Sentence examples for minimal operator mathbf{ from inspiring English sources

If the minimal operator (mathbf{H}_{min}=mathbf{H} _{X,A,Q}) is lower semibounded, then the operator (mathbf{H}_{X,A,Q}) is self-adjoint, (mathbf{H}_{X,A,Q}=(mathbf{H}_{X,A,Q})^{ast}).

Note that for a symmetric linear difference equation, its minimal operator may not be densely defined, and its minimal and maximal operators may be multi-valued (cf. [10 12]).

Also, segmentations have to be robust and involve minimal operator input.

We obtain some values of the deficiency index of the corresponding minimal operator.

Finally, a complete characterization of J-self-adjoint operator extensions of the minimal operator in the whole interval is given in Section 6.

In particular, the maximal operator corresponding to Eq. (1.1) is multi-valued, and the minimal operator is non-densely defined in the related Hilbert space (cf. [23]).

Our goal was to design automated protocols that would allow the purification of proteins with minimal operator intervention.

We propose an improved implementation of the SHA-2 hash family, with minimal operator latency and reduced hardware requirements.

These were then scanned and analysed by means of specialized software designed for the purpose, which requires minimal operator contribution.

In all these cases, the minimal operator associated with an n th order differential equation must be symmetric, see [7, 8] for necessary and sufficient conditions.

By Theorem 5.1 of [16], d+ and d- are equal to the positive and negative defect indices of the minimal operator generated by (1.1), respectively.