Possible variations

It turns out though that there are several possible variations on this general theme We could for example keep the magnetic field constant and continuously vary the radiofrequency until it matched the energy difference between the nuclear spin states Or we could keep the rf constant and adjust the energy levels by varying the magnetic... 

The standard deviation of the distribution of means equals cr/N. Since cr is not usually known, its approximation for a finite number of measurements is overcome by the Student t test. It is a measure of error between p and x. The Student t takes into account both the possible variation of the value of x from p on the basis of the expected variance and the reliability of using 5- in... 

Lubricating oil used in intermittent service must show the least possible variation in viscosity with respect to temperature and must be changed at frequent intervals to remove the foreign matter collected during service. The stabiUty of such oil is therefore of less importance than the stabiUty of oil used in continuous service for prolonged periods without renewal. Lubricating oil for continuous service must be extremely stable because the engines in which it is used operate at fairly constant temperature without frequent shutdown. 

Scheme 4 shows in a general manner cyclocondensations considered to involve reaction mechanisms in which nucleophilic heteroatoms condense with electrophilic carbonyl groups in a 1,3-relationship to each other. The standard method of preparation of pyrazoles involves such condensations (see Chapter 4.04). With hydrazine itself the question of regiospecificity in the condensation does not occur. However, with a monosubstituted hydrazine such as methylhydrazine and 4,4-dimethoxybutan-2-one (105) two products were obtained the 1,3-dimethylpyrazole (106) and the 1,5-dimethylpyrazole (107). Although Scheme 4 represents this type of reaction as a relatively straightforward process, it is considerably more complex and an appreciable effort has been expended on its study (77BSF1163). Details of these reactions and the possible variations of the procedure may be found in Chapter 4.04. 

The possible variations among the three atoms comprising this reactive component make this the largest group and the one with the most potential for further development. They are particularly useful in the synthesis of five-, six- and seven-membered ring systems. They also may be conveniently considered according to their atom composition, and the hybridization state of any carbon atoms involved. 

It is, of course, impossible to allow for all possible variations of equation requirements and machine capabihty, but it is hoped that the nomenclature in the table presented at the beginning or the section will prove adequate for most purposes and will be capable of logical extension to other more specialized requirements. 

Table 12-3 is a summary of gaseous fuel speeifieations. The two major areas of eoneern are heating value with its possible variation and eontam-inants. Fuels outside a speeifieation ean be utilized if some modifieation is made. 

The many possible variations and modifications to this sequence have been admirably summarised by Matthews (see Figure 12.23). 

To illustrate the possible variation in failure rates under different operating requirements and maintenance programs assume the following ... 

Another means of realizing multidimensional separation is combination of two complementary separation techniques which use different methods of separation. In such multi-modal separation, different techniques can be coupled in which PC is used as the second dimension and another separation method, as the first. Some possible variations are as follows ... 

The design of the system must take into account possible variation of critical control parameters that could affect performance. The maximum performance of the process should be defined by a reasonable safety margin. In order to comply with cGMP guidelines, established validation protocols, and parameters should allow the process to achieve reproducible purity and yield under stressed conditions. This implies that the industrial SMB system must be stressed to simulate worst-case conditions for process validation. 

If you do not select a non-overloading motor, and variations in head and/or flow occur, the motor could overheat and stop operating. Study the pump-capacity curve shape to recognize the possible variations. 

Liquids used for testing must reproduce all possible variations that are to be expected in the operating plant. 

Since the possible variations in binder alone are limitless, it is possible to produce an infinite number of paints. As the range of raw materials available to the formulator becomes wider, their chemical purity is continually being improved. Mathematical models of binders can be constructed using computers and it is usually possible to predict fairly accurately the properties of a particular formulation before it is made. Nevertheless, the formulation of paints for specific purposes is still considered to be very much a technological art. 

It should also be pointed out than in exploring the effects of the concentration of a particular acid or other chemical on its corrosivity, it is necessary to cover the full possible variation of concentrations thoroughly, since it... 

In all cases where water is used for cooling, but more especially where it is being evaporated, the hardness figure should be obtained from the local water supply authority. Enquiries should also be made as to possible variations in the supply, since many cities draw their water from two or more catchment areas, and the type and quantity of hardness may change. 

Note. In view of the varying stability of solutions of these indicators, and the possible variation in sharpness of the end point with the age of the solution, it is generally advisable (if the stability of the indicator solution is suspect), to dilute the solid indicator with 100-200 parts of potassium (or sodium) chloride, nitrate or sulphate (potassium nitrate is usually preferred) and grind the mixture well in a glass mortar. The resultant mixture is usually stable indefinitely if kept dry and in a tightly stoppered bottle. 

The question arises whether an internal standard can be relied upon to eliminate physical differences among samples, the Class II deviations of Section 7.8. No clear answer is possible. Variations in intensity ratios with particle size and with length of grinding time have been observed, especially in the analysis of minerals, but these effects seem due primarily to a nonuniform distribution of the internal standard, and not to particle size as such. These two possible causes of nonuniformity are difficult to separate. 

These tests were performed to establish the limits in flexibility and operability of a methanation scheme. The two demonstration plants have been operated in order to determine the optimum design parameters as well as the possible variation range which can be tolerated without an effect on catalyst life and SNG specification. Using a recycle methanation system, the requirements for the synthesis gas concerning H2/CO ratio, C02 content, and higher hydrocarbon content are not fixed to a small range only the content of poisons should be kept to a minimum. The catalyst has proved thermostability and resistance to high steam content with a resultant expected life of more than 16,000 hrs. 

For the equilibrium of an isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy the variation of its entropy shall either vanish or be negative. 

More precisely, and accounting for the possible variation of Pj with 0j, one can write equation (6.50) in the form ... 

Table 8. Possible variations in the backbone composition of polyorganosiloxanes ...

Sufficiency. Given the example, the theory we employ to deduce the conditions must guarantee that the conditions on equivalence or dominance will be satisfied, since the example itself is simply an instance of the particular problem structure, and may not capture all the possible variations. The sufficient theory will thus end up being specialized by the example, but since we have asserted the need for validity of this process, it will still be guaranteed to satisfy the abstract necessary and sufficient conditions on dominance and equivalence. 

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