Feature of the magnetotransport of a quasi-one-dimensional electrons on the superfluid helium

The magnetotransport in a nondegenerate quasi-one-dimensional (Q1D) electron system over superfluid helium has been investigated experimentally. The measurements are performed in the presence of a perpendicular magnetic field B up to 2.6 T in the temperature range T=0.48–2.05 K in the system of conducting channels of 100–400 nm width. It is shown that the value of longitudinal magnetoresistance ρ_xx increases with B. In the electron-gas scattering region (T>0.9 ), the behaviour of ρ_xx agrees with classical Drude law. In the quantum transport regime, the self-consistent Born approximation (SCBA) theory for a 2D electron system over liquid helium describes the experimental data qualitatively. The deviation due to the difference of the experimentally studied Q1D system of the electrons in a parabolic potential well differs from theoretically analysed one. The experimental data agree with the theoretical calculation for the Q1D electron system at the weak magnetic field and the low temperature.

The negative magnetoresistance of the conducting channels has been observed in both the gas- and the ripplon-scattering region. These effects have been explained by weak carrier localization on the gas atoms at high temperature and by display of the quantum magnetotransport features in a mesoscopic system at low temperature.     

Experimental and quantum chemical study of pyrrole self-association through N-H?π hydrogen bonding

An FT-IR study of pyrrole self-association in CCl₄ solutions was carried out. According to the IR measurements, pyrrole forms self-associated dimeric species via N-H?π hydrogen bonding. This was also confirmed by quantum chemical calculations for pyrrole monomer and dimer at B3LYP/6-31++G(d,p) level of theory. A T-shaped minimum was located on B3LYP/6-31++G(d,p) PES of pyrrole dimer characterized with a hydrogen bond of an N-H?π type, with centers-of-mass separation of monomeric units of 4.520 Å, H?π distance of 2.475 Å, the interplanar angle between the two monomeric units being 72.9°. The anharmonic vibrational frequency shift upon dimer formation calculated on the basis of 1D DFT vibrational potentials is in excellent agreement with the experimental data (84 vs. 87 cm⁻¹). Harmonic vibrational analysis predicts somewhat smaller shift (68 cm⁻¹). On the basis of NIR spectroscopic data, anharmonicity constants for the 2ν(N-H) and 2ν(N-H?π) vibrational transitions were calculated. The orientational dynamics of monomeric and self-associated pyrrole species was studied within the framework of the transition dipole moment time correlation function formalism. The period of essentially free rotation in the condensed phase reduces from 0.05 ps for the monomeric pyrrole to 0.02 ps for the proton-donor molecule within the dimer.     

Anomalous behavior of conductivity of the confined Q1D electron system over liquid helium

Conductivity of electrons in a quasi-one-dimensional (Q1D) system over liquid helium in narrow channels with the parabolic profile of the potential well has been investigated at temperature T, from 0.4 to 1.8 K, for different driving electric fields and radius of channel curvature. The interval of linear electron densities varied from 2.18×10³ up to 1.7×10⁶ cm⁻¹.

The inverse mobility (1/μ_eff) in the electron-ripplon scattering region at the high linear densities of charges in the channel increases with temperature decreasing. This anomalous behavior of the electron transport in the low-temperature region has been explained by either the electron ordering or the polaronic effects in confined conducting channels. The nonlinear behavior of the electron velocity as a function of a driving electric field is supposed to be due to Breg–Cherenkov radiation of the ripplons. The radiation occurred if the velocity of electrons in the channel approaches to the critical value.     

Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

4,5‐Di­hydro‐3‐methyl‐5‐(4‐methyl­phenyl)‐1H‐pyrazole‐1‐carboxamidinium acetate acetone hemisolvate

The X‐ray structure analysis of the unexpected product of the reaction between 4‐(4‐methyl­phenyl)­but‐3‐en‐2‐one and amino­guanidine revealed the title compound, C₁₂H₁₇N₄⁺·C₂H₃O₂^?·0.5C₃H₆O, consisting of a protonated amidine moiety joined to a substituted pyrazoline ring at the N1 atom. The amidine group is protonated and the positive charge is delocalized over the three C—N bonds in a similar manner to that found in guanidinium salts. The amidinium moiety of the cation is linked to the acetate anions through four N—H?O hydrogen bonds, with N?O distances of 2.749 (4), 2.848 (4), 2.904 (4) and 2.911 (4) Å. The pyrazoline ring adopts a flattened envelope conformation and the substituted phenyl ring is oriented perpendicular to the attached heterocycle. The acetone solvate molecule lies across a twofold rotation axis.     

1‐Methyl‐1H‐imidazo[4,5‐f]quinolin‐6‐ium chloride monohydrate

The title compound, C₁₁H₁₀N₃⁺·Cl^?·H₂O, belongs to the N1‐methyl‐substituted imidazo­[4,5‐f]­quinoline family, in which the heterocyclic ring is protonated at the pyridine rather than at the imidazole N atom. The mol­ecule as a whole is almost exactly planar. The molecular structure has been compared with that of the 2‐amino analogue described in the literature, and it was found that the extra amino group of the latter is involved in conjugation with the adjacent double bond, i.e. the conjugation does not extend over the entire heterocyclic system. The cation of the title compound forms a strong hydrogen bond with the Cl^? anion and the anions are interconnected by the water solvent mol­ecule.