In this paper a condition is presented on parameters (n1, n2,Λk), for arbitrary partition n = {n1, n2} (n1 ≤ n2) and k = 1, ..., n−1, which guarantees that two different interpretations of characters of fundamental modules L(Λk) for the affine Kac-Moody Lie algebra ŝln generate extended classical Gauss series-product identities.

Let n = 2λm ≥ 526 with m ∈ {2, 3, 5, 7, 11}, and let S be a sequence of elements in Cn⊕Cn with |S| = n2 +2n−2. Let N 0 (S) denote the number of the subsequences with length n2(=|G|) and with sum zero. Among other results, we prove that either N 0 (S) = 1 or N |G| 0 (S) ≥ n2 + 1.

Rhizobium sp. strain ORS571 conducts synergistic, free-living N2 fixation and nicotinate oxidation. Explicitly, ORS571 is able to fix N2 aerobically because 6-OH-nicotinate acts as an intracellular O2 sink. Because 6-OH-nicotinate oxidation is mandatory for aerobic, free-living N2 fixation and because the synergistic processes yield ammonium from substrates (as the nitrogen source for growth), ...

LetKn1,n2,...,np denote the complete p-partite graph, p > 1, on n = n1+n2+ · · ·+np vertices and let n1 ≥ n2 ≥ · · · ≥ np > 0. We show that for a fixed value of n, both the spectral radius and the energy of complete p-partite graphs are minimal for complete split graph CS(n, p− 1) and are maximal for Turán graph T (n, p).

We report an unusual operating regime for a chabazite zeolite in which the adsorption selectivity for N2 over CH4 inverts from being more selective for N2 at 253 K, to becoming less selective with increasing temperature and eventually becoming selective for CH4 over N2 above 293 K.

In this research, a Brønsted acidic ionic liquid namely N1,N1,N2,N2-tetramethyl-N1,N2-bis(sulfo)ethane-1,2-diaminium chloride {[TMBSED][Cl]2} was employed as a highly efficient catalyst for the solvent-free production of some nitrogen- and oxygen-containing heterocyclic compounds including: (i) polyhydroquinolines (from arylaldehydes, dimedone, β-ketoesters and ammonium acetate), (ii) 3,4-dihyd...