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.     

Alkylation/elimination from azetidinium ylides: an entry to functionalized acrylonitriles

Azetidinium triflates were reacted in a one-pot two-steps sequence involving, generation of an azetidinium ylide, its alkylation with an halide, and final regioselective Hofmann elimination of the produced alkylated azetidinium ion to yield substituted α,β-unsaturated nitriles bearing an aminoethyl side-chain. The scope of this sequence was examined, and was found to depend both on the steric hindrance around the reactive center in the starting azetidinium salt, and on the nature of the reacting halide. Produced acrylonitriles were further used in DBU-catalyzed conjugate addition of amines, to yield 4-amino-2-aminomethyl-butyronitriles with fair diastereoselectivity, or, alternatively, to give C₂ symmetrical cyclopropanes.     

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.     

Fluorimetric Determination of Histamine in Fish Using Micellar Media and Fluorescamine as Labelling Reagent

An analytical method based on the use of fluorescamine to produce a fluorescent derivative with histamine and combined with micellar-enhanced fluorescence detection of the formed complex is developed for the sensitive and rapid determination of histamine in fishes. The fluorescence properties of the obtained complex in water and micellar solutions of sodium dodecyl sulfate (SDS), cetyltrimethylammonium chloride (CTAC) and brij-700 are reported. Physicochemical variables influencing the sensitivity of the method (pH, micellar, fluorescamine and NaCl relative concentrations) have been optimized. The stability of the formed complex, as shown by kinetic study, depends on the pH of the solution. Linear calibration curves allowing an effective histamine determination were established with large linear dynamic range (LDR), and low limits of detection (LOD) between 0.5 and 33 ng mL⁻¹, according to the solvent. Application to the analysis of fish samples (sardines) yielded satisfactory results. The method seems to be suitable for environmental fish quality control. Presented in part, at the 39th IUPAC Congress and the 86th Conference of the Canadian Society for Chemistry, August, 10–15, 2003, Ottawa (Canada).     

A serendipitous conversion of enaminolactone nitriles with primary amines: a new synthesis of substituted 2-aminopyridine derivatives

In the course of our studies on Cerpegin analogues synthesis, a serendipitous reactivity of enaminolactone nitrile has been observed. Instead of expecting iminocerpegins, we have gained new class of substituted 2-aminopyridines. The methodology has been applied on a wide range of primary amines, as aliphatic, aromatic, heteroaromatic and also, diamines, hydrazines and chiral amines.     

An efficient route to a 5,6-dihydropyrano[3,4-b]pyridin-8-one core in two steps from enaminolactones

A convenient two step conversion of heterocyclic enaminolactones to heterocyclic fused 2-pyran-1-ones is reported. The use of this method can be applied to a wide variety of aromatic and heteroaromatic amines to give potentially biologically active compounds in good yields.     

Erasure Decoding for Gabidulin Codes

We present a new approach of the decoding algorithm for Gabidulin Codes. In the same way as efficient erasure decoding for Generalized Reed Solomon codes by using the structure of the inverse of the VanderMonde matrices, we show that, the erasure(t erasures mean that t components of a code vector are erased) decoding Gabidulin code can be seen as a computation of three matrice and an affine permutation, instead of computing an inverse from the generator or parity check matrix. This significantly reduces the decoding complexity compared to others algorithms. For t erasures with t ≤ r, where r = n − k, the erasure algorithm decoding for Gab _{n, k} (g) Gabidulin code compute the t symbols by simple multiplication of three matrices. That requires rt + r(k − 1) Galois field multiplications, t(r − 1) + (t + r)k field additions, r ² + r(k + 1) field negations and t(k + 1) field inversions.