E criterion

Proof. It has to be shown that Definition 9.1, with the abbreviations from Definition 9.3, is fulfilled. Lemmas 9.5 and 9.6 cover all the requirements except for the security for the signer, i.e.. Criterion 3 of Theorem 7.34. If values pk = (prek, mk) with prek = ( 1 , "V, K) and hist = (jn, s) are given, where hist is a possible history. Lemma 9.7 can be applied. Together with Lemma 9.6, it immediately yields... 

As with the E criterion, the Threshold criterion is minimized since minimizing this criterion will result in a few large coefficients which is typically preferred for data compression. 

It should be noted that in bare charge experiments the E criterion has been found not to apply to some explosives (5), or to apply only over a limited impact velocity range in others (6). Obviously these limitations also apply to covered experiments. However, the criterion does apply to a sufficient number of commonly used explosives to make its adaptation to covered charges worthwhile. 

Equations (7-8) and (7-9) are then used to calculate the compositions, which are normalized and used in the thermodynamic subroutines to find new equilibrium ratios,. These values are then used in the next Newton-Raphson iteration. The iterative process continues until the magnitude of the objective function 1g is less than a convergence criterion, e. If initial estimates of x, y, and a are not provided externally (for instance from previous calculations of the same separation under slightly different conditions), they are taken to be... 

Convergence of the iteration requires the norm of the objective vector 1g to be less than the convergence criterion, e. The initial estimates used, if not provided externally, are, in addition to Equation (7-28)... 

More correctly, the regression problem involves means instead of averages in (1). Furthermore, when the criterion function is quadratic, the general (usually nonlinear) optimal solution is given by y = [p u ], i.e., the conditional mean of y given the observation u . 

After an initial starting geometry has been generated and optimized (e.g., in a force field), the new conformation is compared with all the previously generated conformations, which are usually stored as a list of unique conformations. If a substantially different geometry is detected it is added to the list otherwise, it is rejected. Then a new initial structure is generated for the next iteration. Finally, a preset stop criterion, e.g., that a given number of loops has been performed or that no new conformations can be found, terminates the procedure. 

Criterion I and Other Class Furnace Refractories, C-E Refractories, Valley Forge, Pa., 1977. 

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