The Secretary of the Interior or any duly authorized representative shall be entitled to admission to, and to require reports from the operator of, any metal or nonmetallic mine which is in a State ( excluding any coal or lignite mine ), the products of which regularly enter commerce or the operations of which substantially affect commerce, for the purpose of gathering data and information necessary for the study authorized in the first section of this Act.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

The diagonalizable operator is the special case of this in which Af for each i.

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

By Theorem 10, D is a diagonalizable operator which we shall call the diagonalizable part of T.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

The diagonalizable operator D and the nilpotent operator N are uniquely determined by ( A ) and ( B ) and each of them is a polynomial in T.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

) Now Af is a diagonalizable operator which is also nilpotent.

Such an operator is obviously the zero operator ; ;

for since it is nilpotent, the minimal polynomial for this operator is of the form Af for some Af ; ;

but then since the operator is diagonalizable, the minimal polynomial cannot have a repeated root ; ;

hence Af and the minimal polynomial is simply x, which says the operator is 0.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

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 ).

The HRF was soon joined by the Height / Fuze Indicator ( HFI ), this was marked with elevation angles and height lines overlaid with fuze length curves, using the height reported by the HRF operator, the necessary fuze length could be read off.

The word STENDEC was reported by the radio operator at Santiago airport as the last word of a " loud and clear " Morse code message, sent " very fast " at 5. 41 PM.

In early 2005, several Irish newspapers reported that Meteor Mobile Communications, the third mobile phone operator, was up for sale by its owners, Western Wireless.

Admiral Callaghan wasted further time trying to reconcile the ranges and bearing information reported by radar with his limited sight picture to no avail, mostly because the radar operator without the direction of a modern Command Information Center ( CIC ) was reporting on vessels that were out of sight, and Callaghan was trying to coordinate the battle from the bridge, not a Command Center.

It first announced that it had acquired Excite Italia B. V. ( the operator of Excite Europe ), from Tiscali, S. p. A .; and, secondly, the company reported that it had reached a comprehensive settlement with InfoSpace regarding Excite in the United States, whereby Ask Jeeves and InfoSpace would share marketing costs and revenue from the Excite web search function.

These changes did result in improvements though: the Class 90s were probably the main factor in the 17 % improvement in the ' miles per five-minute delay ' figure in the year up to October 2006, but this still left the operator behind all the other ex-InterCity services, in terms of performance, as reported in the January 2007 edition of Modern Railways.

Regulated Radio frequencies often have unlicensed users who are unaware of the protocol on a certain channel and are asked to sign off if they fail to identify a callsign as a licensed operator, or are reported by licensed operators to the licensing body for possible advisement or citation.

If awareness is reported a case review is immediately performed to identify machine, medication, or operator error.

Contemporary Irish are more tuned to their heritage, as can be seen in the example of the Irish Bog Psalter, which was discovered and reported by an alert machine operator in July 2006.

In late 2006, independent from the definition of isolated horizon theory, it was reported that in loop quantum gravity the eigenvalues of the area operator are symmetric by the ladder symmetry.

After a Canadian operator reported him for selling such calls for $ 1 at the university, he was suspended and fined $ 25 but soon reinstated ; he later graduated in philosophy and moved to Tennessee.

Cosmorom was the mobile arm of Romanian national incumbent operator Romtelecom and had never reported any profit.

No ship or land-based operator reported receiving a distress signal from the crew.

According to USAF the incident was a rather unusual case of friendly-fire: the B-52G defensive gun operator is reported to have locked onto a friendly F-4G Wild Weasel jet on his fire-control radar, suspecting it to be an Iraqi MiG.

In the midst of the Cold War assaults on UE, the union's newspaper reported such success stories as the promotion of a black worker at Johnson Machine to lathe operator.

In August 2010, CEO ( Managing Director ) Thomas Minninger reported the airline was the first operator in Germany obtain authorization to operate the Dassault Falcon 7X commercially.

In early May 2011, the operator of the plant reported that its fuel supplier, General Electric, notified it that mathematical errors were made which could resulted in reactor fuel ’ s getting hotter than operator thought.

In early May 2011, the operator of the plant reported that its fuel supplier, General Electric, notified it that mathematical errors were made which could resulted in reactor fuel ’ s getting hotter than operator thought.

Back in Nantes on 20 January, he came back to the Cléments who reported to him suspicious activities by the radio operator Gaessler, seen hanging around in bars and talking with German soldiers.

In 2005, TfL reported that Arriva London had more complaints a year than any other bus operator in London, although at the time Arriva did operate the biggest percentage of bus services in London.

A number of problems have been reported, including RF burns received while transmitting data on some settings, comparatively heavy compared to equivalent Clansman radio sets, unergonomic wiring and user interfaces on the manpack radio, short-lived batteries, inadequate " ruggedisation " and inflexibility with assigning unique call sign indicators to individuals which are now instead permanently programmed into the radios themselves instead of the Clansman BATCO assigned system, which would change every 12 hours and could be used on any number of different radio sets by the operator as required.

For simplicity, we shall here use the shorthand notation for representing the over operator.

As a result of the tokenizing process, programmers could not use any variable name that had the name of one of the BASIC commands ( e. g. a person could not use the name " SCORE " because the " OR " would invoke a disjunction operator, and " BACKGROUND " could similarly not be used because " GR " would invoke the low-resolution graphics system ; both would create syntax errors ).

Charter bus operators may be completely independent businesses, or charter hire may be a subsidiary business of a public transport operator who might maintain a separate fleet or use surplus buses, coaches, and dual purpose coach seated buses.

Some buses, while not economical to keep running as service buses, are often converted in some way for use by the operator, or another user, for purposes other than revenue earning transport.

The algebra M < sub > n </ sub >( C ) of n-by-n matrices over C becomes a C *- algebra if we consider matrices as operators on the Euclidean space, C < sup > n </ sup >, and use the operator norm ||.|| on matrices.

When the bridge was in use, boaters would signal the operator, who would start a diesel engine and rotate the bridge to the open position on a large gear.

To do this, we also use the definition of the logarithm ( as the inverse operator of exponentiation ) that

Proposals made in 1995 to use it or replace it with a new bridge for pedestrians were opposed by the city of New York and the private ferry operator at that time.

This could be achieved at a speed of 30 wpm by strictly observing the " cadence " of rhythm of the system when the distributor gave the operator the use of the line.

In two or more dimensions we must use, the del or gradient operator, which generalises the first derivative, obtaining

It is the first African mobile service operator to use ForgetMeNot Africa's eTXT service to enable their customer base to send and receive email via any mobile capable of a simple SMS

This may reduce staff productivity due to slower response times and slower mouse-based operator actions, yet it is often seen as an " upgrade ", because the interface style is familiar to unskilled users and is easy for them to use.

As it was used by British Rail, the single operator before franchising, its use also maintains continuity and public familiarity ; and it avoids the need to replace signage.

It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radices, and hexadecimal displays needed to display more numerals.

Another common example is the use of the "+" operator which allows similar or polymorphic treatment of numbers ( addition ), strings ( concatenation ), and lists ( attachment ).

The product operator for the product of a sequence is denoted by the capital Greek letter Pi < span style =" font-family: times, serif ; font-size: 150 %">∏</ span > ( in analogy to the use of the capital Sigma < span style =" font-family: times, serif ; font-size: 150 %">∑</ span > as summation symbol ).

The operator might be able to use a different routing to complete the call.

By removing the need to load the particle with the properties of space and time, a fully deterministic, local and causal description of quantum phenomena is possible by use of a simple dynamical operator on a Universal Invariant Set.

There are several different types of CAD, each requiring the operator to think differently about how to use them and design their virtual components in a different manner for each.

3D parametric solid modeling requires the operator to use what is referred to as " design intent ".

While fire and forget missiles have definitive advantages in terms of guidance and operator safety, and include abilities such as top attack mode, older missiles continue in use, both in the front line armies of less developed countries, and in reserve service the world over, due to their lower cost or existing stockpiles of less advanced weapons.

This method required early practical application of two technologies that later gained widespread use: Teflon, used as a gasket material, and closed-circuit television, used to give the crane operator a better view of the process.

In these cases, scammers use TRS, a US federally funded relay service where an operator or a text / speech translation program acts as an intermediary between someone using an ordinary telephone and a deaf caller using TDD or other teleprinter device.

Rafting photographers already use pigeons as a sneakernet to transport digital photos on flash media from the camera to the tour operator.