Reduced notation

The zero-body operator, Iq, merely shifts the zero of energy. To reduce notational complexity, we will occasionally omit the second subscript on Lq. ... 

The stiffness tensor Cy is a tensor of fourth rank, with 81 elements. To enable it to be written as a matrix, a reduced notation for the independent elements of stress and strain is used,... 

Solution In Example 2.1 it was found that 5 = Aa. In reduced notation, 5 = Aa, while S2 through Sa are all zero. Using the reduced notation and the stiffness matrix for a cubic material [1] ... 

For inclusion of the target states it is useful to define a further reduction of the notation by separating the radial coordinate of the projectile from the projectile-spin—angle and target coordinates. The variables displayed in the state vectors indicate the context of the reduced notation. The coordinate—spin representation of an N + l)-electron state is given in the notation of (7.26) as... 

The symmetric group S(n) is of fundamental importance in quantum chemistry as well in nuclear models and symplectic models of mesoscopic systems. One wishes to discuss the properties of the symmetric group for general n and concentrate on stable results that are essentially n—independent. Here the reduced notation(6)-(9) proves to be very useful. The tensor ir-reps A of S(n) are labelled by ordered partitions(A) of integers where A I- n. In reduced notation the label Ai, A2,. .., Ap for S(n) is replaced by (A2,...,AP). Kronecker products can then be fully developed in a n-independent manner and readily programmed. Thus one finds, for example, the terms arising in the reduced Kronecker product (21) (22) are... 

A comparison of the nuclear and electronic stopping cross-sections expressed in reduced notation is shown in Fig. 5.3. Recall that s is proportional to ion energy and that (s)m is proportional to ion velocity. 

Increasing megnitude of ionic atmosphere ions reduces notation efficiency through increased screening of electrical interactions. 

Suppose that the piezoelectric thin film is bonded to an isotropic elastic substrate that does not exhibit piezoelectric behavior. If this film-substrate system is exposed to an electric field 8, then the film material will tend to undergo the stress-free strain specified by (3.83). However, the film is constrained from deforming freely by the substrate. As a result, a stress is generated in the film, and this stress may result in a detectable curvature of the substrate. If the X3—axis is normal to the film-substrate interface then the components of mismatch strain in the film are, in reduced notation. 

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