Recent findings revealed that the commonly used (15)N2 tracer assay for the determination of dinitrogen (N2) fixation can underestimate the activity of aquatic N2-fixing organisms. Therefore, a modification to the method using pre-prepared (15-15)N2-enriched water was proposed. Here, we present a rigorous assessment and outline a simple procedure for the preparation of (15-15)N2-enriched water....

This report establishes that trigonally coordinated "[PhBPiPr3]M" platforms (M = Fe, Co) will support both pi-acidic (N2) and pi-basic (NR) ligands at a fourth binding site. The N2 complexes of iron that are described are the first thoroughly characterized examples to exhibit a 4-coordinate geometry. Methylation of monomeric {Fe0(N2)-} and {Co0(N2)-} species successfully derivatizes the beta-N ...

Let F (m; n1, n2) denote the number of lattice walks from (0, 0) to (n1, n2), always staying in the first quadrant {(n1, n2); n1 ≥ 0, n2 ≥ 0} and having exactly m steps, each of which belongs to the set {E = (1, 0),W = (−1, 0), NE = (1, 1), SW = (−1,−1)}. Ira Gessel conjectured that F (2n; 0, 0) = 16 (1/2)n(5/6)n (2)n(5/3)n . We pose similar conjectures for some other values of (n1, n2), and gi...

Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 G2 of G1 and G2. We show that: τ(G1 G2) ≥ 2(n1−1)(n2−1) n1n2 (τ(G1)n1) n2+1 2 (τ(G2)n2) n1+1 2 and τ(G1 G2) ≤ τ(G1)τ(G2) [ 2m1 n1 − 1 + 2m2 n2 − 1 ](n1−1)(n2−1) . We also characteri...