For more on this matter, see interior operator below.

Here and below, the operator g is the equivalent of " the percentage rate of growth of " the variable that follows.

The example below illustrates the special case when an ( unbounded ) symmetric operator does have a set of eigenvectors which constitute a Hilbert space basis.

We consider generalizations of this operator below.

In fact it turns out that the operator is self-adjoint, as follows from the theory outlined below.

Many operators that occur in analysis are bounded below ( such as the negative of the Laplacian operator ), so the issue of essential adjointness for these operators is less critical.

A bounded operator T on a Banach space is invertible, i. e. has a bounded inverse, if and only if T is bounded below and has dense range.

An operator may be injective, even bounded below, but not invertible.

This shift operator is an isometry, therefore bounded below by 1.

Flight Sergeant George Chalmers, radio operator on " O for Orange ", looked out through the astrodome and was astonished to see that his pilot was flying towards the target along a forest's firebreak, below treetop level.

The eigenstate of the annihilation operator has a Poissonian number distribution ( as shown below ).

In the mathematical formulation of quantum mechanics, states are given by non-zero vectors in a Hilbert space V ( where two vectors are considered to specify the same state if, and only if, they are scalar multiples of each other ) and observables are given by self-adjoint operators on V. However, as indicated below, not every self-adjoint operator corresponds to a physically meaningful observable.

With printing-press operator Frank Jenkins as his running mate, his platform included a one-year tax moratorium for every taxpayer with an annual income below $ 6, 000, and one free pint of milk a day in school for every child.

The machinery house is above the upper-deck lift span with an operator's room suspended below the house so that the operator can view river traffic as well as the upper deck.

This process continued until the press operator determined that the quality of the pressed juice or wine was below standard, or all liquids had been pressed.

The front control panel is hinged below the cassette slot, so that it may be tilted outward to a more comfortable viewing angle for the operator.

The figures below are the official number of passengers entering and exiting each day released by each train operator.

is an excitation operator which, when acting on, produces a linear combination of excited Slater determinants ( see section below for greater detail ).

This dog has two possible positions to which it can be pivoted by hand: a " safe " position, in which the dog is pushed towards the muzzle of the firearm, and an " operating " position, where the dog is pulled towards the operator so that the pyrite in its jaws can engage either the top of the pan cover ( see below ), or ( in the absence of the pan cover ) the edge of a steel wheel bearing longitudinal grooves around its circumference.

The solutions to the resulting non-linear equations behave as if each particle is subjected to the mean field created by all other particles ( see the Fock operator below ).

The solution to a singularly perturbed problem cannot be approximated in this way: As seen in the examples below, a singular perturbation generally occurs when a problem's small parameter multiplies its highest operator.

In this new split-screen configuration, which was the forerunner to Prevue Guide ( below ), the upper half of the screen displayed static or animated graphical advertisements and logos created locally by each cable system operator.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

As an example, the over operator can be accomplished by applying the following formula to each pixel value:

We know that is opaque and thus follows that is opaque, so in the above equation, each operator can be written as a convex combination:

It is also interesting to note that the operator fulfills all the requirements of a non-commutative monoid, where the identity element is chosen such that ( i. e. the identity element can be any tuple with.

The classical definition of angular momentum as can be carried over to quantum mechanics, by reinterpreting r as the quantum position operator and p as the quantum momentum operator.

Thus, the vector space B ( X, Y ) can be given the operator norm

Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.

Most cranes accommodate both the camera and an operator, but some can be operated by remote control.

In practice, the above definition is rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived.

Store employees are also needed to authorize " age-restricted " purchases, such as alcohol, solvents or knives, which can either be done remotely by the employee observing the self-checkout, or by means of a " store login " which the operator has to enter.

If all layers of an image change regularly but a large number of layer still need to be composited ( such as in distributed rendering ), the commutativity of a compositing operator can still be exploited to speed up computation through parallelism even when there is no gain from pre-computation.

According to Bertrand Russell's Theory of Descriptions, the negation operator in a singular sentence can take either wide or narrow scope: we distinguish between " some S is not P " ( where negation takes " narrow scope ") and " it is not the case that ' some S is P '" ( where negation takes " wide scope ").

If the operator already has this in place, which is often the case today, the network can be upgraded to EDGE by activating an optional software feature.

Although the resulting energy eigenfunctions ( the orbitals ) are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian ( that is, the energy eigenstates ) can be chosen as simultaneous eigenstates of the angular momentum operator.

Because it is unitary, we can regard it as a symmetry operator.

If negation is cyclic and "∨" is a " max operator ", then the law can be expressed in the object language by ( P ∨ ~ P ∨ ~~ P ∨ ... ∨ ~...~ P ), where "~...~" represents n − 1 negation signs and "∨ ... ∨" n − 1 disjunction signs.

The main benefit is one operator can control the loading of grain, coal, gravel, etc.

In addition, the same operator can move the train as needed.

A well-formed formula ( wff ) is any atomic formula, or any formula that can be built up from atomic formulæ by means of operator symbols according to the rules of the grammar.

This job can also be performed somewhat crudely by a human operator who can see the target and the missile, and guides it using either cable or radio based remote-control, or by an automatic system that can simultaneously track the target and the missile.