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a traditional name. Any replacement by con- and f : A → B, with f : a → b. Notice that
sistent terminology would produce unnecessary according to this definition, which is standard in
confusion in the polymer literature. Synony- algebra, the map f : x → 1 is not a function
x
mous with viscosity number. f : R → R since it is not defined in 0 ∈ R.
Of course, it is a function on the smaller space
reference material A substance or mixture R −{0}.
ofsubstances, thecompositionofwhichisknown
within specified limits, and one or more of the
relative molar mass Molar mass divided by
properties of which is sufficiently well estab- −1
1 g mol (the latter is sometimes called the
lished to be used for the calibration of an appar-
standard molar mass).
atus, the assessment of a measuring method or
for assigning values to materials. Reference
materials are available from national laborator-
relative molecular mass, M M M r r r Ratio of the
ies in many countries [e.g., National Institute for mass of a molecule to the unified atomic mass
Standards and Technology (NIST), U.S., Com- unit. Sometimes called the molecular weight or
munity Bureau of Reference, U.K.].
relative molar mass.

regulatory motif A conserved topological
motif which reduces or increases the activity of relative responsivity See responsivity.
a gene, enzyme, or macromolecular complex.
Comment: See also biochemical, chemical,
relative viscosity The ratio of the viscosity
dynamical, functional, kinetic, mechanistic,
η of the solution to the viscosity η of the sol-
s
phylogenetic, thermodynamic, and topological
vent, i.e., η = η/η . Synonymous with viscos-
s
r
motives.
ity ratio.
relation (between two sets) A relation
between A and B is any subset R ⊂ A×B of the relative viscosity increment The ratio of
Cartesian product of the two sets. If (a, b) ∈ R the difference between the viscosities of solution
we say that a is related to b (in that order), and and solvent to the viscosity of the solvent, i.e.,
we write aR b. If R can be produced by some η = (η − η )/η , where η is the viscosity of the
s
i
s
operation or procedure r, then we often call r the solution and η is the viscosity of the solvent.
s
relation. The use of the term “specific viscosity” for
For example, consider A = {a, b, c} and B = this quantity is discouraged, since the relative
{1, 2, 3}, and let r(a , b ), a ∈ A, b ∈ B, 1 ≤ viscosity increment does not have the attributes
i
i
i
i
i ≤ 3. Then R = {(a, 1), (b, 2), (c, 3)}. of a specific quantity.
Consider a relation r between two sets A
and B. A is called the domain of r and B its
codomain. The elements of B related, via a rela- relaxation oscillator For some oscillatory
tion r to an element a ∈ A is called the image of a dynamics with a limit cycle, parts of the cycle are
under r, and denoted by r(a). The union r(A) of traversed quickly in comparison with other parts.
all r(a), a ∈ A, is called the range of r, and can This is often referred to as a relaxation oscilla-
also be denoted I. Thus, r(A) may be a proper tor. This phenomenon suggests that the under-
subset of B. So, the range is not necessarily the lying ordinary differential equations for such a
same as the codomain. system have a small parameter which is present
See also domain, image, and range, and rela- in a crucial place to cause this rapid variation in
tion. the solution. A widely used class of models for
A relation f is called a function if for each such phenomena is a system du/dt = f(u,α),
a ∈ A there exists a unique b ∈ B such that af b. dα/dt = "g(u,α) which can be analyzed by
If f is a function and a f b we writef (a) = b singular perturbation for small ".

© 2003 by CRC Press LLC
© 2003 by CRC Press LLC