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.     

Theoretical study of the <Superscript>1,3</Superscript>Σ<Superscript>+</Superscript> states of the NaH molecule in the adiabatic and diabatic representations

Adiabatic and diabatic study for all the states dissociating below the ionic limit [i.e., Na (3s, 3p, 4s, 3d, 4p, 5s, 4d, and 4f) + H (1s)] in ¹Σ⁺ and ³Σ⁺ symmetries are presented. Adiabatic results are also reported for ^1,3Π and ^1,3Δ symmetries. Pseudo-potential, operatorial core-valence correlation, and full valence CI approaches combined with an efficient diabatization procedure are used in these ab initio calculations. Our vibrational-level spacings and spectroscopic constants are in good agreement with the available experimental data for the low-lying states. Diabatic potentials and dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The hydrogen electron affinity correction was taken into account by the use of the efficient diabatization method. This leads to a better agreement with the available experimental data. Experimental suggestions are also given for the higher excited states based on their unusual behavior.     

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.     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

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.     

Crystal structure and electrical properties study of 4-aminopyridinium chloridobismuthate (III) (C5N2H7)4.HBi2Cl11

The crystal structure of (C₅N₂H₇)₄.HBi₂Cl₁₁ has been determined at room temperature by single crystal X-ray diffraction. The compound crystallizes in the triclinic system with Pī space group. The crystal structure consists of two asymmetric inequivalent molecules of 4-aminopyridinium and anionic HBi₂Cl₁₁ chains. The HBi₂Cl₁₁ anionic chains stacked along the a-axis are formed with Bi₂Cl₁₁ dimers connected to each other via hydrogen atoms. The crystal packing is stabilized with N–H...Cl hydrogen bonds connecting aminopyridinium units to the HBi₂Cl₁₁ anionic chains. The title compound exhibits an order–disorder phase transition at 338 K. The AC electrical conductivity properties of (C₅N₂H₇)₄.HBi₂Cl₁₁ compound have been investigated by means of impedance spectroscopy measurements over wide ranges of frequencies and temperatures, 200 Hz to 5 MHz and 303 to 418 K, respectively. Detailed analysis of the impedance spectrum suggests that the electrical properties of the material are strongly temperature dependent. The frequency-dependent conductivity data were fitted in the Jonscher's law: $ \sigma \left( \omega \right) = \sigma (0) + A{\omega^n} $ . The nature of variation of DC conductivity suggests Arrhenius type of electrical conductivity.