A finiteness theorem for a class of exponential congruences

For given elements and belonging to the ring of integers of a number field we consider the set of all tuples in for which divides for any and prove under some reasonable assumptions that the set of solutions is finite.

     

Discrepancy of Fractions with Divisibility Constraints

We provide bounds for the absolute discrepancy of sequences of fractions with denominators streaming in a given arithmetic progression and satisfying divisibility constraints. Supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.     

On a separation criterion for cohomology groups of (q, n - q)-coronae

We give a separation theorem for (q, n - q)-coronas improving a recent result due to Laurent-Thiébaut and Leiterer.     

Cohomological q-convexity versus local q-completeness with corners

We show that if (D, π) is an unramified Riemann domain over a distinguished complex manifold X such that D is cohomologically q-convex, then π is locally q-complete with corners. We call X distinguished if for every point x of X there is a holomorphic line bundle $\cal L$ on X (which may depend on x) so that the global sections $\Gamma (X \cal L)$ of $\cal L$ generate its 1-jets at x. Examples of distinguished complex manifolds include all complex submanifolds of C^m × Pⁿ; in particular all Stein or projectively algebraic manifolds.     

Intermolecular interactions in nitrogen-containing aromatic systems

π–π and CH···N interactions are vital in biological systems. In this study, stacking and hydrogen-bonded interactions in pyrazine and triazine dimers were investigated by density functional theory combined with symmetry-adapted perturbation theory (DFT-SAPT) and counterpoise (CP)-corrected supermolecular MP2, SCS-MP2, B3LYP-D and CCSD(T) calculations. All interaction energies were computed using the optimized structures at the CP-corrected SCS/aug-cc-pVDZ level, which gave 1–2 kJ/mol lower interaction energies than the ones computed at the MP2 level. For both dimers, doubly hydrogen-bonded and cross-(displaced) stacked orientations were found to be the lowest energy ones. The reference CCSD(T) calculations favored the former structure in both dimer systems, whereas MP2 and SCS-MP2 located the latter as the lowest energy isomer. In particular, the former was found to be lower in energy than the latter by 2.28 and 1.01 kJ/mol at the CCSD(T)/aug-cc-pVDZ level for pyrazine and triazine, respectively. B3LYP-D produced interaction energies in agreement with the CCSD(T) at the equilibrium geometries, but it overestimates them at the short range and underestimates at the long intermonomer separations. Furthermore, it tends to give smaller equilibrium distances compared to the CCSD(T). DFT-SAPT method was in a good agreement with the reference CCSD(T) calculations. This suggests that DFT-SAPT can be employed to compute the full potential energy surface of these dimers. Moreover, DFT-SAPT calculations showed that the electrostatic and dispersion contributions are the most important energy components stabilizing these dimers. The present study aims to show which theoretical method is the most promising one for the investigation of intermolecular interactions dominated by π–π and CH···N. Therefore, the findings obtained in this study can be used to unravel the structures of nucleic acid bases and other systems stabilized by π–π and CH···N interactions.