Sentence examples for permutations of elements from inspiring English sources

More precisely, he proposes that identity should count as logical because it allows us to express "quantifier conditions" (properties of predicates that are invariant under permutations of elements of the domain) that we could not express otherwise.

Notice that each list (S^{r_i}) represents a permutation of elements of (S).

Real combinatorial chemistry, meaning the combinatorial permutation of element combinations or synthesis parameters involving statistical synthetic approaches leading to true combinatorial libraries of new functional materials supported by computer aided designs, was not presented yet in scientific community of inorganic solid state chemistry.

Later texts present the conception that the universe was formed by combinations and permutations of five elements: ether-space (akasha), wind (vayu), fire (agni), water (apas), and earth (bhumi).

First consider the group \(S_{3}\) of permutations of 3 elements under composition.

Bootstrap is a resampling and estimating method based on the sample through setting up random seeds and repeatedly executing permutations of the elements in the vector.

In the same way, Tarski suggests (1986, 149), the logical notions are just those that are invariant under the widest possible group of transformations: the group of permutations of the elements in the domain.

The nth harmonic number (H_{n}) can be expressed as H_{n}=frac{ {n+1 brack 2} }{n!}, where ({n brack k}) denotes the Stirling number of the first kind, counting the permutations of n elements that are the product of k disjoint cycles.

Once the distance matrices had been unfolded into vectors of each unique pair, the MRM calculations were simply ordinary least square (OLS) multiple linear regressions, except that significance testing was performed by 10,000 permutations of the elements in the response matrix that maintain the dependence structure among the plots [57], [58].

The statistical significance of correlations between distance matrices was obtained from 5,000 random permutations of matrix elements.

The appropriate null distribution for this test is generated by random permutations of the elements of x and.