Common multiple balancing method

Balancing chemical equations is a primary task in basic chemical education. In the course of an examination, it may happen that a student can balance a chemical equation, but he cannot explain the general algorithm how he succeeded. In textbooks this topic is actually unclearly presented, making use of common multiples and the method of successive rectification of the equation with respect to a certain atom, etc. 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

Although it is common practice to calibrate the Coulter Counter using a standard powder, it is possible to calibrate the instrument with the powder being examined. This is the preferred British Standard method [17]. It is reiterated that this procedure cannot be carried out with some instruments due to count loss. Essentially one balances the volume of particles passing through the measuring aperture with the known volume in the measurement sample. This serves a multiple purpose in that ... 

It is therefore necessary to provide a sensitive method for detecting earth fault currents. The most common method is to provide a core balance current transformer at the circuit breaker or contactor. This current transformer has a current or turns ratio, which is independent of the ratios used by the transformers connected in the three-phase conductors. This is because a particular level of current is to be detected rather than a fraction or multiple of the stator load current. The switchgear manufactnrer will normally recommend the ratio of the core balance transformer and the matching relay. The relay will be either instantaneous 50 N or an inverse time 51 N type depending upon whether the motor is controlled by a circuit breaker or a contactor. 

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