The hyperbolic geometry of continued fractions <b>K</b>(1|<i>b_n</i>)

The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fraction K(1|bn) diverges. H. S. Wall asks whether just convergence, rather than absolute convergence of ∑bn is sufficient for the divergence of K(1|bn). We investigate the relationship between ∑|bn| and K(1|bn) with hyperbolic geometry and use this geometry to construct a sequence bn of real numbers for which both ∑|bn| and K(1|bn) converge, thereby answering Wall's question

Anisotropic Dielectric Breakdown Strength of Single Crystal Hexagonal Boron Nitride

Dielectric breakdown has historically been of great interest from the perspectives of fundamental physics and electrical reliability. However, to date, the anisotropy in the dielectric breakdown has not been discussed. Here, we report an anisotropic dielectric breakdown strength (EBD) for h-BN, which is used as an ideal substrate for two-dimensional (2D) material devices. Under a well-controlled relative humidity, EBD values in the directions both normal and parallel to the c axis (EBD+c & EBD//c) were measured to be 3 and 12 MV/cm, respectively. When the crystal structure is changed from sp3 of cubic-BN (c-BN) to sp2 of h-BN, EBD+c for h-BN becomes smaller than that for c-BN, while EBD//c for h-BN drastically increases. Therefore, h-BN can possess a relatively high EBD concentrated only in the direction parallel to the c axis by conceding a weak bonding direction in the highly anisotropic crystal structure. This explains why the EBD//c for h-BN is higher than that for diamond. Moreover, the presented EBD value obtained from the high quality bulk h-BN crystal can be regarded as the standard for qualifying the crystallinity of h-BN layers grown via chemical vapor deposition for future electronic applications

Optical Properties of BN in the cubic and in the layered hexagonal phases

Linear optical functions of cubic and hexagonal BN have been studied within first principles DFT-LDA theory. Calculated energy-loss functions compare well with experiments and previous theoretical results both for h-BN and for c-BN. Discrepancies arise between theoretical results and experiments in the imaginary part of the dielectric function for c-BN. Possible explanation to this mismatch are proposed and evaluated; lattice constant variations, h-BN contamination in c-BN samples and self-energy effects.Comment: RevTex 42 pages, 16 postscript figures embedde

BN domains included into carbon nanotubes: role of interface

We present a density functional theory study on the shape and arrangement of small BN domains embedded into single-walled carbon nanotubes. We show a strong tendency for the BN hexagons formation at the simultaneous inclusion of B and N atoms within the walls of carbon nanotubes. The work emphasizes the importance of a correct description of the BN-C frontier. We suggest that BN-C interface will be formed preferentially with the participation of N-C bonds. Thus, we propose a new way of stabilizing the small BN inclusions through the formation of nitrogen terminated borders. The comparison between the obtained results and the available experimental data on formation of BN plackets within the single walled carbon nanotubes is presented. The mirror situation of inclusion of carbon plackets within single walled BN nanotubes is considered within the proposed formalism. Finally, we show that the inclusion of small BN plackets inside the CNTs strongly affects the electronic character of the initial systems, opening a band gap. The nitrogen excess in the BN plackets introduces donor states in the band gap and it might thus result in a promising way for n-doping single walled carbon nanotubes

The languages of peace during the French religious wars

The desirability of peace was a common topos in sixteenth-century political rhetoric, and the duty of the king to uphold the peace for the benefit of his subjects was also a long-established tradition. However, the peculiar circumstances of the French religious wars, and the preferred royal policy of pacification, galvanized impassioned debate among both those who supported and those who opposed confessional coexistence. This article looks at the diverse ways in which peace was viewed during the religious wars through an exploration of language and context. It draws not only on the pronouncements of the crown and its officials, and of poets and jurists, but also on those of local communities and confessional groups. Opinion was not just divided along religious lines; political imperatives, philosophical positions and local conditions all came into play in the arguments deployed. The variegated languages of peace provide a social and cultural dimension for the contested nature of sixteenth-century French politics. However, they could not restore harmony to a war-torn and divided kingdom

van der Waals epitaxy of monolayer hexagonal boron nitride on copper foil : growth, crystallography and electronic band structure

We investigate the growth of hexagonal boron nitride (h-BN) on copper foil by low pressure chemical vapour deposition (LP-CVD). At low pressure, h-BN growth proceeds through the nucleation and growth of triangular islands. Comparison between the orientation of the islands and the local crystallographic orientation of the polycrystalline copper foil reveals an epitaxial relation between the copper and h-BN, even on Cu(100) and Cu(110) regions whose symmetry is not matched to the h-BN. However, the growth rate is faster and the islands more uniformly oriented on Cu(111) grains. Angle resolved photoemission spectroscopy measurements reveal a well-defined band structure for the h-BN, consistent with a band gap of 6 eV, that is decoupled from the copper surface beneath. These results indicate that, despite a weak interaction between h-BN and copper, van der Waals epitaxy defines the long range ordering of h-BN even on polycrystalline copper foils and suggest that large area, single crystal, monolayer h-BN could be readily and cheaply produced