was introduced by Blinder and Oaxaca (23,24) in 1973.
If G [??] F and |E(G)| is divisible by 3 then G admits a [P.sub.4] decomposition
SVM receives more than adjacent BIMF through BEMD decomposition
and constitutes a new multiple-BIMF (m-BIMF)  method.
, a detailed mathematical model for the bulk polymerization of St in the presence of DEKTP was developed, considering reaction temperatures at which the initiator decomposition
is mostly sequential (120-130[degrees]C).
Symmetric Tensor Decomposition
. Symmetric high order tensors appear mostly as multivariate functions (more than two variables), and high order tensors decomposition
allows deducing the geometric and invariance properties of a tensor.
The two typical three-component model-based decompositions
: FMD and AMD were used for testing.
We are interested in the decomposition
of f into two components, f = u + v [3-5], or three components, f = u + v + r [6-9], where u represents piecewise-smooth (cartoon or structure) component of f and v represents the oscillatory component of f, that is, texture, and r represents the residual (noise).
With the concentration of detected gas increasing, the gas response amplitude increases apparently, nevertheless the response and recovery property changes slightly which indicates a very good and satisfying reproducibility of prepared sensor against the decompositions
. Figure 9 shows the long-term stability and repeatability of the sensor against 50 [micro]L/L of S[O.sub.2], S[O.sub.2][F.sub.2], and SO[F.sub.2].
In the case of least square problem, the most popular techniques are the classical Cholesky decomposition
and QR factorization as will be detailed in section 2.
 Hung-Chih Lee, Balanced Decompositions
of Graphs and Factorizations of Digraphs, Ph.
An application of the iterative modification of tree decompositions
is the following: Let G be a graph, [H.sub.[pi]] = [PSI](G) be a triangulation of G and let (T, [tau]) = [PHI] [omicron] [PSI](G) be its tree decomposition
as defined in algorithm 2 from [H.sub.[pi]].
Theorem 11 will then imply that [G.sup.*] admits a ([C.sub.2], [C.sub.3])-free Euler tour, and hence a [P.sub.4] decomposition
. We will then show how this [P.sub.4] decomposition
of [G.sup.*] yields a [P.sub.4] decomposition