Specified relation

Equation (21) already has the form of a fluctuation theorem. However, in order to get a proper flucmation theorem we need to specify relations between probabilities for physically measurable observables rather than paths. From Eq. (21) it is straightforward to derive a fluctuation theorem for the total dissipation S. Let us take b C) = With this choice we get... 

In an expert system some essential components can be identified. A first part is a set of facts which specify relations between defined objects. This part is often referred to as the data base. A second part is a collection of rules which specify how to reach conclusions by combining the facts. In most cases a rule is equivalent to a statement about relations between object clauses, or it may be given as a relation between not fully defined objects. Thus, the boundary line between rules and facts is rather illdefined. 

Abstract models are very powerful, but at the same time, the abstractness is their Achilles heel. Many people have problems operating on such a high level of abstraction and have difficulties grasping the concept. A middle ground where XML-based formats provide the scaffold for expressing the basics and RDF or other mechanisms are used to specify relations may provide more suitable practical applications. 

Through analysis of batch surveys and stability data, determine and identify specified related substances ( 0.1%) unspecified related substances (typically occurring at levels between 0.05 and 0.10%) should also be determined. 

Goal All related substances must be chromatographically resolved from the active substance nothing should coelute with a specified related substance. Unspecified related substances could coelute with each other but must not coelute with the active, specified related substance or an excipient of the formulation. 

The study of protein function is increasingly focused on the interactions between protein structure, electrochemical potentials, and molecular motion. For membrane proteins, insertion through a phospholipid bilayer imparts a defined orientation to the protein and a specified relation between the macroscopic electrical field and the axis of the molecule normal to the membrane. These constraints can be exploited to obtain detailed information about membrane protein function and dynamics, particularly for proteins that form aqueous pores through membranes. The ability to record currents that... 

Pulse duration The time interval between the points on the leading and trailing edges of a pulse at which the instantaneous value bears a specified relation to the peak pulse amplitude. 

First, let us identify all of the given values and specified relations for the problem ... 

Given specified relations = 14(9 + 5 as shown above) So we have... 

Total known/specified relations = 34 + 14 = 48 Total unknowns = 48... 

This allows a definition of logic algorithm correctness that is only in terms of the specifications of the used predicates. It establishes an equivalence between the specified relation and the set of Herbrand-logical consequences of the logic algorithm. 

Select an induction parameter such that, given a ground instance of it, the specified relation holds for at most one ground instance of the other parameters. 

Select a well-founded relation that reflects the definition of the type of some other parameter, or that reflects the structure of the specified relation. 

Let be the relation one has in mind when elaborating a specification of a procedure for predicate r. We call the intended relation, in contrast to the relation actually specified, called the specified relation. This distinction is very important in general, but crucial with incomplete specifications, where one deliberately admits a gap between the two. 

Definition 6-2 The specified relation of a specification by examples and properties is the set of tuples extracted from the set of its Herbrand-logical consequences. 

We now formally define the notion of specified relation. It consists of the set of /2-tuples for which the specified predicate r n is true according to the specification, and of the set of /2-tuples for which r n is false according to the specification ... 

It is clear that the specified relation is usually different from the intended relation. It is usually expected to be a subset of the intended relation, though. It is also clear that EP r) is not always the complement of EP (r), We however assume that EP(r) is internally consistent, that is that the intersection between EP (r) and EP (r) is empty. 

The specified relation of a consistent specification is thus a subset of the intended relation. Moreover, if LA(r) is partially or totally correct wrt E(r) (respectively P(r)), and E(f) (respectively P(r)) is consistent with then LA(f) is partially correct wrt If there is no formal definition of the intended relation then some correctness criteria cannot be applied in a formal way. But they can be used to state features and heuristics of a synthesis mechanism. 

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