A bstract In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent shift, the n -point N k MHV tree-level amplitude in $$ \mathcal{N} N = 4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding canonical “dlog” forms on ce...

Abstract It is known that if G a group such the centre factor $$G/\zeta (G)$$ G / ζ ( ) polycyclic, then also commutator subgroup $$G'$$ ′ polycyclic. The aim of this paper to des...

Based on theoretical spectra computed using Density Functional Theory we study the properties of Polycyclic Aromatic Hydrocarbons (PAH). In particular bin-average PAH molecules with varying number carbons investigate how intensity mid-infrared emission bands, 3.3, 6.2, 7.7 and 11.3 microns, respond to changes in carbons, charge molecule, hardness radiation field that impinges molecule. We confi...

Abstract Most approaches to 3D printing at various scales are layer based, meaning they start with a CAD model that is sliced into planar print paths be translated machine code. However, this approach entails number of drawbacks, such as slow speeds, limited build volumes, allowable geometric properties, and material diversity. To overcome these limitations, the authors have developed novel add...