The observed functional dependency of suspension flux vs . pressure can therefore be used to derive bilayer elasticity / flexibility as well as permeability, based on theoretical description of the underlying enforced transport, viewed as an activated transport process.
32.
We say that a functional dependency f is logically implied by F, and denote it with F \ models f if and only if for every instance r of R that satisfies the functional dependencies in F, r also satisfies f.
33.
We say that a functional dependency f is logically implied by F, and denote it with F \ models f if and only if for every instance r of R that satisfies the functional dependencies in F, r also satisfies f.
34.
In other words, for each of the partitions of variables, by simplifying the expression for the distribution over the partition's variables and examining the distribution's functional dependency on the variables in question, the family of the distribution can usually be determined ( which in turn determines the value of the constant ).
35.
A notion of logical implication is defined for functional dependencies in the following way : a set of functional dependencies \ Sigma logically implies another set of dependencies \ Gamma, if any relation " R " satisfying all dependencies from \ Sigma also satisfies all dependencies from \ Gamma; this is usually written \ Sigma \ models \ Gamma.
36.
A notion of logical implication is defined for functional dependencies in the following way : a set of functional dependencies \ Sigma logically implies another set of dependencies \ Gamma, if any relation " R " satisfying all dependencies from \ Sigma also satisfies all dependencies from \ Gamma; this is usually written \ Sigma \ models \ Gamma.
37.
Another advantage of associated types over functional dependencies is that the latter requires clients using the type class to state all of the dependent types in their contexts, including ones they do not use; since associated types do not require this, adding another associated type to the class requires updating only the class's instances, while clients can remain unchanged.
38.
Furthermore, with respect to a set of inference rules A, we say that a functional dependency f is derivable from the functional dependencies in F by the set of inference rules A, and we denote it by F \ vdash _ { A } f if and only if f is obtainable by means of repeatedly applying the inference rules in A to functional dependencies in F.
39.
Furthermore, with respect to a set of inference rules A, we say that a functional dependency f is derivable from the functional dependencies in F by the set of inference rules A, and we denote it by F \ vdash _ { A } f if and only if f is obtainable by means of repeatedly applying the inference rules in A to functional dependencies in F.
40.
Furthermore, with respect to a set of inference rules A, we say that a functional dependency f is derivable from the functional dependencies in F by the set of inference rules A, and we denote it by F \ vdash _ { A } f if and only if f is obtainable by means of repeatedly applying the inference rules in A to functional dependencies in F.
