Sentence examples for in addition to the exact from inspiring English sources

In addition to the exact eigenvector eigenvalue relations, I also derive eigenvalue perturbation formulae for rank-one modifications.

In addition to the exact wave speed solutions, we also provide efficient approximate formulas for the semirelativistic magnetosonic speeds.

In addition to the exact mathematical modelling of the interested players of transmission planning problem, the methodology can design the future transmission system not only for improving the system social welfare but also for encouraging competition among horizon year generating companies.

The time resolution in the assay processes provides high content information regarding the extent of the cytotoxicity in addition to the exact time, while the cytotoxicity takes place at different effect to ratio.

In addition to the exact integration approach, there are several approximation methods available for computing HI: one of which is the elevation-relief ratio method suggested by Pike and Wilson (1971) is less cumbersome and faster method used to calculate HI for the sub-watersheds of Agula.

In addition to the exact ILP formulation, we also introduce a data reduction heuristic that identifies "reducible" sets of taxa.

In addition to the toll exacted in the North by American bombing raids, many civilians were massacred by the Communists for ideological reasons.

Important tactical questions also remain as to the exact role of US special forces within this new security environment, in addition to the capacity and exact force posture of the Iraqi military and police, who have been criticised in the past for a checkpoint-centric approach not based around the "active patrolling" and population-focused surge strategy the US pursued.

So, in addition to the frictional parameters, the exact orientation of the stress field has to be constrained in hydrothermally altered zones in order to be able to assess their mechanical characteristics.

In addition to, the graphics of the exact and approximate solutions for different values of N are given in Figure 1 and Figure 2. Figure 1 Graphs of exact and approximate solutions for u in Example  1. Figure 2 Graphs of exact and approximate solutions for v in Example  1.

Since the reconstruction engine needs to position the 2D image in the 3D volume, in addition to the image data itself, the exact position and orientation of the US probe are required for each 2D image taken.