INDEX operator

Now we are ready to formulate the basic idea of the correction algorithm in order to correct the four-indexed operator f1, it is enough to correct the two-indexed operators fc and f 1 in the supermatrix representation (7.100). The real advantage of this proposal is its compatibility with any definite way of f2 and P7 correction [61, 294], The matrix inversion demanded in (7.99) is divided into two stages. In the fi, v subspace it is possible to find the inverse matrix analytically with the help of the Frobenius formula that is well known in matrix algebra [295]. The... 

Because P is not symmetric under simultaneous transposition of bead indices and (implicit) Cartesian indices, a comma is used before the bead subscript to indicate that the Cartesian component associated with this index operates to the right. 

A procedure for the evaluation involves two parts one being the numerical operations of matrix elements, the other being the index operations of the sub-PPDs. It is obvious that the index operation is independent of the system that is being studied. To save CPU time in VB applications, all index operations are pre-computed and stored in the file that accompanies the source code of the package. In addition, all sub-PPDs that are required in the evaluation are computed first and are labeled. This will enable one to avoid repeated computations of sub-PPDs and minimize the computational effort in the calculation. 

The coding in Table I illustrates the central problem of simulations. The number of pairs is N(N—1)/2. The number of floating point operations (FLOPS) per pair is about 25, assuming the branches are executed 50% of the time. Thus for 100 atoms (a minimal simulation) we will need 1.2 x 10 FLOPS for a single time step. The number of memory and indexing operations is similarly large. Typically one needs to execute between 10 and 10 time steps. Thus the simulations are limited by the number of floating point operations one can afford. 

A(I(N))-B(J(N)). The contents of the I and J arrays would obviously need to be known before the vector subtract indexed operation but this would almost certainly be the case in structural chemical calculations of any size. 

In this study a new index—operational readiness rate (R) was introduced. The index can be assumed as a first step of optimization process. The closer the value of the indicator is to 1.00, then the higher is the level of system utilization. It can be seen that all analyzed subsystems are not fully utilized. Therefore another steps of optimizing calculation should be conducted. 

Figure 4 The development of seal strength as a function of sealant resin melt index (I2) for a 0.915 g/cm LLDPE at various sealing dwell times. The preferred melt index operating range bracketed by the vertical broken lines within the plot.

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