Sentence examples for product decomposition from inspiring English sources

Moreover here (M'_i) is either (M_i) or its complex conjugate, and the product decomposition corresponds to the product decomposition (146) of the fundamental group of Z.

In each domain, the information is organized according to the product decomposition structure.

"Triangular" kinetics for the main, total oxidation and product decomposition reactions were utilised (Wellauer et al., 1986).

The algorithm uses direct product decomposition, and splitting fields determined using subgroups information in order to generate a canonical basis for the irreducible representations.

We finally employ another unique sum-of-line product decomposition of algebraic curves to study their dynamical behavior when defined by state-space equations.

If a product is only produced by one industry, then (as stated above) the product TIM and the industry TIM are identical, and therefore, the product decomposition of the corresponding industry TIM is the result we are looking for: it also constitutes the product decomposition of the product TIM.

Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions.

We discuss several general problems, including the commutativity and cocommutativity ones, the existence of tensor product or free wreath product decompositions, and the Tannakian aspects of the construction.

Special emphasis has been laid on low rank tensor product decompositions of orbitals, which take into account the strongly anisotropic character of these systems in one direction.

The natural cycling of carbon is directly and indirectly affected by land-use changes through deforestation, reforestation, wood products decomposition, and abandonment of agricultural land.

An additional step is necessary to achieve a product-by-product decomposition (denoted as ({mathbf{m}}^{p})).