The Webster scalar curvature problem on the three dimensional CR manifolds

In this paper, we prove some existence results for the Webster scalar curvature problem on the three dimensional CR compact manifolds locally conformally CR equivalent to the unit sphere S³ of C². Our methods are based on the techniques related to the theory of critical points at infinity.     

Isolation and structure determination of a novel furanic ester from the aerial part of Prasium majus

The aerial part of Prasium majus provided a new furanic ester, 2-2-[(5-formyl-6[(5-formylfuran-2-yl)methoxy] succinic acid dimethyl ester, (+/-)-hiziprafuran. Its structure was principally established by one- and two-dimensional NMR spectroscopy.     

Self-adjointness of the perturbed wave operator on

We give classes of unbounded real-valued for which is self-adjoint on , , where is the wave operator defined on .

     

Structure-antibacterial activity relationship of secondary metabolites from Ajuga pseudoiva Rob. leaves

A selection of steroids, glycerides, clerodane diterpenoids, and a beta-hydroxy fatty acid methyl ester, all previously isolated from Ajuga pseudoiva leaves, were tested for their antibacterial activity toward three Gram- rods and one Gram+ coccus using the dilution method; MIC values were determined. The results suggested some importance for a free beta-hydroxy group in the fatty acid ester and also in the glycerides and clerodane derivatives; the absolute configurations of the latter, notably at C2, had little influence on activity.     

Echiofruzine, a novel naringenin diglycoside from Echiochilon fruticosum growing in Tunisia

The aerial parts of the Tunisian plant Echiochilon fruticosum yielded a novel flavonol diglycoside: naringenin-5-O-beta-D-glycopyranoside-3-O-alpha-L-rhamnopyranoside, named Echiofruzine (1), together with the known compounds vomifoliol-9-O-beta-D-glucopyraroside (2), 1-oxo-alpha-ionyl-9-O-beta-D-glucopyranoside (3) and 1-O-[beta-D-xylopyranosyl(1 --> 6)-beta-D-glucopyranosyl] eugenol (4), described for the first time in the indicated plant. The structures of the four isolated compounds were established on the basis of chemical and spectroscopic evidence.     

Multiple Solutions for a Class of Nonhomogeneous Fractional Schrödinger Equations in $$\mathbb {R}^{N}$$

This paper is concerned with the following fractional Schrödinger equation

$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$

where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.

     

Non-isothermal model-free predictions

Suitable thermal treatment of metal organic precursors is a key process to obtain oxide films. To this purpose, non-isothermal model-free predictions are specially suited. In this article we will explore the ability of these methods to provide an accurate prediction of the evolution of the decomposition of yttrium trifluoroacetate, a precursor used in the synthesis of YBaCuO superconducting thin-films. A good agreement has been obtained between the predicted and the measured reaction courses.