Sentence examples similar to notation lower from inspiring English sources

Notation: lower-case and upper-case boldface letters denote vectors and matrices, respectively; T, H,−1, det and t r denote the transpose, conjugate transpose, matrix inversion, determinant and trace, respectively; C denotes the set of complex numbers, I N is the N×N identity matrix.

Notations: Lower case and capital letters in bold denote vectors and matrices.

The German system was a hybrid the top voice part was shown in ordinary musical notation, the lower parts by the letters of the musical scale (A, B, etc).. Special signs indicated when a note should be sharped (D♯ usually indicating E♭, etc.; but signs for flat notes appeared occasionally) and ornamented.

Large-scale approximations of the uplink and downlink SINRs are derived in Section 3. A power control algorithm is proposed in Section 4. Simulation results are provided in Section 5 before we conclude the paper in Section 6. Notation: Boldface lower and upper case symbols represent vectors and matrices, respectively.

Based on the (hat {T}_{i,j}) notation, the lower bound on the achievable rate in (25) is rewritten as begin{aligned} {lim}_{n to infty} frac{1}{n} Ileft(mathrm{x}^{n};mathbf{y}^{n}right) & geq sum_{i,j} mu_{i} P_{i,j} left(log_{2} left(frac{1}{P_{i,j}} right) + hat{T}_{i,j} right) text end{aligned} (29).

When you start playing one, you'll know it's working if you see the "HTML5 – WEBM" notation in the lower bar.

If is a first-class discontinuity point of, then, simplifying the customary notation, denotes the lower limit of at and denotes the right limit of at.

(Notation: Upper and lower case bold symbols are used to denote matrices and column vector, respectively. denotes transpose. denotes Hermitian transpose. stands for conjugation. is expectation operator. and denote real and imaginary parts, respectively. is the identity matrix, denotes Kronecker product, and is the probability operator).

Notations: All boldface lower case and upper case letters represent vectors and matrices, respectively, and calligraphy letters represent sets.

Conclusions are drawn in section 7. Notations: Upper and lower bold face letters will be used for matrices and column vectors, respectively.

Typical deficiencies that were corrected included obsolete notations, upper and lower cases mixed up, missing characters, parts of other information such as the emergent/impulsive character of the onset attached to phase names as well as mere artefacts of parsing poorly tabulated or formatted original files.