Compared to the 0%S, the 25%S and 50%S treatments had a significantly higher SOC lability (L), lability index (LI), C pool index (CPI) and CPMI at a 0 21 cm soil depth.
One can easily show that γ(m LI,μ LI C) goes to γ(m LI,m LI (η+1)) for P S,P R →∞ where (eta = {bar {gamma }_{SR}}/bar {gamma }_{LI}).
With these notations we have: w ¯ jk n + 1 = w ¯ jk n + 2 μ ∑ i, m M, N h ji c km K i a ¯ km, b ¯ km − ∑ l, m, i M, N, N w ¯ jl c ¯ li c ¯ km F lk a ¯ li, b ¯ li, a ¯ km, b ¯ km (66).
Using the notations of Section 4.1, we have: E e j 2 n = σ 0 2 + ∑ i, l M h ji h jl G il − 2 ∑ i, k M h ji w jk ∑ m = 1 N c km K i a km, b km + ∑ k, l M ∑ i, m N w jl w jk c li c km F lk a li, b li, a km, b km (89).
Which can be expressed as: E e j 2 n = σ 0 2 + ∑ i, l M h ji h jl E g i x i n g l x l n − 2 ∑ i, k M h ji n w jk ∑ m = 1 N c km E g i x i n f a km x k n + b km + ∑ k, l M ∑ i, m N w jl w jk c li c ki E f a li x l n + b li f a km x k n + b km (88).
Using the scalar notation we have: w ¯ jk n + 1 = w ¯ jk n + 2 μ E ∑ i = 1 M h ji g i x i n − ∑ l = 1 M w jl N N l n ) × ∑ m = 1 N c km f a km x k n + b km ≈ w ¯ jk n + 2 μ ∑ i, m M, N h ji c ¯ km E g i x i n f a ¯ km x k n + b ¯ km − ∑ l, m, i M, N, N w ¯ jl c ¯ li c ¯ km E f a ¯ li x l n + b ¯ li f a ¯ km x k n + b ¯ km (65).
Certainly, if a well-studied species is not classified as a hyperaccumulator of given mineral elements and is not collected from a polluted or geoanomalous site, a high load of element in its fruit body (example is Se, Hg, Fe, Cr, Co, Li, Cd, V, Ni, Ba, Sr, Zr) is not expected.
In several articles (old and new) on trace minerals in mushrooms, unreliable data were published on elements (Se, Hg, Fe, Co, Cr, V, Ni, Rb, Ba, Cs, Sr, U, Zr and on the rare earth elements such as Ga, Nb, Ce, Th, Nd, and also Li, Cd, and Pb) sequestered in fruit bodies.
While many elements were significantly correlated within each of the five experiments, only three pairs of elements were correlated in every population×environment we analyzed: Li-Na, Mg-Ca, and Cu-Zn, although Li-As, Li-Cd, Li-K, Li-Zn, P-Fe, Mg-Zn and Zn-Cd were found in 4 of the 5 experiments (Figure 1).
In particular, the effects of Li-ion binding energy on the Li-Li, Li-H, and Li-C pair distribution functions are revealed, along with the effect on charge distribution.
A similar linear variation has also been observed in Zn-Mg [20, 21], Li-Mg [22], Zn-Mg-Cu [23], and Li-Cd [24] ferrites.
