Error Proofing

The proof of protection is more difficult to establish in this case for two reasons. First, the object is to restore passivity to the rebar and not to render it virtually immune to corrosion. Second, it is difficult to measure the true electrode potential of rebars under these conditions. This is because the cathodic-protection current flowing through the concrete produces a voltage error in the measurements made (see below). For this reason it has been found convenient to use a potential decay technique to assess protection rather than a direct potential measurement. Thus a 100 mV decay of polarisation in 4 h once current has been interrupted has been adopted as the criterion for adequate protection. It will be seen that this proposal does not differ substantially from the decay criterion included in Table 10.3 and recommended by NACE for assessing the full protection of steel in other environments. Of course, in this case the cathodic polarisation is intended to inhibit pit growth and restore passivity, not to establish effective immunity. 

The proof of this relationship is one of the triumphs of probability theory. The underlying considerations will be outlined here because they are basic to an understanding of the counting error. These considerations are most obviously applicable to radioactive systems, and it was to these that they were first applied.3... 

This chapter has shown, however, that errors can be investigated and evaluated with more assurance in x-ray emission spectrography than in the general run of analytical methods. The standard counting error (10.3) can serve as a satisfactory criterion of operating conditions and as a standard of reference to which the other errors are conveniently -compared. But it is manifestly unwise to assume without proof, as has often been done, that the standard counting error gives the precision of the analytical result. 

Proof of Theorem 4-9. The proof of Theorem 4-9 is somewhat lengthy, but the intuitive idea behind it is simple. We will first show that the equivocation per digit between source and output is at least (BT — CT)Tt. This average uncertainty about the input given the output can be broken into two terms first the uncertainty about whether an error was made and second the uncertainty about the source digit when errors are made. These are the terms on the right side of Eq. (4-66). 

To complete the proof, we must relate the equivocation on the ft digit, H(Un Fn), to the probability of error on the digit, Pe,n. It will be shown in the rext few paragraphs that... 

In this section, we shall state the final theorem necessary to give unity to the previous results if RT < CT, then reliable communication is possible with as small an error probability as desired. This remarkable theorem was first stated and essentially proved in 1948 by C. E. Shannon.10 The first rigorous proof of the theorem was given by Feinstein,11 and a number of other proofs and generalizations have subsequently been given. 

The implications and interpretations of this theorem require considerable discussion and this will precede the proof. First observe that Eq. (4-91) yields a bound on error probability independent of the source statistics thus it is applicable to any source of rate less than R after appropriate source coding. 

Note added in proof The calculated spin alignment spectra for diffusive motion plotted in Fig. 12 are incorrect, in particular the oscillations in the central part, due to a sign-error in the computer program. 

The proof of convergence of scheme (19) reduces to the estimation of a solution of problem (21) in terms of the approximation error. In the sequel we obtain such estimates using the maximum principle for domains of arbitrary shape and dimension. In an attempt to fill that gap, a non-equidistant grid... 

In recent years some theoretical results have seemed to defeat the basic principle of induction that no mathematical proofs on the validity of the model can be derived. More specifically, the universal approximation property has been proved for different sets of basis functions (Homik et al, 1989, for sigmoids Hartman et al, 1990, for Gaussians) in order to justify the bias of NN developers to these types of basis functions. This property basically establishes that, for every function, there exists a NN model that exhibits arbitrarily small generalization error. This property, however, should not be erroneously interpreted as a guarantee for small generalization error. Even though there might exist a NN that could... 

The above explanation of autoacceleration phenomena is supported by the manifold increase in the initial polymerization rate for methyl methacrylate which may be brought about by the addition of poly-(methyl methacrylate) or other polymers to the monomer.It finds further support in the suppression, or virtual elimination, of autoacceleration which has been observed when the molecular weight of the polymer is reduced by incorporating a chain transfer agent (see Sec. 2f), such as butyl mercaptan, with the monomer.Not only are the much shorter radical chains intrinsically more mobile, but the lower molecular weight of the polymer formed results in a viscosity at a given conversion which is lower by as much as several orders of magnitude. Both factors facilitate diffusion of the active centers and, hence, tend to eliminate the autoacceleration. Final and conclusive proof of the correctness of this explanation comes from measurements of the absolute values of individual rate constants (see p. 160), which show that the termination constant does indeed decrease a hundredfold or more in the autoacceleration phase of the polymerization, whereas kp remains constant within experimental error. 

However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the interfacial and bulk pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of Ajy is also basis of other methods, like spin-labeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the Aj by means of these methods may be loaded with an error of up to 50mV [19]. For some the potentials determined by these methods, Ajy values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of A>. 

The drag is safe and effective but the approval system rejects it, because it demands more proof. We will call this a type I error . 

It is certainly true that for any arbitrarily chosen equation, we can calculate what the point described by that equation is, that corresponds to any given data point. Having done that for each of the data points, we can easily calculate the error for each data point, square these errors, and add together all these squares. Clearly, the sum of squares of the errors we obtain by this procedure will depend upon the equation we use, and some equations will provide smaller sums of squares than other equations. It is not necessarily intuitively obvious that there is one and only one equation that will provide the smallest possible sum of squares of these errors under these conditions however, it has been proven mathematically to be so. This proof is very abstruse and difficult. In fact, it is easier to find the equation that provides this least square solution than it is to prove that the solution is unique. A reasonably accessible demonstration, expressed in both algebraic and matrix terms, of how to find the least square solution is available. 

A proof of this statement can be found in Hamilton (1964). The square-root of of2 is usually referred to as the standard error of mean. 

Section Five Is a review of writing basics. The parts of speech and common grammatical errors are explained and made goof-proof. Spelling, punctuation marks, and capitalization are also covered. 

Spelling errors are unacceptable in your college admissions essay. Learn the Goof-Proof Spelling Rules to write error-free. 

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