Multiplicity results for a Kirchhoff singular problem involving the fractional p-Laplacian

The aim of this paper is to study the multiplicity of solutions for a Kirchhoff singular problem involving the fractional p-Laplacian operator. Using the concentration compactness principle and Ekeland"s variational principle, we obtain two positive weak solutions.     

Flat orbits and kernels of irreducible representations of the group algebra of a completely solvable Lie group

We show that the kernel of an irreducible unitary representation π of the group algebra L¹(G) of a completely solvable Lie group G is given by the functions, whose abelian Fourier transform vanish on the Kirillov orbit Oπ of π if and only if this orbit Oπ is flat. This is a generalization of a result obtained before for nilpotent Lie groups.     

Type-definable groups in C-minimal structures

This Note studies type-definable groups in C-minimal structures. We show first for some of these groups, that they contain a cone which is a subgroup. This result will be applied to show that in any geometric locally modular non-trivial C-minimal structure, there is a definable infinite C-minimal group.     

Fluorimetric properties of a 2-hydroxypropyl-β-cyclodextrin: 9-methyl-benzo[a]phenothiazine inclusion complex in aqueous media. Analytical usefulness

The formation of an inclusion complex between 9-methyl-12H-benzo[a]phenothiazine (MeBPHT) and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) was investigated in aqueous medium. A 12-fold fluorescence emission intensity enhancement was found for the complexed relative to the free analyte. MeBPHT forms a 1:1 stoichiometry complex with HP-β-CD. A formation constant of 460 (±100) M⁻¹ was calculated using the Benesi-Hildebrand method and fluorimetric data. The limit of detection was 7 ng ml⁻¹ for MeBPHT in the presence of HP-β-CD instead of 60 ng ml⁻¹ in the absence of HP-β-CD.     

A gas transport system for fast chemistry

The gas transport system (GTS) brings short-lived radioactive nuclides to low back-ground areas for chemical separation and/or on-line α-, γ- and X-ray analysis. A pressure difference of a few Torr (3–5) is enough to maintain the transport, thus eliminating the need for costly pumping systems and making it possible to perform chemistry at atmospheric pressure. This technique was applied to a variety of radioactive sources. There is some Z-dependence on the transportation efficiency for the various transported nuclides as a function of the transporting gas and extracting solvent.     

Effect of the organic fragment on the mesogenic properties of a series of organogold(I) isocyanide complexes. X-ray crystal structure of [Au(CCC5H4N)(CNC6H4O(O)CC6H4OC10H21)]

Rod-like organogold(I) complexes [AuR(CNC₆H₄O(O)CC₆H₄OC₁₀H₂₁-p)] were prepared and their liquid crystal behaviour was studied. Depending on the nature of R, the synthetic methodology was different. Thus, for R = substituted alkynyl ligands, the new compounds were prepared in two steps:(i) reaction of [AuCl(tht)] (tht = tetrahydrothiophene) with R′CCH(R′ = C₅H₄N, C₆H₄CN, C₆H₄CCC₅H₄N) in the presence of NaOAc to give insoluble [Au(CCR′)]_n; (ii) reaction of the latter polymers with the isonitrile CNC₆H₄O(O)CC₆H₄OC₁₀H₂₁-p.For R = fluorinated aryls, the complexes were prepared by displacement of tht from the compounds [AuR(tht)] (R = C₅F₄N, C₆F₄C₅H₄N, C₆F₅) with isonitrile.In addition, an unexpected ionic derivative [Au(CCC₅H₄NC₁₀H₂₁)₂][Au(CCC₅H₄N)₂] was formed in the reaction between [PPh₄][Au(CCC₅H₄N)₂] and C₁₀H₂₁I. All these compounds have been characterized by IR and NMR spectroscopy and mass spectrometry. The X-ray crystal structure of the compound with R = CCC₅H₄N shows a linear molecule in which the gold atom is surrounded by the pyridine-containing acetylene and the isonitrile ligand, and no direct gold-gold interaction occurs. Six of the neutral compounds are liquid crystals and their optical, thermal and thermodynamic data were analyzed and compared in terms of molecular polarizability.     

The direct electrochemical synthesis of tin,cobalt, copper,zinc, cadmium and silver 7-formyl-8-hydroxyquinoline complexes

Summary Main group and transition metal complexes of 7-formyl-8-hydroxyquinoline have been synthesized by an electrochemical technique using a sacrifical anode in a non-aqueous solution of the ligand, and characterized by elemental analyses and i.r. spectra. The ligand acts as a monobasic tri-dentate chelating agent coordinating through C=N, C=O and OH groups by replacement of a proton from the latter group. The electrical conductivities of the complexes were measured at different temperatures and annealing times. Their activation energies were calculated; the value obtained for the Zn^II complex lay in the range reported for semiconducting materials.Physics Department, Faculty of Science, Sana'a University.     

Occurrence, shape, and dimensions of large surface hemimicelles made of semifluorinated alkanes. Elongated versus circular Hemimicelles. Pit- and tip-centered hemimicelles

The formation of large (approximately 20-35 nm) surface hemimicelles in monolayers of semifluorinated alkanes, C(n)F(2)(n)(+1)C(m)H(2)(m)(+1) (FnHm), observed after transfer onto silicon wafers, is a general phenomenon. F6H16 and F8H14 exclusively form highly monodisperse circular hemimicelles, organized in a hexagonal array. The other FnHm investigated form both circular and elongated hemimicelles. The longer FnHm is, the larger the area fraction of elongated micelles; both the hydrocarbon block (H-block) and the fluorocarbon block (F-block) affect this area fraction. The length of the elongated micelles increases with the total length of the diblocks. The diameter of the circular micelles increases with the length of the H-block but, unexpectedly, not with that of the F-block. Model calculations account for these observations. Close examination of the circular micelles showed that they generally present a pit or a tip at their center. The width of the elongated micelles is comparable to the radius of the circular micelles, suggesting that the latter arise from a partition of elongated micelles, followed by coalescence of the edges of the resulting fragments. The elongated micelles become shorter and fewer when surface pressure increases, further suggesting a conversion of elongated into circular micelles. This conversion is reversible. The surface pressure-molecular area isotherms do not present any feature that forebears the existence of hemimicelles. The obtaining of stable surface patterns from simple, "nonpolar" molecular fluorocarbon/hydrocarbon diblocks opens a new approach for producing featured nanostructures from organic templates.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

Methyl group dynamics as a probe of the protein dynamical transition

Hydrated proteins undergo a dynamical transition around 200 K from glasslike to liquidlike motion. Molecular dynamics simulations have been used to study the temperature dependence of the dynamics of ribonuclease A in the hydrated crystal, a model dehydrated powder, and aqueous solution. Changes in the dynamics accompanying the transition throughout the protein have been quantified in terms of the mean-squared fluctuations (MSFs) of methyl hydrogen atoms on the 100 ps time scale. In solution at 300 K the MSFs span a broad distribution, consistent with NMR relaxation measurements. The MSF distribution in the hydrated crystal at 300 K is qualitatively similar to the solution result, except for a slight shift to lower values, and dehydration results in a dramatic shift of the MSFs to lower values. As the temperature is lowered, the whole distribution of methyl group fluctuations in the hydrated crystal shifts to lower values. Most of the methyl groups in the hydrated protein display a nonlinear temperature dependence with a dynamical transition at approximately 200 K, but most methyl groups do not undergo a transition in the dehydrated protein. We conclude that the dynamical transition occurs throughout most of the protein and that solvent is required for the transition.