta-hydroxyeremophil-3,7(11)-dien-12,8alpha;15,6alpha-diolide and 8beta-methoxyeremophil-3,7(11)-dien-12,8alpha;15,6alpha-diolide from the ethyl acetate extract of L. atroviolacea by a one-step separation using a two-phase solvent system composed of light petroleum (60-90 degrees C)-ethyl acetate-methanol-water (9:1:8:2, v/v/v). The chemical structures of the two eremophilenolides were identified by ESI-MS, (1)H-NMR and (13)C-NMR analysis. The anti-HBV activity of the two purified compounds was measured; both of them showed suppressive activity on the expression of HBsAg in the HepG2.2.15 cell line. The results support the continued and expanded exploitation and utilization of L. atroviolacea. Copyright (c) 2008 John Wiley & Sons, Ltd.     

Front Cover: Enhancement of dielectrophoresis-based particle collection from high conducting fluids due to partial electrode insulation

Dielectrophoresis (DEP) is a successful method to recover nanoparticles from different types of fluid. The DEP force acting on these particles is created by an electrode microarray that produces a nonuniform electric field. To apply DEP to a highly conducting biological fluid, a protective hydrogel coating over the metal electrodes is required to create a barrier between the electrode and the fluid. This protects the electrodes, reduces the electrolysis of water, and allows the electric field to penetrate into the fluid sample. We observed that the protective hydrogel layer can separate from the electrode and form a closed domed structure and that collection of 100 nm polystyrene beads increased when this occurred. To better understand this collection increase, we used COMSOL Multiphysics software to model the electric field in the presence of the dome filled with different materials ranging from low-conducting gas to high conducting phosphate-buffered saline fluids. The results suggest that as the electrical conductivity of the material inside the dome is reduced, the whole dome acts as an insulator which increases electric field intensity at the electrode edge. This increased intensity widens the high-intensity electric field factor zone resulting in increased collection. This informs how dome formation results in increased particle collection and provides insight into how the electric field can be intensified to the increase collection of particles. These results have important applications for increasing the recovery of biologically-derived nanoparticles from undiluted physiological fluids that have high conductance, including the collection of cancer-derived extracellular vesicles from plasma for liquid biopsy applications.     

Living Cationic Ring-Opening Polymerization of Hetero Diels–Alder Adducts to Give Multifactor-Controlled and Fast-Photodegradable Vinyl Polymers

Precise control of multiple structural parameters associated with vinyl polymers is important for producing materials with the desired properties and functions. While the development of living polymerization methods has provided a way to control the various structural parameters of vinyl polymers, the concomitant control of their sequence and regioregularity remains a challenging task. To overcome this challenge, herein, we report the living cationic ring-opening polymerization of hetero Diels–Alder adducts. The scalable and modular synthesis of the cyclic monomers was achieved by a one-step protocol using readily available vinyl precursors. Subsequently, living polymerization of the cyclic monomers was examined, allowing the synthesis of vinyl polymers while controlling multiple factors, including molecular weight, dispersity, alternating sequence, head-to-head regioregularity, and end-group functionality. The living characteristics of the developed method were further demonstrated by block copolymerization. The synthesized vinyl polymers exhibited unique thermal properties and underwent fast photodegradation even under sunlight.     

Influence of the nature of membrane ionogenic groups on water dissociation and electrolyte ion transport: A rotating membrane disk study

Polarization properties of electromembrane systems (EMS) consisting of a heterogeneous membrane, either the MK-41 phosphonic acid membrane or the MK-40 sulfonic acid membrane, and dilute sodium chloride solutions are investigated with the rotating membrane disk method. For the MK-41/0.01 M NaCl and MK-41/0.001 M NaCl EMS, effective ion transport numbers and partial current-voltage curves (CVC) are measured for sodium and hydrogen ions, and limiting-current densities and the diffusion-layer thickness are calculated as functions of the rotation rate of the membrane disk. With the theory of the overlimiting state of EMS, internal parameters of the systems under investigation—the diffusion-layer thickness, the space-charge distribution, and electric-field strengths in the diffusion layer and in the membrane—are calculated from experimentally obtained CVC and the dependence of effective transport numbers on current density. The catalytic influence of ionogenic groups on the dissociation rate of water is analyzed quantitatively. Partial CVC for H⁺ ions are calculated for the space-charge region in MK-40 and MK-41 membranes. Analogous CVC for bipolar membranes containing sulfonic acid and phosphonic acid groups are compared. The dissociation mechanism of water is the same in all EMS and is independent of the membrane type and the nature of the functional groups.     

Monotone nonparametric regression with random design

In this paper we study the nonparametric least squares estimator of a regression function in a random design setting under the constraint that this function is monotone, say, nonincreasing. The errors are not assumed conditionally i.i.d. given the observation points. In particular, this includes the case of conditional heteroscedasticity and the case of the current status model. The -error is shown to be of order n ^−p/3 and asymptotically Gaussian with explicit asymptotic mean and variance.      

Do bacteria have an electric permanent dipole moment?

In the scientific literature in the last 40 years, some data for the permanent dipole moment and the electric polarizability of Escherichia coli can be found [S.P. Stoylov, Colloid Electro-Optics - Theory, Techniques and Application, Academic Press, London, 1991]. In this paper the data based mainly on electro-optic investigation is considered as much as some dipolophoretic (most often called dielectrophoretic) studies. Serious grounds are found to doubt the conclusions made for the electric dipole moments of bacteria by one of the authors of this paper (SPS) and by some other researchers. This concerns both the permanent dipole moment and the electric charge dependent polarizabilities of E. coli. Here, along with the discussion of the old experimental data, new experimental data are shown for a strain of E. coli HB101. The conclusions from the analysis of the old and the new experimental data is that they do not provide correct evidence for the presence of a permanent dipole moment. It seems that all statements for the existence of electric permanent dipole moment in bacteria [S.P. Stoylov, Colloid Electro-Optics - Theory, Techniques and Application, Academic Press, London, 1991; S.P. Stoylov, S. Sokerov, I. Petkanchin, N. Ibroshev, Dokl. AN URSS 180 (1968) 1165; N.A. Tolstoy, A.A. Spartakov, A.A. Trusov, S.A. Schelkunova, Biofizika 11 (1966) 453; V. Morris, B. Jennings, J. Chem. Soc. Faraday Trans. II 71 (1975) 1948; V. Morris, B. Jennings, J. Colloid Interface Sci. 55 (1978) 313; S.P. Stoylov, V.N. Shilov, S.S. Dukhin, S. Sokerov, I. Petkanchin, in: S.S. Dukhin (Ed.), Electro-optics of Colloids, Naukova Dumka, Kiev, 1977 (in Russian).] based on electro-optic studies are result of incorrect interpretation. Therefore, they should be further ignored.