Destruction operator, definition

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. 

The proof is by induction. It is clearly true for two factors since then it reduces to the definition of the contraction symbol. Furthermore, it is sufficient to prove the theorem under the assumption that Z is a creation operator and that all the operators UV XY are destruction operators. If UV- - -XY are all destruction operators and Z is a creation operator, we may then add any number of creation operators to the left of all factors on both sides of Eq. (10-196) within the N product, without impairing the validity of our theorem, since the contraction between two creation operators gives zero. If on the other hand Z is a destruction operator and UV - - - are creation operators, then Eq. (10-196) reduces to a trivial identity... 

The basic condition of the Standard application - the availability of stable coupled probabilistic or the multiple probabilistic relations between then controlled quality indexes and magnetic characteristics of steel. All the probabilistic estimates, used in the Standard, are applied at confidence level not less than 0,95. General requirements to the means of control and procedure of its performance are also stipulated. Engineers of standard development endeavoured take into consideration the existed practice of technical control performance and test at the enterprises that is why the preparation of object control for the performance of nondestructive test can be done during the process of ordinary acceptance test. It is suggested that every enterprise is operated in correspondence with direct and non-destructive tests, obtained exactly at it, for detailed process chart and definite product type, however the tests have long since been performed after development of the Standard displayed that process gives way to unification. 

Catalytic combustion is the most promising technology for the destruction of VOCs [131,162,519-522], This approach is preferred to a thermal one due to the lower temperature required and its greater selectivity, which implies a considerable saving of energy. Other advantages are its definitive character and the fact that it can operate with dilute effluent streams (<1% VOCs) [131,162,519-522], For this reason, supported noble metals (Pt, Pd, Rh) or metal oxides (Cu, Cr, Mn) were the conventional catalysts used [523-529],... 

The number of people or value of assets used is sufficiently reduced (such that the consequences are below the threshold of a system s definition of accident, for example that the destruction of a remotely operated vehicle may be regarded differently to the destruction of a human operator). 

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