Partial verification

In the ideal study, the results of aU patients tested with the test under evaluation are contrasted with the results of a single reference standard. If fewer than all patients are verified with the reference standard, then partial verification exists, and verification bias may occur if the selection of subjects for reference testing is not purely random. For example, if selection is associated with the outcome of the index test, or the strength of prior suspicion, or both, then verification bias is certain. In a typical case, some patients with negative test results (test-negatives) are not verified by the reference standard if this involves a costly or invasive procedure, and these patients are not included in the analysis. This may result in an underestimation of the number of false-negative results. 

At equilibrium the gaa i must therefore have the same partial pressure on eaoh side of the membrane. It seems that this relation has not been very adequately confirmed, although Planckf reported a partial verification using a hydrogen-palladium system. It is possible that a more complete test of (3 27) could be carried out by use of the remarkable zeolites which have been shown by Barrer to act as molecular sieves. 

Formal verification that this result actually satisfies Equation (14.13) is an exercise in partial differentiation, but a physical interpretation will confirm its validity. Consider a small group of molecules that are in the reactor at position z at time t. They entered the reactor at time i = t — (zju) and had initial composition a t, z) = ai (t ) = ai (t — z/u). Their composition has subsequently evolved according to batch reaction kinetics as indicated by the right-hand side of Equation (14.14). Molecules leaving the reactor at time t entered it at time t — t. Thus,... 

In our view the final verification was given to this conclusion in paper [66] in which simultaneous O2 adsorption on partially reduced ZnO and resultant change in electric conductivity was studied. It was established in this paper that the energies of activation of chemisorption and that of the change of electric conductivity fully coincide. The latter is plausible only in case when localization of free electron on SS is not linked with penetration through the surface energy barrier which is inherent to the model of the surface-adjacent depleted layer. 

More specifically, the basic notions of a Turing Machine, of computable functions and of undecidable properties are needed for Chapter VI (Decision Problems) the definitions of recursive, primitive recursive and partial recursive functions are helpful for Section F of Chapter IV and two of the proofs in Chapter VI. The basic facts regarding regular sets, context-free languages and pushdown store automata are helpful in Chapter VIII (Monadic Recursion Schemes) and in the proof of Theorem 3.14. For Chapter V (Correctness and Program Verification) it is useful to know the basic notation and ideas of the first order predicate calculus a highly abbreviated version of this material appears as Appendix A. 

Appendix A contains a brief summary of sane relevant ideas of satisfiability and validity of well-formed formulas in the predicate calculus. Using these ideas it gives a definition of partial and total correctness of a scheme with respect to a well-formed formula as output criterion. The treatment is cursory and nonrigorous. Readers who have not seen these ideas before should examine this appendix before we return to the treatment of correctness and program verification in Chapter V, and finally conclude this treatment in Chapjter VII. 

In this chapter we discuss techniques for program verification and their mathematical justification. The basic idea behind these methods was originally presented by Floyd mathematical formulations and logical justifications were developed by Cooper and Manna, and others, and continued in King s Ph.D. thesis in which he presented the development of a partial implementation for these techniques. A sanewhat different axiomatic approach has been pursued by Hoare et al. The reader who has never made acquaintance with the formalism of the first order predicate calculus should at this point turn to Appendix A for a brief and unrigorous exposition of the material relevant to this chapter. 

Send verification conditions into a THEOREM PROVER. If all conditions are proven correct, print "PARTIALLY CORRECT WITH RESPECT TO A AND B ". If any verification condition is either proven incorrect by the THEOREM PROVER or else is rejected or not handled by the THEOREM PROVER, return to either 2) or 3), calling for new input. 

First we discuss a version of the verification procedure which provides a sufficient condition for partial correctness - if the procedure gives a positive answer, then tie program is indeed partially correct for the given input and output criteria. However, the condition is not necessary - the program can be partially correct yet no choice of inductive assertions will make the procedure "work". This leads us to the complete procedure, which is rather more complex and lengthy. 

After all this has been done, we apply the usual verification procedure to the main program and to each procedure body - constructing verification conditions and sending them to a THEOREM PROVER just as before. We claim that if all the verification conditions hold for the main program and all procedures, then the whole program is partially correct for A and B. ... 

Now we have a method that is both necessary and sufficient to demonstrate partial correctness. We have already seen that if these verification conditions all hold, then the program is indeed partially correct for the given criteria. The arguments used in Chapter V can be adapted to show that if partial correctness holds, then some choice of inductive assertions will make the verification conditions true. 

This enables one to detail an interactive verification procedure for flowchart based programs such that if the procedure returns a yes answer, then the program is indeed partially correct with respect to the given input and output criteria. The catch, discussed in Chapter V and justified in Chapter VI, is that it may not be possible to find I In fact, there can be no mechanical procedure which, when I exists, will eventually locate it and establish the validity of the interpreted formula. 

Show that (PqjD is partially correct with respect to A and B by first generating the verification conditions for (P, I) and this choice of inductive assertions Aa and Ag and of input predicate B, and then checking the verification conditions. You may be reasonably informal in establishing that the verification conditions hold for all x,yl,y2 z domain of 1 ... 

A discussion of the applicability of the MPT model to a particular electroless system ideally presumes knowledge of the kinetics and mechanisms of the anodic and cathodic partial reactions, and experimental verification of the interdependence or otherwise of these reactions. However, the study of the kinetics, catalysis, and mechanistic aspects of electroless deposition is an involved subject and is discussed separately. 

Godeffoid, P. (1991) Using Partial Orders to Improve Automatic Verification Methods. Proceedings of the 2nd Workshop on Computer-Aided Verification, vol. 531 of LNCS, Springer, Berlin, pp. 176-185. 

Electroless Deposition in the Presence of Interfering Reactions. According to the mixed-potential theory, the total current density, is a result of simple addition of current densities of the two partial reactions, 4 and However, in the presence of interfering (or side) reactions, 4 and/or may be composed of two or more components themselves, and verification of the mixed-potential theory in this case would involve superposition of current-potential curves for the electroless process investigated with those of the interfering reactions in order to correctly interpret the total i-E curve. Two important examples are discussed here. 

The metal is chelated by an ene-1,2-dithiolate (dithiolene) of the dihydropyran ring which is fused to a partially reduced pteridine 178. The syntheses of these molybdopterin-related proligands were described as model compounds for verification of the stability in vitro <2001CC 123>. The proligand 179 is a relatively stable compound however, after several weeks, the pyran ring opened and oxidation to the diol derivatives 180 was observed (Scheme 35). 

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