This appears to be much more natural, since only the invertibility
of S is needed to get a time scale symplectic system.
Based on the definition of invertibility
, which has been described earlier, the result demonstrates clearly that the S-matrix based watermark embedding is invertible since the attacker was able to extract his faked watermark [W.
Lucrezia Reichlin is working on the problem of invertibility
in multivariate time-series models, and developing new diagnostic procedures for assessing the likelihood of neglected moving average components in VAR analyses.
of the polynomial [1 - [theta](L)[delta](L)[omega](L)L], and hence the absence of instrument instability depends upon the expectation formation mechanism, [delta](L).
sigma]] does not require invertibility
of [PHI], whereas [[omega].
One novelty of their approach is that they allow the mappings to slip freely along the boundaries of the domains, where it is most difficult to establish the existence, uniqueness, and invertibility
properties of the extremal mappings.
Scan-based Side Channel Attack: Scan-chain based attack works because of the invertibility
of the states of the cipher.
They are also applied in studies on the invertibility
of operators and the solvability of infinite systems of linear equations, for instance in [6,8].
condition for U([zeta]) (which reduces to the classical one [2, 7] in the Gabor multiplier case), is equivalent to linear independence of the system of projection operators involved, see  for details.
Namely, the corresponding invertibility
conditions (ii) differ only at t = b, and the final inequalities in (iii) are strict in the case of positivity.
32) This invertibility
condition, also required by King and Watson (1998) and Klein (2000), obtains except for degenerate special cases of (1) that can be solved by simpler methods than considered here.
His monograph, which can also serve as an introduction to this field of numerical analysis, works through stability, stable regularizability, including Moore-Penrose invertibility
, compactness, including compact sequences and central rank characterizations, Fredholm properties, including sequences and stability, essential fractality, including singular values and finite sections algebras, and applications, including approximation numbers, rank-preserving disretizations, the Arevson dichotomy (in band-dominated operators and the general setting), essential spectra, essential pseudospectra, pseudomodes and determinants.