The phrase "elements of the basis" is a grammatically correct phrase that can be used in written English.
It is typically used to refer to the fundamental or essential components of something. Example: "The elements of the basis for our argument include the data analysis, expert opinions, and real-life examples."
Specifically, the center elements of the basis functions coincide with cluster centers, while the respective widths are calculated by taking into account the topology of the hybrid clusters.
In other words, the formula (23) cannot be exact for all elements of the basis f ( x ) = x j ; j = 0, 1, 2, …, 2 n − 1.
If only J < ∞ are elements of the basis that can be used to approximate Ф, the continuation value becomes: {Phi}^Jleft {t}_n,{P}_{t_n}right)={displaystyle {sum}_{j=0}^M{varphi}_j t){L}_jleft t,{P}_tright)} (12).
According to the explained comments, (25) must be exact for all elements of the basis f ( x ) = { 1, x, x 2, x 3 } if and only if x 1, x 2 are two roots of S ¯ 2 ( 1, 1, − 2 a − 2 b + 2, − 2 a ; x ).
Let H ( β 1, β 2 ) be a generalized real quaternion algebra, the algebra of the elements of the form a = a 1 ⋅ 1 + a 2 e 2 + a 3 e 3 + a 4 e 4, where a i ∈ R, i ∈ { 1, 2, 3, 4 }, and the elements of the basis { 1, e 2, e 3, e 4 } satisfy the following multiplication table: We denote by n ( a ) the norm of a real quaternion a.
It is pertinent to emphasize that although the term-order-free reverse engineering method generates the same solution as the LS-algorithm (provided we use a term order to order the elements of the basis
This suggests that GEIs may have arisen multiple times independently during evolution, and can thus only be seen as a superfamily of elements on the basis of analogous core and structural features, rather than being phylogenetically related (Juhas et al., 2007b; Vernikos & Parkhill, 2008).
The principal objective of all storage structures is to facilitate the processing of data elements on the basis of their relationships; the structures thus vary with the type of relationship they represent.
These methods construct transition models of target elements on the basis of prior knowledge discovered in the target field such as meteorology.
To start with a simple example, we will first indicate how the IGT accounts for the grouping of image elements on the basis of connectedness.
However, there are other conditions where the grouping of image elements on the basis of connectedness and good continuation is associated with substantial delays (Crundall, Dewhurst, & Underwood, 2008; Jolicoeur, Ullman, & MacKay, 1986 , 1991 Pringle & Egeth, 1988; Roelfsema, Scholte, & Spekreijse, 1999).
