An upper bound on the Chebotarev invariant of a finite group

A subset {g ₁,..., g _d } of a finite group G invariably generates \(\left\{ {g_1^{{x_1}}, \ldots ,g_d^{{x_d}}} \right\}\) generates G for every choice of x _i ∈ G. The Chebotarev invariant C(G) of G is the expected value of the random variable n that is minimal subject to the requirement that n randomly chosen elements of G invariably generate G. The first author recently showed that \(C\left( G \right) \leqslant \beta \sqrt {\left| G \right|} \) for some absolute constant β. In this paper we show that, when G is soluble, then β is at most 5/3. We also show that this is best possible. Furthermore, we show that, in general, for each ε > 0 there exists a constant c _ε such that \(C\left( G \right) \leqslant \left( {1 + \in } \right)\sqrt {\left| G \right|} + {c_ \in }\).     

On a supplementary conservation law for the energy equation in a rigid heat conductor

We consider a rigid heat conductor with specified constitutive equations and show that the internal energy equation may be written in the form of a symmetric and conservative hyperbolic system of first order quasi-linear equations for which the Cauchy problem is well-posed. Moreover, such a system is useful to study shocks. Several particular cases are examined.     

Bubble dynamics: a review and some recent results

Several aspects of small-amplitude oscillations of bubbles containing gas, vapor, or a gas-vapor mixture are discussed. An application to pressure-wave propagation in a bubbly liquid is described. Nonlinear forced oscillations are considered in the light of recent research on forced oscillations of nonlinear systems. The growth of vapor bubbles, an extension of the Rayleigh-Plesset equation to non-Newtonian liquids and appreciable mass transfer at the interface, and a boundary integral numerical method for nonspherical cavitation bubble dynamics are also briefly discussed.     

Molecular dynamics simulations of the adsorption of bone morphogenetic protein-2 on surfaces with medical relevance

Bone morphogenetic protein-2 (BMP-2) plays a crucial role in osteoblast differentiation and proliferation. Its effective therapeutic use for ectopic bone and cartilage regeneration depends, among other factors, on the interaction with the carrier at the implant site. In this study, we used classical molecular dynamics (MD) and a hybrid approach of steered molecular dynamics (SMD) combined with MD simulations to investigate the initial stages of the adsorption of BMP-2 when approaching two implant surfaces, hydrophobic graphite and hydrophilic titanium dioxide rutile. Surface adsorption was evaluated for six different orientations of the protein, two end-on and four side-on, in explicit water environment. On graphite, we observed a weak but stable adsorption. Depending on the initial orientation, hydrophobic patches as well as flexible loops of the protein were involved in the interaction with graphite. On the contrary, BMP-2 adsorbed only loosely to hydrophilic titanium dioxide. Despite a favorable interaction energy between protein and the TiO(2) surface, the rapid formation of a two-layer water structure prevented the direct interaction between protein and titanium dioxide. The first water adlayer had a strong repulsive effect on the protein, while the second attracted the protein toward the surface. For both surfaces, hydrophobic graphite and hydrophilic titanium dioxide, denaturation of BMP-2 induced by adsorption was not observed on the nanosecond time scale.     

A practical and expeditious method for the preparation of the potential anticancer agent 5,6,11,12,17,18,23,24-octahydrocyclododeca[1,2-b:4,5-b′:7,8-b″:10,11-b?]tetraindole (CTet)

A new synthetic method to obtain the potential anticancer agent 5,6,11,12,17,18,23,24-octahydrocyclododeca[1,2-b:4,5-b′:7,8-b′′:10,11-b′′′]tetraindole (CTet), starting from 1H-indole-3-carboxaldehyde and sulfamide, is described. Although a mixture of CTet and cyclic indole trimer (CTr) is formed, higher CTet/CTr ratio (4:6) and CTet yield (15%) make our protocol more favorable than those reported in the literature. A discussion on the possible reaction mechanism is reported.     

Microanalytical method development for Fe, Cu and Zn determination in colorectal cancer cells

Microanalytical methods suitable for the determination of Fe, Cu in HT-29 (human colon adenocarcinoma) cells treated with different iron compounds (Fe(II) sulfate, Fe(III) chloride, Fe(III) citrate and Fe(III) transferrin) and cultured in medium supplemented or not with 10% (v/v) fetal calf serum (FCS) by total reflection X-ray fluorescence spectrometry (TXRF) and simultaneous graphite furnace atomic absorption spectrometry (GF-AAS) were developed. The developed TXRF method was also suitable for Zn determination in the samples. The main advantage of the proposed methods is the execution of all sample preparation steps following incubation and prior to the elemental analysis in the same Eppendorf tubes. Sample preparation was performed at microscale (115 μL sample volume) with 65% nitric acid and 30% hydrogen peroxide. According to scanning electron microscopic measurements, the organic matrix of the cell samples could be eliminated to the extent that accurate results were obtained for Cu and Fe by analyzing the same samples by TXRF and GF-AAS. Concerning the iron uptake, HT-29 cells incubated in FCS-free medium contained Fe in cca. 5-50 times higher amounts compared to cells cultured in FCS supplemented medium. Pronounced differences in the iron uptake compared to the iron supply (inorganic vs. organic chelated as well as iron(II) vs. iron(III)) were observed in the case of cell lines incubated in FCS-free medium.     

A study of resveratrol-copper complexes by electrospray ionization mass spectrometry and density functional theory calculations

Resveratrol is a polyphenolic compound found in plants and human foods which has shown biological activities including chemoprevention, acting through a mechanism which involves the reduction of Cu(II) species. By electrospray ionization (ESI) mass spectrometry we have produced and detected the resveratrol-copper complexes [Resv+Cu](+), [Resv+Cu+H(2)O](+) and [2Resv+Cu](+) by using a resveratrol/CuSO(4) solution in CH(3)CN/H(2)O. The most stable structures of the detected complexes have been calculated at the B3LYP/6-311G(d) level of theory. Resveratrol interacts with the copper ion through nucleophilic carbon atoms on the aromatic ring and the alkenyl group. The fact that only singly charged ions were observed implies that Cu(II) is reduced to Cu(I) in the ESI process. For investigating the structure-reactivity correlation, we have carried out a similar study on the synthetic analogue dihydroresveratrol (DHResv). For the latter only the [DHResv+Cu](+) complex has been detected.     

Improved high-efficiency organic solar cells via incorporation of a conjugated polyelectrolyte interlayer

The power conversion efficiencies of bulk heterojunction (BHJ) solar cells can be increased from 5 to 6.5% by incorporating an ultrathin conjugated polyelectrolyte (CPE) layer between the active layer and the metal cathode. Poly[N-9'-heptadecanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl-2',1',3'-benzothiadiazole)] (PCDTBT) and [6,6]-phenyl C(71) butyric acid methyl ester (PC(71)BM) were chosen for the photoactive layer. CPEs with cationic polythiophenes, in both homopolymer and block copolymer configurations, were used to improve the electronic characteristics. The significant improvement in device performance and the simplicity of fabrication by solution processing suggest a promising and practical pathway for improving polymer solar cells with high efficiencies.