Sentence examples for and defined using the from inspiring English sources

We also prove that an eta invariant for normal covering spaces introduced by Cheeger and Gromov (J. Differential Geom.21 (1985), 1 34) and defined using the von Neumann trace, is a homotopy invariant for Bieberbach groups.

Using the derived values of the dispersion coefficients (D or D i ) from each of the fitted solute transport models, dispersivity, λ (cm), and the Peclet number, Pe, were calculated and defined using the following equations (Peck and Watson 1979): lambda = D/v (16) Pe = lv/D = l/lambda.

The analyzed ChIP-PET cluster sequences were 500 bp long, and defined using the center of the PET cluster as the middle of the cluster and then expanding 250 bp on each side.

The questionnaire were designed and defined using the WHO MONICA criteria [ 2].

These features were extracted and defined using the parameterized callosal boundaries.

Signal transduction pathways associated with gene expression changes were analyzed and defined using the bioresource for array genes (BioRag, www.biorag.org).

The method applied was based on the degree of dependence between the prisoner's dilemma and SVO measurements, and was defined using the Pearson's x2 statistical tool.

Gene modules corresponded to the branches of the resulting dendogram and were defined using the "Dynamic Hybrid" branch cutting algorithm [ 31].

Region of interest comprised entire tumour volumes and were defined using the T 2 -weighted images to include tumour but exclude surrounding skin.

Overweight and obesity were defined using the age- and sex-specific BMI cut-offs recommended by the International Obesity Task Force.

The strains originating from 1964 67 and 1975 80 were defined using the PhP-system, and the BPTs obtained were compared with the BPTs defined in the material from 1994 98.