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First, we provide a brief description of Legendre polynomials, and then we try to find the relation between the Legendre polynomials and the normalized Bernstein polynomials by introducing the transformation matrices W and G.

We begin by introducing the replicator dynamics.

By rescaling the raw exposure of a user's friends by its activity, we introduce the normalized exposure and show that this metric is able to distinguish between the original and randomized data as well as to distinguish between model data generated with different values of the friends' influence parameter.

As an improvement of the least mean squares (LMS) algorithm that has been introduced by Widrow and Hoff [14], Nagumo and Noda [15] have introduced the normalized least mean squares (NLMS) algorithm.

In the 'Methods' section, we introduce the normalized co-occurrence score, betweenness and PageRank.

For numerical implementations, we introduce the following normalized (non-dimensional) quantities: (31) where.

All photos were normalized introducing the scale of amplification.

Two parameters are introduced, namely, the normalized axial stiffness and the normalized bending stiffness.

Another measure introduced is the normalized Google correlation which represents the relatedness where the effect of fame is removed.

Let us first introduce the definition of normalized central moments which is the most important part of natural vector method.

The arrival rates αj can be related to a normalized distribution on D by introducing a unit arrival period T such that Σ j = 1 O (D ) Tαj = 1 or pj = Tαj.

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