We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

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:

We now give an operator theoretic proof for the Cauchy – Schwarz inequality which passes to the C *- algebra setting.

We also note that a two-body Dirac equation composed of a Dirac operator for each of the two point particles interacting via the Coulomb interaction can be exactly separated in the ( relativistic ) center of momentum frame and the resulting ground state eigenvalue has been obtained very accurately using the Finite element methods of J. Shertzer.

We can also define a number operator N which has the following property:

We are provided with ( quantum black box ) access to a subroutine in the form of a unitary operator, U < sub > ω </ sub >, which acts as:

He further wrote: " We didn't learn for years — until the reactor vessel was physically opened — that by the time the plant operator called the NRC at about 8 am, roughly ½ of the uranium fuel had already melted.

We now utilize quantum mechanical ladder operators, which are defined for a general angular momentum operator as

We consider generalizations of this operator below.

We see that there is a bijection between symmetric extensions of an operator and isometric extensions of its Cayley transform.

We also define the total number operator for the field which is a sum of number operators of each mode:

Thus we define the representations of G on an Hilbert space H to be those group homomorphisms, ρ, which arise from continuous actions of G on H. We say that a representation ρ is unitary if ρ ( g ) is a unitary operator for all g ∈ G ; i. e., for all v, w ∈ H. ( I. e.

We differentiated according to the product rule and noted that is the time derivative of the operator we started with.

Take X to be a complex manifold with a complex vector bundle V. We let the vector bundles E and F be the sums of the bundles of differential forms with coefficients in V of type ( 0, i ) with i even or odd, and we let the differential operator D be the sum

There were worries that if Arriva Trains Wales were granted this service, it would push Wrexham – London operator Wrexham & Shropshire out of business, with Wrexham & Shropshire Managing Director, Andy Hamilton, saying " We believe that this proposal – if approved – would push the date of profitability of WSMR by at least a year.

We drop the t < sub > 0 </ sub > index in the time evolution operator with the convention that and write it as U ( t ).

And when, the next day, Woodward — this is probably Sunday or maybe Monday, because the burglary was Saturday morning early — called the number and asked to speak to Mr. Hunt, and the operator said, ‘ Well, he's not here now ; he's over at ,’ such-and-such a place, gave him another number, and Woodward called him up, and Hunt answered the phone, and Woodward said, ‘ We want to know why your name was in the address book of the Watergate burglars .’ And there is this long, deathly hush, and Hunt said, ‘ Oh my God !’ and hung up.

We call hyperreflexive if there is a constant K such that for every operator T in B ( H ),

We say that the operator mutation is cis-dominant, it is dominant to wild type but affects only the copy of the operon which is immediately adjacent to it.

We define an operator between two functional spaces of continuous functions, Picard's operator, as follows:

We can measure the spin of this electron's state by applying an operator to the state, and we will always obtain ( or spin 1 / 2 ) since the spin-up and spin-down states are both eigenstates of this operator with the same eigenvalue.

We can also define the functional calculus for not necessarily bounded Borel functions h ; the result is an operator which in general fails to be bounded.

Whenever someone asked to be put through to an undertaker, the operator would connect them to her husband.

With the wire services coming into a device that would punch paper tape, rather than the linotype operator having to retype all the incoming wire stories, the paper tape could be put into a paper tape reader on the linotype and it would create the lead slugs without the operator re-typing the stories.

If TBTC fails on an individual train then it would be put into Restricted Manual mode, which means that the train operator can drive the train at 5 – 10 mph ( 8 – 16 km / h ) to the next station, where the train would be taken out of service until the fault is mended by technicians.

A former operator of this plant reported that he learned how much fuel to put into the engine so that it would run out at the desired time ( saved him a trip down the hill ).

J. E. Galloway was the first mayor ; Perry Rodkey, first postman ; E. D. Dexter, first hotel operator ; W. H. Dill ran the first telephone company ; John D. Richards had the first hardware store ; McGee Brothers put in the first cotton gin and E. E. Shook established the first lumber yard.

When the long-term operator died unexpectedly, the carousel was put up for auction, with fears that it would leave Coney Island or be broken up for sale to collectors.

The canonical version of the dynamics was put on firm ground by Thomas Thiemann who defined an anomaly-free Hamiltonian operator, showing the existence of a mathematically consistent background-independent theory.

In the run up to the bidding process for the South Central / Gatwick Express combined franchise, reports emerged suggesting that Transport for London, the operator of the London Overground service, wished to take control of all overground services in South London, including the ' Metro ' area of the South Central franchise, however such a transfer never took place and the entire franchise was put forward for tender by the Department for Transport.

The motorized versions are popular because of their low cost as they are put together from salvaged motorcycles and often do not require the operator to have a driving license.

When synchronisation is lost and the phase break is deenergised, the train's operator should put the controller ( throttle ) into neutral and coast through an isolated phase break section.

Because the RV has no way of " knowing " that the operator failed to disconnect either water or sewer, this scheme will ensure that warning is given unless all three lines have been properly put away before the owner is ready to drive off.

McCracken had been the local ferry operator, but when a large accident occurred during a dinner break killed four passengers, the owner put the ferry under his control and later fired McCracken.

For example, rather than put all the control panels in the operator's booth, and thus potentially confuse whoever is operating the lift, Yan operator booths contain only two switches: a switch that stops and starts the lift, and one that selects its speed.

The accuracy achieved by MCLOS missiles is hard to put a firm figure on, since it is highly dependent on the skill of the operator and any distractions the operator has to contend with ( such as being fired upon ).

* If the manifold is allowed to have boundary, then some restrictions must be put on the domain of the elliptic operator in order to ensure a finite index.

) The press operator would load the grapes or pomace into the wooden cylinder, put the top plate in place and lower it until juice flowed from the wooden slats.

If the local operator possesses an Equipment Identity Register ( EIR ), it then will put the device IMEI into it, and can optionally communicate this to the Central Equipment Identity Register ( CEIR ) which blacklists the device in all other operator switches that use the CEIR.

* 1886: Gilliland's Automatic circuit changer is put into service between Worcester and Leicester featuring the first operator dialing allowing one operator to run two exchanges.

The Russian Foreign Ministry reacted and declared his country is concerned about the situation with Mobile TeleSystems ’ Uzbekistan subsidiary Uzdunrobita, after Uzbek authorities suspended the mobile operator ’ s license and put a senior official into custody.

BEC's Railwalker re-railing devices can also put its locomotives back on-track without the risk of injury to the operator.