Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Algebraic topological methods for the supercritical Q-curvature problem

We study the problem of existence of conformal metrics with prescribed Q-curvature on closed four-dimensional Riemannian manifolds. This problem has a variational structure, and in the case of interest here, it is noncompact in the sense that accumulations points of some noncompact flow lines of a pseudogradient of the associated Euler–Lagrange functional, the so-called true critical points at infinity of the associated variational problem, occur. Using the characterization of the critical points at infinity of the associated variational problem which is established in [42], combined with some arguments from Morse theory, some algebraic topological methods, and some tools from dynamical system originating from Conley's isolated invariant sets and isolated blocks theory, we derive a new kind of existence results under an algebraic topological hypothesis involving the topology of the underling manifold, stable and unstable manifolds of some of the critical points at infinity of the associated Euler–Lagrange functional.     

A Combined Experimental and Computational Study of Chrysanthemin as a Pigment for Dye-Sensitized Solar Cells

The theoretical study of chrysanthemin (cyanidin 3-glucoside) as a pigment for TiO₂-based dye-sensitized solar cells (DSSCs) was performed with the GAUSSSIAN 09 simulation. The electronic spectra of neutral and anionic chrysanthemin molecules were calculated by density functional theory with B3LYP functional and DGDZVP basis set. A better energy level alignment was found for partially deprotonated molecules of chrysanthemin, with the excited photoelectron having enough energy in order to be transferred to the conduction band of TiO₂ semiconductor in DSSCs. In addition, we used the raw aqueous extracts of roselle (Hibiscus sabdariffa) calyces as the source of chrysanthemin and the extracts with various pH values were tested in DSSCs. The extracts and photosensitized semiconductor layers were characterized by UV-Vis spectroscopy, and DSSCs based on raw extracts were characterized by current density-voltage measurements.     

Unprecedented Kinetic Inertness for a Mn2+‐Bispidine Chelate: A Novel Structural Entry for Mn2+‐Based Imaging Agents

The search for more biocompatible alternatives to Gd³⁺‐based MRI agents, and the interest in ⁵²Mn for PET imaging call for ligands that form inert Mn²⁺ chelates. Given the labile nature of Mn²⁺, high inertness is challenging to achieve. The strongly preorganized structure of the 2,4‐pyridyl‐disubstituted bispidol ligand L₁ endows its Mn²⁺ complex with exceptional kinetic inertness. Indeed, MnL₁ did not show any dissociation for 140 days in the presence of 50 equiv. of Zn²⁺ (37 °C, pH 6), while recently reported potential MRI agents MnPyC3A and MnPC2A‐EA have dissociation half‐lives of 0.285 h and 54.4 h under similar conditions. In addition, the relaxivity of MnL₁ (4.28 mm ^?1 s^?1 at 25 °C, 20 MHz) is remarkable for a monohydrated, small Mn²⁺ chelate. In vivo MRI experiments in mice and determination of the tissue Mn content evidence rapid renal clearance of MnL₁. Additionally, L₁ could be radiolabeled with ⁵²Mn and the complex revealed good stability in biological media.     

Noise waveforms with repetitive phase and nonrepetitive amplitude

By use of frequency-shifted feedback lasers, noise with a stationary amplitude and a periodically stationary phase is generated. The ensemble-averaged time correlation function is periodic, whereas the power spectrum is broadband, resulting in a waveform that does not obey the Wiener-Khintchine relations. An application to multiple-access communications is discussed.     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.     

Phase behavior of (CO2 + methanol + lauric acid) system

In this study the phase equilibrium behaviors of the binary system (CO₂ + lauric acid) and the ternary system (CO₂ + methanol + lauric acid) were determined. The static synthetic method, using a variable-volume view cell, was employed to obtain the experimental data in the temperature range of (293 to 343) K and pressures up to 24 MPa. The mole fractions of carbon dioxide were varied according to the systems as follows: (0.7524 to 0.9955) for the binary system (CO₂ + lauric acid); (0.4616 to 0.9895) for the ternary system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (2:1); and (0.3414 to 0.9182) for the system (CO₂ + methanol + lauric acid) with a methanol to lauric acid molar ratio of (6:1). For these systems (vapor + liquid), (liquid + liquid), (vapor + liquid + liquid), and (solid + fluid) transitions were observed. The phase equilibrium data obtained for the systems were modeled using the Peng–Robinson equation of state with the classical van der Waals mixing rule with a satisfactory correlation between experimental and calculated values.     

Regioselective remote CH fluoroalkylselenolation of 8-aminoquinolines

Herein, the direct C-5 fluoroalkylselenolation of 8-aminoquinolines is described. The Pd-catalyzed reaction is performed with the in situ generated fluoroalkylselenyl chloride and various 8-aminoquinoline amides or sulfonamides. The desired products were formed in moderate to excellent yields.     

Syntheses, structures, and photophysical properties of mono- and dinuclear sulfur-rich gold(I) complexes

The dinuclear gold complexes [{Au(PPh 3)} 2(mu- dmid)] ( 1) ( dmid = 1,3-dithiole-2-one-4,5-dithiolate) and [{Au(PPh 3)} 2(mu- dddt)] ( 2) ( dddt = 5,6-dihydro-1,4-dithiine-2,3-dithiolate) were synthesized and characterized by X-ray crystallography. Both complexes exhibit intramolecular aurophilic interactions with Au...Au distances of 3.1984(10) A for 1 and 3.1295(11) A for 2. A self-assembly reaction between 4,5-bis(2-hydroxyethylthio)-1,3-dithiole-2-thione ( (HOCH 2 CH 2 ) 2 dmit) and [AuCl(tht)] affords the complex [AuCl{ (HOCH 2 CH 2 ) 2 dmit}] 2 ( 4), which possesses an antiparallel dimeric arrangement resulting from a short aurophilic contact of 3.078(6) A. This motif is extended into two dimensions due to intra- and intermolecular hydrogen bonds via the hydroxyethyl groups, giving rise to a supramolecular network. Three compounds were investigated for their rich photophysical properties at 298 and 77 K in 2-MeTHF and in the solid state; [Au 2(mu- dmid)(PPh 3) 2] ( 1), [Au 2(mu- dddt)(PPh 3) 2] ( 2), and [AuCl{( HOCH 2 CH 2 ) 2 dmit}] ( 4). 1 exhibits relatively long-lived LMCT (ligand-to-metal charge transfer) emissions at 298 K in solution (370 nm; tau e approximately 17 ns, where M is a single gold not interacting with the other gold atom; i.e., the fluxional C-SAuPPh 3 units are away from each other) and in the solid state (410 nm; tau e approximately 70 mus). At 77 K, a new emission band is observed at 685 nm (tau e = 132 mus) and assigned to a LMCT emission where M is representative for two gold atoms interacting together consistent with the presence of Au...Au contacts as found in the crystal structure. In solution at 77 K, the LMCT emission is also red-shifted to 550 nm (tau e approximately 139 mus). It is believed to be associated to a given rotamer. 2 also exhibits LMCT emissions at 380 nm at 298 K in solution and at 470 nm in the solid state. 4 exhibits X/MLCT emission (halide/metal to ligand charge transfer) where M is a dimer in the solid state with obvious Au...Au interactions, resulting in red-shifted emission band, and is a monomer in solution in the 10 (-5) M concentration (i.e., no Au...Au interactions) resulting in blue-shifted luminescence. Both fluorescence and phosphorescence are observed for 4.