Global sum operation

One of the most important type of message passing operation is the global sum operation. This often occurs in molecular simulation where a... 

A standard replicated data approach to parallelising this algorithm would involve each processor taking part in the energy evaluation, followed by a global sum operation (so that each processor could have the total energy... 

Applying the - column sum operator (divided by two) to any sequence matrix SM, a global index for each k value different from zero, called the molecular sequence... 

If, besides the quality-related measure, z, one also wishes to include operating costs, in the analysis, because quality loss functions express quality costs on a monetary basis, commensurate with operating costs, the final global performance metric, y, which reflects total manufacturing cost, is simply the sum of both quality and operating costs (Clausing, 1993),... 

To understand these seemingly opposite facts, we have to leave the global S expression and rather write the spin-orbit Hamiltonian as a sum of one-particle operators... 

Suppose that a basis F, of dimension n, can be decomposed into several bases F , whose dimensions are smaller (n,), each of which is globally stable with respect to all the symmetry operations of the group. Suppose also that it is not possible to decompose any of the representations Fi into representations whose dimensions are smaller than n . The reducible representation F is said to have been decomposed into a sum of irreducible representations F,-, which is written ... 

The objective function includes the investment cost for the design (/o) and the sum of the operation costs if,) for all periods r = 1,. .., P., as well as the above referred weighted terms of global emissions of pollutants. Specific integer variables (binary, 0-1) in appropriate restrictions of the mathematical model allow the selection of operation on/off status and operations modes, e.g. extraction or condensing steam turbine. 

We note that Tg, Eq. (3.11) cannot be simply written in the form of Eq. (3.4). In such a case the general prescription is to introduce a suitable orthogonal basis set that diagonalizes the operator under study, or is to enable efficient evaluation of its operation (using the so-called discrete variable representation [240]). In the former approach, even a wave function spatially confined (such as would be the case when the angular coordinate represents molecular vibration) would be a coherent sum of a potentially large number of spatially global basis functions. Here we outline a spatially local method devised by Dateo and Metiu [106] based on the Fourier transform. 

This control sequence synthesis technique has its roots in the global slicing technique in the Bridge system[17]. It is improved by using CVs. The sum of function unit utility vector for all nodes in step k (FUVALL 5, ) indicates the number of all kinds of operations to be executed in c-step k. Therefore, if some components of FUVALL are zero, no operation will be carried out in c-step k under the conditions corresponding to the 0 components of FUVs. Consequently, c-step k can be skipped under such conditions. 

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