Error statements

Verify that DC convergence has been achieved. View the error statements in the text editor to verify that the convergence problem pertains exclusively to the transient simulation. 

For a very poor set of data, with a very large standard deviation, it is foolish to show the error statements to one more decimal place than the least significant figure. If the room measurements just cited actually had a standard deviation of 0.0756 m, it means that you were silly to think of measuring to the nearest 0.001 m, and in any case you should round the standard deviation to 0.076 m. The decision as to when you do, or do not, write the error statement to one more decimal place than the least significant figure is arbitrary. (Some professors say that you should use the extra decimal place if the standard deviation is less than 0.4% of the average of the measurements.)... 

As mass spectrometry is a live technique, we also apologize in advance for the inevitable errors, statements and assumptions that a book like this may contain (or not), and new chemists are dare to comment and correct such errors in future. In closing, we wish to dedicate these chapters to our mentors who embedded within us the passion for chemistry and particularly for mass spectrometry. If this book can educate somehow and inspire more young researchers in the same way that they did, then we will regard this book as a great success and our personal satisfaction. 

To retrieve data from a file, the file must exist in the folder that houses the program. If the file does not exist or is not in the proper folder, the computer will indicate this with an error statement To retrieve the data stored in the above file, the following statements are used ... 

This book was carefidly produced. Nevertheless, editors, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or otiier items may inadvertently be inaccurate. 

A statement that the difference between two values can be explained by indeterminate error retained if the significance test does not fail Ho). 

Statement that a periodic signal must be sampled at least twice each period to avoid a determinate error in measuring its frequency. 

The need for the indicator s color transition to occur in the sharply rising portion of the titration curve justifies our earlier statement that not every equivalence point has an end point. For example, trying to use a visual indicator to find the first equivalence point in the titration of succinic acid (see Figure 9.10c) is pointless since any difference between the equivalence point and the end point leads to a large titration error. 

Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. The design of experiments may then often be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliabihty of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 

There are a variety of ways to express absolute QRA results. Absolute frequency results are estimates of the statistical likelihood of an accident occurring. Table 3 contains examples of typical statements of absolute frequency estimates. These estimates for complex system failures are usually synthesized using basic equipment failure and operator error data. Depending upon the availability, specificity, and quality of failure data, the estimates may have considerable statistical uncertainty (e.g., factors of 10 or more because of uncertainties in the input data alone). When reporting single-point estimates or best estimates of the expected frequency of rare events (i.e., events not expected to occur within the operating life of a plant), analysts sometimes provide a measure of the sensitivity of the results arising from data uncertainties. 

The goal of any statistical analysis is inference concerning whether on the basis of available data, some hypothesis about the natural world is true. The hypothesis may consist of the value of some parameter or parameters, such as a physical constant or the exact proportion of an allelic variant in a human population, or the hypothesis may be a qualitative statement, such as This protein adopts an a/p barrel fold or I am currently in Philadelphia. The parameters or hypothesis can be unobservable or as yet unobserved. How the data arise from the parameters is called the model for the system under study and may include estimates of experimental error as well as our best understanding of the physical process of the system. 

Since derivations and literature references are typically not given in detail (often not at all) it is difficult for users to recognize errors or assess the validity of some statements when applied to a particular situation. It would be helpful for the user to appreciate limitations of applicability and to consider risk tolerance when adopting a specific practice based on minimum safe practices given in codes. 

A probabilistic statement of the likelihood of human-error events presents each error in the task analysis as the right limb in a binary branch of the HRA event tree. These binary branches form the chronological limbs of the HRA event tree, with the first potential error siai ting from the highest point on the tree. (Figure 4.5-4). Any given [ask appears as a two-limb branch the left limb represents the probability of success the right limb represents the probability of failure. 

Input validation. statements should be used to automatically check input data, to pioduce a clear message when an error is found, and to allow reentiy of eiioneous data. Data input should be echoed foi user veiification and an oppoi tiinity allowed for alteration of specific data items. 

Since equation 8.4 can be trivially solved for Oi t - 1) (= 4 [aj t) A/)] 0/c ai t + 1)), we see that any pair of consecutive configurations uniquely specifies the backwards trajectory of the system. Moreover, this statement holds true for arbitrary (and, in particular, irreversible) functions < ). An important consequence of this, first pointed out by Fredkin [vich84a], is that a numerical roundoff in digital computers need not necessarily result in a loss of information. In particular, if the computation is of the form given by equation 8.4, where roundoff error, the resulting dynamics will nonetheless be reversible and no information will be lost throughout the computation. ... 

It is desirable for the record to have an objective statement of the nature and degree of color deterioration. The simplest, but least desirable, method is comparison of sample color with color charts or plates such as those used in the Munsell system, Ridgeway s color standards, or the Maerz and Paul dictionary of color. Such a method is limited in value because of the difficulty of obtaining true color matches, and because of variations due to human error. The use of color charts or plates may be much improved in the Munsell system by employing a disk colorimeter (29). Kramer and Smith (21) have pointed out that the results obtained in its application to foods are sometimes difficult to explain and compare, and that the method requires special training of the operator and is tedious and cumbersome. 

The procedure illustrated here, besides containing only trivial technical calculations, lacks important features that are required in production programs. Extensive error checking and recovery must be performed. The procedure must detect the occurrence of a self-referential system of formulas, which would result in attempting endless recursive calls. Access to multiple raw material and formula databases adds power to the program, but must be implemented by complex code to allow flexible control of that access. The structural and input/output statements to support these features may greatly exceed the number of statements that perform modelling calculations. 

The statement of the Dirichlet difference problem providing a higher-order approximation. On the basis of the cross scheme it is possible to construct a scheme with the error of approximation 0( h j ) or 0 h ) on a solution in the case of a square (cube) grid. In order to raise the order of approximation, we exploit the fact that u = u x) is a solution of Poisson s equation... 

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