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An operator can be a mobile or fixed communication network.
As each operator can be a buyer or seller, dependent on current demand estimations, double auctions are naturally used as the trading and pricing mechanism in spectrum allocation auctions.
The detection of potential pitfalls for the ultrasound operator can be a useful topic for further investigations.
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In site selection for artificial recharge, the fuzzy algebraic product operator can be an appropriate combination operator, because at each location, the combined fuzzy membership value of the thematic maps to illustrate water depth, slope, drainage, soil, infiltration, lithology and landuse, and their characteristics is obtained.
The same applies for static objects that an operator can be considered noninteresting, which is a common issue in open spaces, where waste containers and other static objects are moved in the scene but do not represent a dangerous situation.
A quasi-hyperbolic operator can be characterised by a simple spectral property or as the restriction of a hyperbolic operator to an invariant subspace.
The random operator can be considered as a perturbation of a periodic one.
Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts.
Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity.
It is interesting to note that a second-order differential operator can be written in a Sturm-Liouville form if it is self-adjoint.
We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on Lp but unbounded on Lq for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com