Penalty factor

General Process Hazards Penalty Factor Range Penalty Factor Used(i)... 

D. Dust explosion covers for the possibility of a dust explosion. The degree of risk is largely determined by the particle size. The penalty factor varies from 0.25 for particles above 175 pm, to 2.0 for particles below 75 pm. 

The dynamics of inter- vs intrastrand hole transport has also been the subject of several theoretical investigations. Bixon and Jortner [38] initially estimated a penalty factor of ca. 1/30 for interstrand vs intrastrand G to G hole transport via a single intervening A T base pair, based on the matrix elements computed by Voityuk et al. [56]. A more recent analysis by Jortner et al. [50] of strand cleavage results reported by Barton et al. [45] led to the proposal that the penalty factor depends on strand polarity, with a factor of 1/3 found for a 5 -GAC(G) sequence and 1/40 for a 3 -GAC(G) sequence (interstrand hole acceptor in parentheses). The origin of this penalty is the reduced electronic coupling between bases in complementary strands. 

Once we fix the initial state ip,) and the final state ipj), the optimal field E(t) is obtained by some numerical procedures for appropriate values of the target time T and the penalty factor a. Though there should be many situations corresponding to the choice of ip,) and ipj), we only consider the case where they are Gaussian random vectors. It is defined by... 

Figure 5. Time evolution of the Husimi distribution for quantum kicked rotors with H = 0.3436 under an optimal field after 100 iterations. The Zhu-Botina-Rabitz scheme was used with the penalty factor a = 1 and the target time T = 400. From left to right, quantum states immediately after the kick at t = 0, 1, 2, 10, 100, 200, 300, 398, 399, and 400 are depicted, (a) The parameters are = 1 (regular case), (0 ,/) ) = (l- j l- ) (S/jf/) = (1-0, 1-0) (b) K = 1...

In the ZBR scheme, we must choose a small penalty factor a to make the final overlap large enough. In our analytical results, if we take the limit a 0, we find that... 

This result parallels Eq. (6.6.-30) the quotient Sjja there corresponds, for m = 1, to the minimum of S 6j) in Eq. (7.5-14). The parameterization penalty factor holds again here, and holds also for block-diagonal or... 

Finally, to make decision about the best route, the Penalty factor would be considered in the first step. The route with the smallest Penalty factor is considered as the safest route. At the second level, among the routes with the same and smallest Penalty factors, the best one is the route with the largest Safety-Cost Ratio. 

The Petri net model of the supemet (Figure 2e) is implemented in Visual C++ and the total number of routes generated by Petri net is found to be 8. The results of Total Safety-Cost Ratio and Penalty factor estimations for these routes are presented in Table 1. 

What is striking is that we find a probability that a coincidence is random of 0.007 % for the Condon survey of radio sources in positional coincidence with extragalactic infrared sources (IRAS). This probability becomes 0.755 % if we assume each doublet and the triplet as one event. The probability has lower significance because we didn t include any penalty factor for making the cuts in the catalogue. 

Because ensuring that cusp conditions are met helps to minimize fluctuations, at least in the energy, optimization will be aided by satisfying these conditions. However, note that optimization also can be used to obtain good cusps this can be done by including a penalty factor into the minimization procedure to force the various parameters of the trial wavefunc-tion to build the exact or nearly exact cusps. 

Figure 7.7 The intermediate, optimal objective functional I, penalty factor a, and the constraint norm q versus outer iterations...

The selectitMi of correct numerical parameters (penalty factors, convergence limits, increment sizes, remeshing criterion)... 

The process of calculating the index is shown in Fig. 9.3 it is briefly commented upon below. For any concrete application, however, [9] should be consulted. Penalty factors are assigned to hazardous elements and credit factors to good safety features. 

Sub-atmospheric pressure Sub-atmospheric pressure is important for processes where ingress of air may cause a hazard. A penalty factor of 0.5 is used. 

Operation in or near the flammable range There are certain operating conditions which can cause air to enter and be entrained into the system. The ingress or entry of air could lead to the formation of a flammable mixture and create a hazard. The penalty factor amounts in this case to 0.30, 0.50 or 0.80 depending on the situation. 

Dust explosion The maximum rate of pressure rise and maximum pressure generated by a dust explosion are largely influenced by the particle size. In general both quantities increase with decreasing particle size. The penalty factor ranges from 0.25 to 2 depending on particle size. 

Relief pressure Where operating pressures are above atmospheric, a penalty is applied for the higher discharge rates caused by higher pressure in the event of a leak. Depending on the situation the penalty factor lies between 0.86 and 1.50. 

Corrosion and erosion Although good design makes allowances for corrosion and erosion, corrosion or erosion problems may still occur in certain processes. A possible cause may be impurities in process streams. Penalty factors between 0.10 and 0.75 are used depending on the situation. The latter is applied if stress-corrosion cracking might develop. 

Leakage— joints and packing Gaskets, seals of joints or shafts can be sources of leaks of flammable or combustible materials. Depending on the quality of the design of the process unit and the type of material involved penalty factors between 0.1 and 1.5 are assigned. 

Use of fired equipment The penalties for the use of fired equipment are determined applying the tables in [9]. Depending on the quantities of substances and their temperatures of ignition penalty factors between 0.25 and 1.15 are used. 

Hot oil heat exchange systems Since most hot oil (heat exchange) fluids will burn and are frequently used above their Hash points or boiling points, they represent an additional hazard in any process unit that uses them. A penalty factor between 0.25 and 1.15 is applied depending on quantity and temperature. 

Rotating equipment A penalty factor of 0.50 is assigned for hazards due to equipment with rotating parts (e.g. compressors or pumps with large powers). 

The penalty factors applicable to the process unit considered are summed up resulting in the factor for general process hazards Fi and that for specific process hazards F2. The starting point is a base factor of 1 for both Fi and F2, which is the final word if no penalties have to be considered. A value of 0 is used for items, which are not applicable. 

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