Isometries of Quaternionic Lie Groups

We study connected Lie groups whose Lie algebra is obtained as the tensor product of a real associative algebra and the algebra of quaternions. It is proved that they carry a natural integrable -structure. We endow such quaternionic Lie groups with a left-invariant Hermitian metric and study the identity connected component of their isometry groups. The determination of such identity connected component is illustrated with a family of examples.     

Gas sensing properties of nanostructured MoO3 thin films prepared by spray pyrolysis

Thin films of molybdenum trioxide (MoO₃) were deposited on common glass using the chemical spray pyrolysis technique. A (NH₄)₆Mo₇O₂₄4H₂0 solution 0.1 M was used as the precursor one. The influence of substrate temperature on the crystallographic structure, surface morphology and electrical behavior of MoO₃ thin films was studied. MoO₃ can exist in two crystalline forms, the thermodynamically stable orthorhombic α-MoO₃ and the metastable monoclinic β-MoO₃ phase. XRD-spectra showed a growth of α-MoO₃ phase percentage as substrate temperature increases from 420 K up to 670 K. Films deposited in the 500–600 K range have a clearly porous surface structure of nanometer order as can be seen in SEM images. Changes up to six magnitude orders were observed in MoO₃ thin films electrical resistance when films temperature varied from 100 K up to 500 K. The sensing property of these MoO₃ films was also studied. The sensitivity was investigated in the temperature range 160 and 360 K for H₂O and CO gases, respectively. Both of them are of reducing nature. In all studied cases sensitivity decreases slowly as film temperature is raised. At room temperature the sensitivity changes from 12 up to 75% depending on substrate temperature. The sensitivity for CO gas was found to be lower than that of H₂O.     

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.     

Fractional Hamiltonian systems with positive semi-definite matrix

We study the existence of solutions for the following fractional Hamiltonian systems $$ \left\{ \begin{array}{ll} - _tD^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u(t))-\lambda L(t)u(t)+\nabla W(t,u(t))=0,\\[0.1cm] u\in H^{\alpha}(\mathbb{R},\mathbb{R}^n), \end{array} \right. ~~~~~~~~~~~~~~~~~(FHS)_\lambda $$ where $\alpha\in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}^n$, $\lambda>0$ is a parameter, $L\in C(\mathbb{R},\mathbb{R}^{n^2})$ is a symmetric matrix, $W\in C^1(\mathbb{R} \times \mathbb{R}^n,\mathbb{R})$. Assuming that $L(t)$ is a positive semi-definite symmetric matrix, that is, $L(t)\equiv 0$ is allowed to occur in some finite interval $T$ of $\mathbb{R}$, $W(t,u)$ satisfies some superquadratic conditions weaker than Ambrosetti-Rabinowitz condition, we show that (FHS)$_\lambda$ has a solution which vanishes on $\mathbb{R}\setminus T$ as $\lambda \to \infty$, and converges to some $\tilde{u}\in H^{\alpha}(\R, \R^n)$. Here, $\tilde{u}\in E_{0}^{\alpha}$ is a solution of the Dirichlet BVP for fractional systems on the finite interval $T$. Our results are new and improve recent results in the literature even in the case $\alpha =1$.     

Arresting wave collapse by wave self-rectification

We put forward a mechanism for tailoring, and even arresting, the collapse of wave packets in nonlinear media, whose dynamics is governed by nonlocal two-dimensional nonlinear Schr?dinger-like equations. The key ingredient of the scheme is the self-generation of nonlocal nonlinearities mediated by wave rectification.     

Mean oscillation of functions and the Paley-Wiener space

The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown. Acknowledgements and Notes. Supported in part by NSF grants DMS 9303363 and DMS 9623251.     

Theoretical study of the coadsorption of CO and O2 on doped cationic gold clusters MAun + (M = Ti, Fe, Au; n = 1, 6, 7)

We present a study based on first-principles calculations of the adsorption of CO on selected equilibrium configurations of MAu_nO₂ ⁺ (M = Ti, Fe; n = 1, 6, 7) complexes resulting from the adsorption of O₂ on doped cationic gold clusters MAu_n ⁺. Empirical rules for the formation of CO₂-MAu_nO⁺ complexes are outlined. The desorption energy of CO₂ is calculated. The adsorption of a second CO molecule on the residual MAu_nO⁺ complex leads in some cases to the formation of CO₂-MAu_n ⁺. The desorption of a second CO₂ molecule brings back to the initial doped gold cluster MAu_n ⁺.     

Mechanically Interlocked Single‐Wall Carbon Nanotubes

Extensive research has been devoted to the chemical manipulation of carbon nanotubes. The attachment of molecular fragments through covalent‐bond formation produces kinetically stable products, but implies the saturation of some of the C? C double bonds of the nanotubes. Supramolecular modification maintains the structure of the SWNTs but yields labile species. Herein, we present a strategy for the synthesis of mechanically interlocked derivatives of SWNTs (MINTs). In the key rotaxane‐forming step, we employed macrocycle precursors equipped with two π‐extended tetrathiafulvalene SWNT recognition units and terminated with bisalkenes that were closed around the nanotubes through ring‐closing metathesis (RCM). The mechanically interlocked nature of the derivatives was probed by analytical, spectroscopic, and microscopic techniques, as well as by appropriate control experiments. Individual macrocycles were observed by HR STEM to circumscribe the nanotubes.     

A Unique Tryptophan C‐Prenyltransferase from the Kawaguchipeptin Biosynthetic Pathway

Cyanobactins are a rapidly growing family of linear and cyclic peptides produced by cyanobacteria. Kawaguchipeptins A and B, two macrocyclic undecapeptides reported earlier from Microcystis aeruginosa NIES‐88, are shown to be products of the cyanobactin biosynthetic pathway. The 9 kb kawaguchipeptin (kgp) gene cluster was identified in a 5.26 Mb draft genome of Microcystis aeruginosa NIES‐88. We verified that this gene cluster is responsible for the production of the kawaguchipeptins through heterologous expression of the kgp gene cluster in Escherichia coli. The KgpF prenyltransferase was overexpressed and was shown to prenylate C‐3 of Trp residues in both linear and cyclic peptides in vitro. Our findings serve to further enhance the structural diversity of cyanobactins to include tryptophan‐prenylated cyclic peptides.     

Ozonolysis of oleic acid adsorbed to polar and nonpolar aerosol particles

Single-particle kinetic studies of the reaction between oleic acid and O 3 have been conducted on two different types of core particles: polystyrene latex (PSL) and silica. Oleic acid was found to adsorb to both particle types in multilayer islands that resulted in an adsorbed layer of a total volume estimated to be less than one monolayer. The rate of the surface reaction between surface-adsorbed oleic acid and O 3 has been shown for the first time to be influenced by the composition of the aerosol substrate in a mixed organic/inorganic particle. A Langmuir-Hinshelwood mechanism was applied to the observed dependence of the pseudo-first-order rate constant with [O 3], and the resulting fit parameters for the ozone partition coefficient ( K O 3 ) and maximum first order rate constant ( k 1,max ) suggest that the reaction proceeded faster on the less polar PSL core at lower [O 3] due to the increased residence time of O 3 on the PSL surface, but the reaction was ultimately more efficient on the silica surface at high [O 3]. Values for the uptake coefficient, gamma oleic , for reaction of oleic acid on PSL spheres decrease from 2.5 x 10 (-5) to 1 x 10 (-5) with increasing [O 3] from 4 to 25 ppm and overlap at high [O 3] with the estimated values for gamma oleic on silica, which decrease from 1.6 x 10 (-5) to 1.3 x 10 (-5). The relationship between gamma oleic and the more common expression for gamma O 3 is discussed.