Sufficiency Check

To ensure that the above result guarantees the minimum, we consider the second order Taylor expansion of / with respect to w at w, keeping the corresponding A fixed at v /2. Thus, for sufficiently small dw, 

Since dJ(w, A) is zero being the necessary condition, and the constraint A = 0 implies dK = 0, we obtain 

d//ds corresponding to w, is indeed the minimum. The above result shows that d//ds is minimized by 

Kamien and N.L. Schwartz. Dynamic Optimization, Chapter 6, page 149. Elsevier, Amsterdam, 1991. 

Kelley. Method of gradients. In G. Leitman, editor, Optimization Techniques, Chapter 6. Academic Press, New York, 1962. 

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Most importantly, none of the methods have, been sufficiently checked to assess how well they reproduce the gas yields or even the LC50 values from the appropriate segments of real-scale fire tests. To begin this process, a comparison procedure has been developed and a few materials have been checked using the NBS bench-scale combustor and the N-gas method (14,15). 

During validation, the relationship between response and concentration is established. Checks also are made to ensure that the linearity of the method does not make too large a contribution to the measurement uncertainty (the uncertainty due to the calibration should contribute less than about 20% of the largest uncertainty component). The calibration schedule required during routine operation of the method is also established. It is wise to carry out sufficient checks on some or all of the following performance parameters, in order to establish that their values meet any specified limits. 

As a first step, test other pure chemicals, such as compounds from the same chemical class and structurally related compounds, chemicals that might have been administered to the commodity or its environment during production and potential (likely) environmental contaminants. Next, test for interference from co-extractives from target matrices by testing representative matrices collected from various sources that reflect the expected profile of sample submissions. Testing of material from a single source is not sufficient. Check also for interference from known metabolites and degradation products. 

A considered assessment of just what is required to ensm-e both the quality of the data produced and more importantly the acceptance of the customer is paramormt to the whole QA concept. Procedures must be matched to requirements to ensure that whilst sufficient checks and controls are put in place, these are not perceived as excessive or overbearing. For example, in a manufacturing environment, a simple spectroscopic comparison reference measurement... 

Check Obtaining the desired target equation is a sufficient check. Be sure to remember to change the sign of AW for any equation you reverse. 

Although this experiment leaves something to be desired as far as precision, one however can, 1 think, look at it as providing a sufficient check of the theoretical princi-... 

A molecule can exist as a pair of enantiomers if it does not exhibit a symmetry plane or a symmetry center. More generally, the nonsuperimposability of the molecule on its mirror image is a necessary and sufficient check to determine whether a molecule is chiral or not chiral (achiral). 

Before the performance of the loading we have to apply 5 up to 12 sensors, according their size, on the cylindrical part of the drums and after a short check of the required sensitivity and the wave propagation the pneumatic pressure test monitored by AE can be performed. The selection of the sensors and their positions was performed earlier in pre-tests under the postulate, that the complete cylinder can be tested with the same sensitivity, reliability and that furthermore the localisation accuracy of defects in the on-line- and the post analysis is sufficient for the required purpose. For the flat eovers, which will be tested by specific sensors, the geometrical shape is so complicated, that we perform in this case only a defect determination with a kind of zone-location. 

Simply doing electronic structure computations at the M, K, X, and T points in the Brillouin zone is not necessarily sufficient to yield a band gap. This is because the minimum and maximum energies reached by any given energy band sometimes fall between these points. Such limited calculations are sometimes done when the computational method is very CPU-intensive. For example, this type of spot check might be done at a high level of theory to determine whether complete calculations are necessary at that level. 

In order to reach a crystalline state, polymers must have sufficient freedom of motion. Polymer crystals nearly always consist of many strands with a parallel packing. Simply putting strands in parallel does not ensure that they will have the freedom of movement necessary to then find the low-energy con-former. The researcher can check this by examining the cross-sectional profile of the polymer (viewed end on). If the profile is roughly circular, it is likely that the chain will be able to change conformation as necessary. 

The program can use conventional, in-core, or direct integral evaluation. The default ah initio algorithm checks the disk space and memory available. It then uses an in-core method if sufficient memory is available. If memory is not available for in core evaluation, the program uses a conventional method if... 

Water. Water mains should be connected to plant fire mains at two or more poiats, so that a sufficient water supply can be deHvered ia case of emergency. The plant loop and its branches should be adequately valved so that a break can be isolated without affecting a principal part of the system. If there is any question of maintaining adequate pressure, suitable booster pumps should be iastaHed. Any connection made to potable water for process water or cooling water must be made ia such a manner that there can be no backflow of possibly contaminated water check valves alone are not sufficient. The municipal supply should faH freely iato a tank from which the water is pumped for process purposes, or commercially available and approved backflow preventers should be used. 

These tests must encompass the complete interlock system, from the measurement devices through the final control elements. Merely simulating inputs and checking the outputs is not sufficient. The tests must duplicate the process conditions and operating environments as closely as possible. The measurement devices and final control elements are exposed to process and ambient conditions and thus are usually the most hkely to fail. Valves that remain in the same position for extended periods of time may stick in that position and not operate when needed. The easiest component to test is the logic however, this is the least hkely to fail. 

For every installation, a check has to be made to determine which ignition source may become effec tive and whether it can be prevented with a sufficient degree of safety. With more sensitive products and complex installations, it becomes more and more difficult to exclude ignition sources with ample safety (Siwek et al., Tgnition Behavior of Dusts, Proc. Lo.s.s Prevention Symposium, Atlanta, April 12-19, 1994). 

Drumming at Follow operating procedures incorrect tempera-, Cool adequately before drumming ture. Possibility of flammable atmo- drums until material has cooled down sphere, or initia- sufficiently tion of thermally Provide adequate fixed fire protection unstable materials.. ventilation Check heat tracing for excessive heat input ACGIH 1986 Bossart 1974 CCPS G-15 CCPS G-22 CCPS G-29 CCPS G-30... 

Checking the bath concentration The concentration of bath solution in caustic-based cleaners can be checked by a simple titration method as noted below, while for the remaining types of cleaners, a visual check of the degreased surfaces will be sufficient. The titration method is as follows ... 

Fault level is normally not mentioned, nor is it requested by the CT manufacturer. Generally, it should be sufficient to meet the likely fault level of the system and its duration in most cases, particularly on an LT system. For critical installations, large feeders and all FIT systems, however, it is recommended to check the suitability of the CTs for the system fault level and its duration. 

A lightning surge protective level is found to be more stringent than the switching surge or FOW protective levels. Hence, it is sufficient to check the protective distance requirement for the lightning surge alone. 

Measuring electrodes for impressed current protection are robust reference electrodes (see Section 3.2 and Table 3-1) which are permanently exposed to seawater and remain unpolarized when a small control current is taken. The otherwise usual silver-silver chloride and calomel reference electrodes are used only for checking (see Section 16.7). All reference electrodes with electrolytes and diaphragms are unsuitable as long-term electrodes for potential-controlled rectifiers. Only metal-medium electrodes which have a sufficiently constant potential can be considered as measuring electrodes. The silver-silver chloride electrode has a potential that depends on the chloride content of the water [see Eq. (2-29)]. This potential deviation can usually be tolerated [3]. The most reliable electrodes are those of pure zinc [3]. They have a constant rest potential, are slightly polarizable and in case of film formation can be regenerated by an anodic current pulse. They last at least 5 years. 

After a sufficient polarization period, which for the well casing is about a year, for flow lines with a high protection current requirement about half a year, and for flow lines with good coating about a month, the cathodic protection for the flow lines can be verified as in Section 10.4. If the cathodic protection is set up as local cathodic protection, checking is only necessary after a year. 

One way to remove the lower half of the liner, when hoisting facilities are not available or operational, Is to float the drum by filling the tank with a sufficiently concentrated solution. Other components that should be periodically checked are ... 

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