Sentence examples for instead of the representation from inspiring English sources

For the proof of the sufficiency part instead of the representation formula (27) in the case (0< p<1) we use the corresponding representation formula, Vert KfVert _{L_{p}}=inf_{Vert Psi Vert _{p^{prime}}=1} int_{0}^{infty} int_{0}^{infty}k ( x,y ) f ( y ),dyPsi ( x ),dx, with the same interpretation of (Vert Psi Vert _{p^{prime}}) as mentioned just after Theorem 7.

Instead of the representation of flux values as edge thickness, flux data might also be visualized using charts, e. g. bar- or line-charts which are assigned to edges or the reaction nodes.

Using has-part instead of rg, the representation of the SNOMED CT concept "Extraction of Foreign Body from Stomach by Excision" can be expressed as the following description logic definition: (2) ExtrOfForeignBodyFromStomachByExcision ≡ ∃ has-part.

Instead of using the representation theorems to define probabilities and utilities, decision theory may use them to establish probabilities' and utilities' measurability when preferences meet structural and normative axioms.

The development of the new model is based on the representation of the fatigue data on the stress ratio (R)–stress amplitude (σa) plane instead of the conventional representation on the mean stress (σm)–stress amplitude (σa) plane.

The reason for the comment was that the half-space representation for the convex hull of a set of points is typically used by software like MBC Toolbox, instead of the vertex representation.

There are attempts in the literature to reduce the computational complexity by introducing special MAP structures instead of the general representation.

Instead of the conventional representation of the weight loss based on the initial sample weight, the weight gain based on the sample weight at 1000°C was proposed.

Instead of the traditional representation of the man of letters with a pen and paper in hand, Rodin created a grotesque figure with a furrowed brow, hunched in a dressing gown to keep warm since he used to write at night.

To address the aforementioned problems, this paper develops a simple but effective tracking-by-detection scheme by exploring the distribution of sparse coefficients instead of the sparse representation error for similarity measure.

In Kaveh and Bakhshpoori's (2013) study, a more defined version of Eq. (5) is presented where instead of the (varepsilon_{t}) representation for a random walk, S is a parameter that represents the length of random walk with LF according to Mantegna's algorithm: x^{t + 1} = x^{t} + alpha cdot S. (6).