Multiplicity theorems for superlinear elliptic problems

In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions. This paper was completed while the first author was visiting the University of Aveiro as an Invited Scientist. The hospitality and financial support of the host institution are gratefully acknowledged. The second and third authors acknowledge the partial financial support of the Portuguese Foundation for Science and Technology (FCT) under the research project POCI/MAT/55524/2004.     

Interfacial behavior and film patterning of redox-active cationic copper(II)-containing surfactants

Herein, we describe the synthesis and characterization of a novel series of single-tail amphiphiles LPyCn (Py=pyridine, Cn=C18, C16, C14, C10) and their copper(II)-containing complexes, which are of relevance for patterned films. The N-(pyridine-2-ylmethyl)alkyl-1-amine ligands and their complexes [CuIICl2(LPyC18)] (1), [CuIICl2(LPyC16)] (2), [CuIICl2(LPyC14)] (3), [CuIIBr2(LPyC18)] (4), [CuIIBr2(LPyC16)] (5), and [CuIIBr2(LPyC10)] (6) were synthesized, isolated, and characterized by means of mass spectrometry, IR and NMR spectroscopies, and elemental analysis. Complexes 1, 2, 3, and 6 had their molecular structure solved by X-ray diffraction methods, which showed that the local geometry around the metal center is distorted square planar. With the aim of using these species as precursors for redox-responsive films, an assessment of their electrochemical properties involved cyclic voltammetry in different solvents, with different supporting electrolytes and scan rates. Density functional theory calculations of relevant species in bulk and at interfaces were used to evaluate their electronic structure and dipole moments. The morphology and order of the resulting films at the air/water interface were studied by isothermal compression and Brewster angle microscopy. Biphasic patterned Langmuir films were observed for all complexes except 3 and 6, and dependence on the chain length and the nature of the halogen coligand determine the characteristics of the isotherms and their intricate topology. Complexes 3 and 6, which have shorter chain lengths, failed to exhibit organization. These results exemplify the first comprehensive study of the behavior of single-tail metallosurfactants, which are likely to lead to high-end technological applications based on their patterned films.     

Structure-dependent reactivity of semiconducting single-walled carbon nanotubes with benzenediazonium salts

The addition of diazonium salts to single-walled carbon nanotubes (SWCNTs) in aqueous surfactant suspensions quenches the intrinsic near-infrared fluorescence of semiconducting SWCNTs through sidewall chemical reactions. Spectrally resolved fluorescence spectroscopy of mixed SWCNT samples has been used to measure structure-dependent relative reactivities in the initial stages of these reactions. For several 4-substituted benzenediazonium salts, Ar-R (Ar = N 2 (+)-C 6H 4 and R = Cl, NO 2, OMe), reactivities at pH 10 were found to be greatest for SWCNTs having the largest band gaps. The magnitude of this band gap dependence varies according to the R-group of the salt, with R = OMe showing the strongest variation. For R = OH, acidification of the sample to pH 5.5 results in reversal of the structural trend, as smaller band gap SWCNTs show slightly greater reactivities. The derivatization reactions observed here proceed concurrently, although at different rates, for semiconducting and metallic SWCNT species. These results therefore provide insight into the difficulties of separating metallic and semiconducting SWCNTs through selective reaction schemes and underscore the need for fluorescence spectroscopy to be used in assessing semiconducting SWCNT reactions.     

Interconvertable modular framework and layered lanthanide(III)-etidronic acid coordination polymers

Isostructural modular microporous Na2[Y(hedp)(H2O)0.67] and Na4[Ln2(hedp)2(H2O)2].nH2O (Ln = La, Ce, Nd, Eu, Gd, Tb, Er) framework-type, and layered orthorhombic [Eu(H2hedp)(H2O)2].H2O and Na0.9[Nd0.9Ge0.10(Hhedp)(H2O)2], monoclinic [Ln(H2hedp)(H2O)].3H2O (Ln = Y, Tb), and triclinic [Yb(H2hedp)].H2O coordination polymers based on etidronic acid (H5hedp) have been prepared by hydrothermal synthesis and characterized structurally by (among others) single-crystal and powder X-ray diffraction and solid-state NMR. The structure of the framework materials comprises eight-membered ring channels filled with Na+ and both free and lanthanide-coordinated water molecules, which are removed reversibly by calcination at 300 degrees C (structural integrity is preserved up to ca. 475 degrees C), denoting a clear zeolite-type behavior. Interesting photoluminescence properties, sensitive to the hydration degree, are reported for Na4[Eu2(hedp)2(H2O)2].H2O and its fully dehydrated form. The 3D framework and layered materials are, to a certain extent, interconvertable during the hydrothermal synthesis stage via the addition of HCl or NaCl: of the 3D framework Na4[Tb2(hedp)2(H2O)2].nH2O, affords layered [Tb(H2hedp) (H2O)].3H2O, whereas layered [Tb(H2hedp)(H2O)2].H2O reacts with sodium chloride yielding a material similar to Na4[Tb2(hedp)2(H2O)2].nH2O. In layered [Y(H2hedp)(H2O)].3H2O, noncoordinated water molecules are engaged in cooperative water-to-water hydrogen-bonding interactions, leading to the formation of a (H2O)13 cluster, which is the basis of an unprecedented two-dimensional water network present in the interlayer space.     

Synthesis, structure, and electronic properties of a dimer of Ru(bpy)2 doubly bridged by methoxide and pyrazolate

The heterobridged dinuclear complex cis,cis-[(bpy) 2Ru(mu-OCH 3)(mu-pyz)Ru(bpy) 2] (2+) ( 1; bpy = 2,2'-bipyridine; pyz = pyrazolate) was synthesized and isolated as a hexafluorophosphate salt. Its molecular structure was fully characterized by X-ray crystallography, (1)H NMR spectroscopy, and ESI mass spectrometry. The compound 1.(PF 6) 2 (C 44H 38F 12N 10OP 2Ru 2) crystallizes in the monoclinic space group P2 1/ c with a = 13.3312(4) A, b = 22.5379(6) A, c = 17.2818(4) A, beta = 99.497(2) degrees , V = 5121.3(2) A (3), and Z = 4. The meso diastereoisomeric form was exclusively found in the crystal structure, although the NMR spectra clearly demonstrated the presence of two stereoisomers in solution (rac and meso forms at approximately 1:1 ratio). The electronic properties of the complex in acetonitrile were investigated by cyclic voltammetry and UV-vis and NIR-IR spectroelectrochemistries. The stepwise oxidation of the Ru (II)-Ru (II) complex into the mixed-valent Ru (II)-Ru (III) and fully oxidized Ru (III)-Ru (III) states is fully reversible on the time scale of the in situ (spectro)electrochemical measurements. The mixed-valent species displays strong electronic coupling, as evidenced by the large splitting between the redox potentials for the Ru(III)/Ru(II) couples (Delta E 1/2 = 0.62 V; K c = 3 x 10 (10)) and the appearance of an intervalence transfer (IT) band at 1490 nm that is intense, narrow, and independent of solvent. Whereas this salient band in the NIR region originates primarily from highest-energy of the three IT transitions predicted for Ru(II)-Ru(III) systems, a weaker absorption band corresponding to the lowest-energy IT transition was clearly evidenced in the IR region ( approximately 3200 cm (-1)). The observation of totally coalesced vibrational peaks in the 1400-1650 cm (-1) range for a set of five bpy spectator vibrations in Ru (II)-Ru (III) relative to Ru (II)-Ru (II) and Ru (III)-Ru (III) provided evidence for rapid electron transfer and valence averaging on the picosecond time scale. Other than a relatively short Ru...Ru distance (3.72 A for the crystalline Ru (II)-Ru (II) complex), the extensive communication between metal centers is attributed mostly to the pi-donor ability of the bridging ligands (pyz, OMe) combined with the pi-acceptor ability of the peripheral (bpy) ligands.     

On attractors and stability for semigroup actions and control systems

The present paper is dedicated to the study of various aspects of attraction and stability for semigroup actions on topological spaces. The main purpose is to present the connections among the distinct notions of attractors and stable sets. The concept of Conley attractor is also investigated and related to the other notions of attractors. All the results are applied to the theory of control systems.     

Synthesis and cytotoxic activity of some 3-benzyl-5-arylidenefuran-2(5H)-ones

3-Benzyl-furan-2(5H)-one (2a) and 3-(4-bromobenzyl)-furan-2(5H)-one (2b) were treated with TBDMSOTf and converted into the corresponding tert-butyldimethyl-silylfuran ethers. These furans were further condensed with several aromatic aldehydes affording compounds 5-14 with general 3-benzyl-5-arylidene-furan-2(5H)-one structures in 31% to 98% yields. Such compounds are analogues of the naturally occurring nostoclide lactones, reported to present moderate cytotoxic activity. Compounds 5-14 were submitted to an in vitro bioassay against the HL-60, HCT-8, SF295 and MDA-MB-435 cancer cell lines using the MTT cytotoxicity assay.     

Understanding solvation in hydrofluoroalkanes: ab initio calculations and chemical force microscopy

Understanding solvation in hydrofluoroalkane (HFA) propellants is of great importance for the development of novel pressurized metered-dose inhaler (pMDI) formulations. HFA-based pMDIs are not only the most widely used inhalation therapy devices for treating lung diseases, but they also hold promise as vehicles for the systemic delivery of biomolecules to and through the lungs. In this work we propose a combined microscopic experimental and computational approach to quantitatively relate the chemistry of moieties to their HFA-philicity. Binding energy calculations are used to determine the degree of interaction between a propellant HFA and candidate fragments. We define a new quantity, the enhancement factor E, which also takes into account fragment-fragment interactions. This quantity is expected to correlate well with the solubility and the ability of the moieties of interest to impart stability to colloidal dispersions in HFAs. We use a methyl-based (CH) segment and its fluorinated analog (CF) to test our approach. CH is an important baseline case since it represents the tails of surfactants in FDA-approved pMDIs. CF was chosen due to the improved solubility and ability of this chemistry to stabilize aqueous dispersions in HFAs. Adhesion force from Chemical Force Microscopy (CFM) is used as an experimental analog to the binding energy calculations. The force of interaction between a chemically modified AFM tip and substrate is measured in a model HFA, which is a liquid at ambient conditions. Silanes with the same chemistry as the fragments used in the ab initio calculations allow for direct comparison between the two techniques. The CFM results provide an absolute scale for HFA-philicity. Single molecule (pair) forces calculated from the CFM experiments are shown to be in very good agreement to the E determined from the ab initio calculations. The ab initio calculations and CFM are corroborated by previous experimental studies where propellants HFAs are seen to better solvate the CF functionality.     

Comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry of monoterpenoids as a powerful tool for grape origin traceability

The establishment of the monoterpenoid profile of Vitis vinifera L. cv. 'Fern?o-Pires' white grape was achieved by headspace solid-phase microextraction coupled with comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GCxGC-ToF-MS). The plot of the first dimension versus the second dimension retention times using the m/z 93, 121, and 136 was used. The grapes were found to contain 56 monoterpenoids identified by GCxGC-ToF-MS. From these, 20 were reported for the first time in grapes. According to their chemical structure, the compounds were organized in different groups: monoterpene hydrocarbons and monoterpene oxygen-containing compounds, this later divided in oxides, alcohols (monoterpenols and monoterpendiols), aldehydes, esters, and ketones. A database composed by the retention indices of monoterpenoids calculated in the bi-dimensional column set was created, representing a developmental step in monoterpenoid analysis using a GCxGC system. Remarkable results were also obtained in terms of compound classification based on the organized structure of the peaks of structurally related compounds in the GCxGC contour plot. This information represents a valuable approach for future studies, as the ordered-structure principle can considerably help the establishment of the composition of samples. This study proposes a methodology and provides data that can be applied to determine the monoterpenoid profile of grapes, and its extension to the analysis of musts, and wines. As monoterpenoids are secondary metabolites whose synthesis is encoded by variety-related genes, the terpenoid profile may be used as a way to trace its varietal origin.