We consider some problems in number theory which turn out to depend on various aspects of Kummer theory; among them are (1) does the assertion “b is in the subgroup generated by a” obey a local-global principle for points of an algebraic group over a number field; (2) if two abelian varieties have the same n-division fields for n > 1, what relation is there between them?

Using density functional theory, the G0W0 method and Bethe-Salpeter equation calculations, we systematically explore the structural, electronic and optical properties of hydrogenated and fluorinated germanene. The hydrogenated/fluorinated germanene tends to form chair and zigzag-line configurations and its electronic and optical properties show close geometry dependence. The chair hydrogenated/...

during recent years, a series of climate projections provided for surface temperature increase and precipitation changes over the next century in various time slices. national institutes are using downscaling projections for more precise results. in this research study, various climate change projections in global, continental, regional and local scales have been examined in special forest ecos...

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop ...

Gradient-corrected density functional theory (DFT) computations were performed to investigate the geometry, electronic property, formation energy, and reactivity of Stone-Wales (SW) defects in zigzag-edge and armchair-edge boron nitride nanoribbons (BNNRs). The formation energies of SW defects increase with an increase in the widths of BNNRs and are orientation-dependent. SW defects considerabl...

The flexibility of the bonds between adjacent layers multi-layered systems and their degradation or presence delaminations strongly affect mechanical response final collapse. formulation accurate efficient models able to capture complex local distributions stresses displacements, which arise due layered structure imperfect bonding, is great importance for design verification systems. In this pa...

By applying the nonequilibrium Green's functions and the density-functional theory, we investigate the electronic structures and transport properties of fluorinated zigzag-edged boron nitride nanoribbons. The results show that the transition between half-metal and semiconductor in zigzag-edged boron nitride nanoribbons can be realized by fluorination at different sites or by the change of the f...