By Levit G.S.

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**Additional info for Biogeochemistry - Biosphere - Noosphere. The theory of V.I. Vernadsky**

**Example text**

2000]. Ø Ø Ø Ø Ø Ø AMSP Autocorrelation of Molecular Surface Properties ! autocorrelation descriptors Andrews curves ! molecular descriptors ( transformations of molecular descriptors) Andrews descriptors ! count descriptors angular distance ! similarity/diversity angular separation ! similarity/diversity ( Table S7) aN-index ! determinant-based descriptors ( general aN-index) j17 j anisometry 18 Ø Ø Ø Ø Ø anisometry ! shape descriptors anisotropy of the polarizability ! electric polarization descriptors Ant Colony ﬁtness function !

The immanant, denoted by dl(M), is deﬁned as X c ðpÞm1; i1 Á m2; i2 Á . . Á mn; in dl ðMÞ ¼ p l where p runs over the n! permutations. cl(p) is an irreducible character of the symmetric group indexed by a partition l of n. The pfafﬁan, denoted by pfa(M), and the hafnian, denoted by haf(M), are analogous to the determinant except for the summation that goes over all the permutations p (i1, i2, . , in) and must also satisfy the limitations i1 < i2 ; i3 < i4 ; . . ; inÀ1 < in ; i1 < i3 < i5 < . .

1988], algebraic operators and set theory are given below. j9 j algebraic operators 10 . characteristic polynomial Let M be a square matrix (n Â n) and x a scalar variable, the characteristic polynomial Ch is deﬁned as ChðM; xÞ ¼ detðMÀxIÞ ¼ n X ai Á x nÀi i¼0 where I is the identity matrix, that is, a matrix having the diagonal elements equal to 1 and all the off-diagonal elements equal to zero, and ai the polynomial coefﬁcients. The characteristic polynomial is obtained by expanding the determinant and, then, collecting terms with equal powers of x.