Sentence examples for by an arbitrary complex from inspiring English sources

We wonder whether 0 CM in Theorem 1.1 can be replaced by an arbitrary complex constant (a^) (≠a) CM or not.

Moreover the best constant is attained by, where is an arbitrary complex number.

The general real solution of (16), for, is given by, where k is an arbitrary complex number.

That is, given an arbitrary complex n-by-n matrix ∼A, find a (R, S -symmetric (or (R, S -symmetricetric) matrix A∼A which is the sorution to the left and Right inverS -skewnvalue problem S -skewat the disymmetrictween ∼A and A∼A is matrixzed in the Frobenius norm.

The estimated visual features are used to animate an arbitrary complex head model by means of the animation of a simple (small number of vertices) face model, requiring only a quick setup procedure.

3DP is one kind of the RP technology, which is a general term for technology driven directly by the CAD model to rapidly manufacture an arbitrary complex 3D entity.

where the superscript denotes the complex conjugate and is the deterministic periodic autocorrelation function for a lag, defined for an arbitrary complex sequence of length by with.

where c is an arbitrary complex constant.

If, is an arbitrary complex number and is an arbitrary real number such that (2.8).

A similar statement in an arbitrary complex dimension appears in Theorem 4.2 in the next section.

In the second proposed method, an arbitrary complex FM signal is embedded in the wavelet domain.