Our basic question: Restricting to covers of the sphere by a compact Riemann surface of a given type, do all such compose one connected family? Or failing that, do they fall into easily discerned components? The answer has often been “Yes!,” figuring in such topics as the connectedness of the moduli space of curves of genus g (geometry), Davenport’s problem (arithmetic) and the genus 0 problem ...

Nowadays NMR spectroscopy becomes a powerful tool in chemistry because of the NMR chemical shifts. Hartree–Fock theory and the Gauge-including atomic orbital (GIAO) methods are used in the calculation of 29Si NMR chemical shifts of various silicate species in the silicate solution as initial components for zeolite synthesis both in gas and solution phase. Calculations have been performed at geo...

We analyze the collective light scattering by cold atoms in free space of a pump-laser beam possessing orbital angular momentum. derive set coupled multiparticle equations for atomic motion which vacuum-mode field is adiabatically eliminated. The resulting describe recoil as due to either transfer linear momentum or For transverse annular distribution initial equilibrium with uniform phases and...

There are four fundamental atomic particles-the proton, the neutron, the electron, and the positron. The proton has mass and a unit positive electrical charge. The neutron has mass and no charge. The electron has very small mass compared with the proton and neutron, and has unit negative electrical charge. The positron is the positively charged counterpart of the electron, having equal mass and...

Density functional theory calculations (DFT), as well as hybrid methods (B3LYP) for Bi8N18-[CoF6]3- complexhave been carried out to study the non-bonded interaction. The geometry of the 1313N18 has been optimized atB3LYP method with EPR-II basis set and geometry of the [CoF6]3 have been optimized at B3LYP method withDe12-TZVP basis set and Stuttgart RSC 1997 Effective Core Potential. The electr...

Hyperfine interaction (HF) is of key importance for the functionality of solid-state quantum information processing, as it affects qubit coherence and enables nuclear-spin quantum memories. In this work, we complete the theory of the basic HF mechanisms (Fermi contact, dipolar, orbital) in carbon nanotube quantum dots by providing a theoretical description of the orbital HF. We find that orbita...