explicit form in a sentence

If the explicit form of the kernel function is known, we just need to compute and store the n \ times n kernel matrix \ operatorname K.
With the help of this equation the explicit form of G ( \ vec R, \ vec R'; N ) is found for a variety of problems.
The pronoun " yo " ( I ) in the explicit form " yo soy " is only required for emphasis or to clear ambiguity in complex texts.
The trucial system took explicit form in 1835, when raids by Bani Yas tribesmen, rivals of the Qawasim, led to a British-imposed truce during the summer pearling season.
Drug education can also take less explicit forms; an example of this is the Positive Futures Programme, funded by the UK government as part of its drug strategy.

This explicit form made sense, since the intonation also communicated the changes between the left and the right choir and their leaders performed these intonations to coordinate these changes.
Where the distribution has two parameters ( \ lambda _ 1 \ neq \ lambda _ 2 ) the explicit forms of the probability functions and the associated statistics are
Equations ( )-( ) hold for any 1D semi-Markovian random walk in a L-state chain, and form the most general solution in an explicit form for random walks in 1d.
Moreover, many results and methods ( such as propagation of uncertainty and least squares parameter fitting ) can be derived analytically in explicit form when the relevant variables are normally distributed.
with " f 0 = 0 " and " f 1 ` " 0 ", then an explicit form of inverse coefficients can be given in term of Bell polynomials as

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