On a generalization of Kelly''s combinatorial lemma

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Down and up conversion luminescence of the lead-free organic metal halide material: (C 9 H 8 NO) 2 SnCl 6 ·2H 2 O

International audienceThe present work deals with the optical properties of hybrid organic metal halide material namely (C9H8NO)2SnCl6.2H2O. Its structure is built up from isolated [SnCl6]2- octahedral dianions surrounded by Hydroxylquinolinium organic cations (C9H8NO)+, abbreviated as [HQ]+. Unlike the usual hybrid materials, where metal halide ions are luminescent semiconductors while the organic ones are optically inactive, [HQ]2SnCl6.2H2O contains two optically active entities: [HQ]+ organic cations and [SnCl6]2- dianions. The optical properties of the synthesized crystals were studied by optical absorption spectroscopy, photoluminescence measurements and DFT calculations of electronic density of states.These studies have shown that both organic and inorganic entities have very close HOMO-LUMO gaps and very similar band alignments favoring the resonant energy transfer process. In addition, measurements of luminescence under variable excitations reveal an intense green luminescence around 497 nm under UV excitation (down conversion) and infrared excitation (up conversion luminescence). The down conversion luminescence is assigned to the π-π* transition within the [HQ] + organic cations involving charge transfer between the organic and inorganic entities, whereas the up conversion luminescence is on based the triplet-triplet annihilation mechanism (TTA)

The (≤5)-hypomorphy of digraphs up to complementation

Two digraphs G=(V,E)and G′=(V,E′)are isomorphic up to complementation if G′is isomorphic to G or to the complement G¯≔(V,{(x,y)∈V2:x≠y,(x,y)∉E})of G. The Boolean sum G+̇G′is the symmetric digraph U=(V,E(U))defined by {x,y}∈E(U)if and only if (x,y)∈E and (x,y)∉E′, or (x,y)∉E and (x,y)∈E′. Let k be a nonnegative integer. The digraphs G and G′are (≤k)-hypomorphic up to complementation if for every t-element subset X of V, with t≤k, the induced subdigraphs G↾Xand G↾X′are isomorphic up to complementation. The digraphs G and G′are hereditarily isomorphic (resp. hereditarily isomorphic up to complementation) if for each subset X of V, the induced subdigraphs G↾Xand G↾X′are isomorphic (resp. isomorphic up to complementation). Here, we give the form of the pair {G,G′}whenever G and G′are two digraphs, (≤5)-hypomorphic up to complementation and such that the Boolean sum U≔G+̇G′and the complement U¯are both connected, and thus we deduce that G and G′are hereditarily isomorphic up to complementation; we prove also that the value 5 is optimal. The case U or U¯is not connected is studied in a forthcoming paper. Keywords: Digraph, Isomorphism, k-hypomorphy up to complementation, Hereditary isomorphy up to complementation, Boolean sum, Symmetric digraph, Tournament, Indecomposabilit

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