Operator contraction

Provide sub-contract operators and drivers relevant information from Section 14. Display information as per Schedule 10. 

State of Massachusetts (2007) Recycled and Environmentally Preferable Products and Services Guide Massachusetts Statewide Contracts Operational Services Division. Volume XXV. 

The investigation team interviewed all contract operators and their supervisor, the temporary water treatment unit vendor s engineers, plant personnel at the process plant unit, procurement personnel, and operations... 

In this case, the causal factor (contract operator falls asleep) is identified as a Human Performance Difficulty (one of the four major problem categories at the top of the tree), and the other three categories are discarded. (Different predefined trees use different terminology and structure, but generally cover similar choices.)... 

In the case of the hsh kill incident, the hrst of the questions, shown in Eigure 9-33, is answered YES because the contract operator was considered to be both fatigued and bored. This indicates that the cause may be related to Human Engineering and/or Work Direction. 

Any two-particle Hermitian matrix may be decomposed into three components that exist in different subspaces of the unitary group. These components reveal the structure of the matrix with respect to the contraction operation [4, 76-80],... 

The three parts of this decomposition reveal the structure of the matrix with respect to the contraction operations. These parts have been called the 0-, 1- and 2-body part of the second-order matrix A, respectively. Following the notation introduced in Ref. [73], each of these parts have been identified by a left-lower index. 

The independence with respect to the type of permutation-symmetry of the decomposition just reported allows one to treat the different spin-blocks of the 2-RDM on an equal footing. Moreover, this decomposition leads to a partitioning of these blocks into three orthogonal parts, which reveal the structure of these blocks with respect to all contraction operations. 

The different parts of this new decomposition reveal the structure of the with respect to all contracting operations into the 0- and 1-body space. Thus, while the first part of this new decomposition, Eq. (95), contains the information... 

Since the 2-CMs are not antisymmetric, four different contracting operations can be performed on them [71,79,83]. Two of these contractions, which can be considered namral because they derive from the contraction ofrelationEq. (113), are... 

Recall that in his Theorems 3 and 4 Hans Kummer [3] defined a contraction operator, L, which maps a linear operator on A-space onto an operator on p-space and an expansion operator, E, which maps an operator on p-space onto an operator on A-space. Note that the contraction and expansion operators are super operators in the sense that they act not on spaces of wavefunctions but on linear spaces consisting of linear operators on wavefunction spaces. If the two-particle reduced Hamiltonian is defined as... 

It has been shown [2-3] that a matrix contracting operation, exactly equivalent to the integration over (N-p) electron variables, can be performed in the following way ... 

It is well known that successive iterations converge, if operator C is a contraction operator (see Appendix B, Banach theorem), that is... 

These iterations are always convergent, because the operator O " is a contraction operator ... 

Taking into account (9.136), we can conclude that C " is a contraction operator if ... 

Thus, wc have proved that O " is a contraction operator for any lossy background media (where CTf,mi > 0). Therefore the fV-th iteration approaches the actual anomalous field... 

It is obvious that such an operator is continuous. Figure B-2 illustrates the definition of a contraction operator. The original points, x and xq, are far apart one from another, while after application of the contraction operator the distance between the resulting points, A (x) and A xo), becomes smaller. 

In other words, the contraction operator does not move the fixed point (Figure... 

When represented in matrix notation the Trace ( ) operation, or Spur, of a tensor is the sum of its diagonal components, its scalar value. The contraction operator implies that the two matrices on either side should be multiplied and the trace of the resulting matrix obtained. This equation, Eq. (2.41), is less troublesome than it first appears, as we shall demonstrate by substituting the results of Eq. (2.38) and (2.40) for the vibration, v= 1. First let us evaluate the a") term. 

The effect of the contraction operator is to select the size of the ellipsoid A, see Fig. 2.3, measured in the direction of the vibration under consideration. This is brought out more fully in the worked example, below. Thus the Debye-Waller factor is determined by an ofi value weighted to contributions in the same direction as the vibration of interest. The pre-exponential factor is ... 

The mode specific vibrational root mean squared displacement vector is thus replaced by the mean square displacement tensor of that atom in that specific mode, it has units of A. The tensor is represented in Eq. (A2.85) by a matrix, in more compact notation it is written, for a specific vibrational mode and atom Bi. The colon-operator ( ) or tensor contraction operation is found by taking the trace (Tr) of the product of the two tensors, see Eq. (2.50). Further we write the total mean square displacement tensor of an atom as the sum over all the individual vibrational contributions. 

In the third term in eq.(21), the contraction between the operators qi and qk is denoted by centred circles and for qj and qi, by filled circles. The meaning of the terms with nonadjacent contracted operators is similar to the one in traditional Wick s theorem ... 

The contract giver should provide the contract accepter with ail the information necessary to carry out the contracted operations correctly in accordance with the marketing authorization and any other legal requirements. The contract giver should ensure that the contract accepter is fully aware of any problems associated with the product, work, or tests that might pose a hazard to premises, equipment, personnel, other materials, or other products. 

The pharmaceutical manufacturer bears responsibility for the quality of the product including the attainment of the objective of irradiation. The contract operator of the radiation facility bears responsibility for ensuring that the dose of radiation required by the manufacturer is delivered to the irradiation container (i.e., the outermost container in which the products are irradiated). 

The fabricator, packager/labeller, distributor or importer provides the contractor with all the information necessary to carry out the contracted operations correctly in accordance with... 

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