Sentence examples for mapping subject to from inspiring English sources

Suppose that (delta: mathcal {A}to mathcal {A}) is a mapping subject to the conditions (2.1) and (2.2).

Finally, to prove the uniqueness of the quadratic mapping subject to (3.3), let us assume that there exists another quadratic mapping which satisfies (3.3).

Finally, to prove the uniqueness of the quartic mapping subject to let us assume that there exists a quartic mapping which satisfies (3.22).

Suppose that (delta: mathcal {A}to mathcal {A}) is a mapping subject to the inequality (2.8) and for some (varepsilonge0), begin{aligned} biglVert deltabigl(x^{2}bigr -2xdelta(x bigrVert leqvarepsilon end{aligned} (3.1) for all (x in mathcal {A}).

This real-valued energy function is thus defined as E(X i,B m )=||G W (X i )−G W (B m )||, where G W is a mapping (subject to learning) to produce output vectors that are nearby for images from the same person, and far away for images from different persons [28].

Suppose that (delta: mathcal {A}to mathcal {A}) is a mapping subject to begin{aligned} BigglVert sum_{j=1}^{l}s_{j} delta(x_{j} BiggrVert leqBigglVert delta Biggl(sum _{j=1}^{l}s_{j}x_{j} Biggr BiggrVert end{aligned} (2.8) for all (x_{1}, x_{2}, ldots, x_{l}in mathcal {A}) and all (lambdain mathbb {T}_{varepsilon}), where (x_{3}= lambda z) ((z in mathcal {A})) and the inequality (2.2).

Consider the self-mapping, subject to ;,, and assume that and ; so that is a -cyclic -contraction.

Consider -cyclic self-maps subject to ;  .

The SOFM transforms the input of an arbitrary dimension into a one- or two-dimensional discrete map subject to a topological (neighborhood-preserving) constraint.

Similar results were obtained for five other maps subject to the same analysis.

Fig. 5 Mapping Subject Beliefs to a Likert Scale.