Certain answers

A certain answer may be found (Lowdin 1955) by considering the first-order density matrix y(x x1) defined by Eq. II.9. By means of the basis y>k and formula III. 14, this matrix may be expressed in the form... 

Answer (d) is correct. I2 (I mol) is the limiting reagent in this reaction. If the reaction were to go to completion, 2 mol HI would be produced. Thus, the only way that 2 mol HI could be produced (answer b) would be if KQ were infinite. 1 mol HI could be produced (answer a), but without knowing the value of Kt for this reaction, we cannot be sure. The only certain answer is that something less than 2 mol HI are produced, answer (d). 

Certain answers to these questions can be offered. The most persuasive answer to the question of the source of O is that oxyhemoglobin itself is the culprit. Although dioxygen is usually released from oxyhemoglobin, some of the time oxyhemoglobin may dissociate to ferrihemoglobin (methemoglobin) and Oz ... 

Most certainly," answered Edward "the title with which chemists were supposed to be most honorably distinguished was, artists of separation." "It is not so any more," replied Charlotte "and it is well that it is not. It is a higher art, and it is a higher merit, to unite. An artist of union is what we should welcome in every province of the universe". 

These questions always have an expectation attached to them. They indicate to the listener the answer the questioner wants to hear. Therefore the patient is led in the direction of a certain answer. They may be used in a positive manner to stimulate the flow of conversation. The idea here is that they should anticipate a likely response to show a common understanding and therefore help to develop a rapport, e.g. It s a lovely day today, isn t it ... 

These data may give a certain answer to the repeatedly discussed question of the amount of hydrogen absorbed in the molecular form on suspended particles of nonmetallic impurities in the aluminum melt. 

In the probabilistic context, we assign a probability to every answer. Intuitively, we consider the certain answers with respect to each possible mapping in isolation. The probability of an answer t is the sum of the probabilities of the mappings for which t is deemed to be a certain answer. We define by-table answers as follows ... 

In the case of by-table semantics, answering queries is conceptually simple. Given a p-mapping pM = (S, T. m) and an SPJ query Q, we can compute the certain answers of Q under each of the mappings me m. We attach the probability Pr(m) to every certain answer under m. If a tuple is an answer to Q under multiple mappings in m, then we add up the probabilities of the different mappings. 

To extend the by-table query-answering strategy to by-tuple semantics, we would need to compute the certain answers for every mapping sequence generated by pM. However, the number of such mapping sequences is exponential in the size of the input data. The following example shows that for certain queries, this exponential time complexity is inevitable. 

As already explained in Sect. 4.3, to represent all possible databases, we must consider the set of all possible target instances consistent with JK and the source instance I. Since there may be several target instances, we must consider the intersection fjy. (/ ), the intersection being called the set of the certain answers of q. 

In Fagin et al. [2005a], the semantics of query answering has been defined by considering the universal solutions. Indeed, it is important to ascertain whether certain answers of a query can be computed by query evaluation on the good target instance that has been chosen for materialization. In Sect. 2, we have already... 

However, the query rewriting algorithm may still be incomplete, as it explicitly avoids recursion. The validity of the incomplete results is proved experimentally, by measuring their approximation with respect to the complete set of certain answers. However, it is still an open problem how to bridge the completeness gap in an efficient way. 

The question again arises whether the effect of ATP is due merely to its presence and to its attachment to the actomyosin, or is due to the process of breakdown. This question is more easily and certainly answered for the dissociation of the two proteins in solution than for the... 

In general, despite the numerous theoretical and experimental advances made in molecular spectroscopy, many fundamental questions remain unanswered. While certain answers could be attained by extending current theoretical models, new ones must be developed to gain a deeper perspective on these problems. 

In the second (AR theory) approach, it is first assumed that a certain answer is achievable, and then we determine what is required to achieve it. 

The conditional entropy H(A B) is calculated analogously to equation (134) but with the conditional probabiIities p(a m) instead of p.. These probabilities are estimated for all answers a and classes m from a prediction set (Chapter 11.2). The entropy which is connected with a certain answer - e.g. answer yes - is given in equation (140). 

During the actual audit, checklists gather information for audit reviews. Certain answers to checklist questions may indicate an audit issue. For example, a no answer to the question Are portable fire extinguishers located at least every 50 feet in the process unit is an audit issue if extinguishers are required to be located at those... 

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