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subset See parts of collections. reaction and where a compound is represented in
the arbitrarily written formal reaction equation.
subspace A subset of a vector space that is, See also dextralateral, direction, dynamic equi-
itself, a vector space. An example is the null librium, formal reaction equation, microscopic
space of a matrix, as well as its orthogonal com- reversibility, product, rate constant, reversibil-
plement. ity, and sinistralateral.

substituent atom (group) An atom (group) successive approximation The iterative
that replaces one or more hydrogen atoms scheme by which an approximation is used for
attached to a parent structure or characteristic the basic design of an algorithm. The sequence
k
group except for hydrogen atoms attached to a generated is of the form x (k+1) = x + A(x ),
k
chalcogen atom. where A is an algorithm map specified by its
approximation to some underlying goal. Typ-
substitution In logic and logic program- ically, this is used to find a fixed point, where
ming, a substitution θ is a finite set of pairs of
A(x) = 0 (e.g., seeking f(x) = x, let A(x) =
the form X = t , where X ∈ X are unique vari- (k+1) k
i i i f(x) − x, so the iterations are x = f(x ),
ables (X = X for all i = j and X ∈ t for any
∗
∗
i j i j converging to x = f(x ) if f satisfies certain
i and j), and t ∈ t are ground terms. Thus, the
i conditions, such as being a contraction map).
result, A , of applying a substitution θ to a com-

plex term A, denoted Aθ, is the term obtained by Here are some special types:

replacing each X in A by t in the new term A , (i.) Inner approximation
i
i
for every pair X = t ∈ θ. (ii.) Outer approximation
i
i
Comment: It is important to realize that θ
(iii.) Successive linear approximation
is a set of mappings or transformations (substi-
tutions) between the variables in the variable- (iv.) Successive quadratic approximation
containing term in the original language, and
a term from the transformed language with all sufficient matrix Let A be an n × n matrix.
variables fully substituted. This mapping pro- Then, A is column sufficient if
duces the ground terms t. Thus, one can as well
[x (A ) ≤ 0 for all i] ⇒
x i
i
write θ = X = t , X = t ,..., X = t . Do
1
1
2
2
n
n
not confuse this usage with the chemical mean- [x (A ) = 0 for all i].
i
x i
ing of substitution.
Ais row sufficient if its transpose is column suffi-
substitution reaction A reaction, elemen- cient. A is sufficient if it is both column and row
tary or stepwise, in which one atom or group in a sufficient. One example is when A is symmetric
molecular entity is replaced by another atom or and positive semidefinite. This arises in linear
group. For example, complementarity problems.
CH Cl + OH − → CH OH|Cl − superset Asetwhichcontainsanotherset. If
3 3
the superset and the contained set can be equal,
substrate (1) (in biochemistry) The specific the relation between them is denoted superset ⊇
molecules which are recognized by an enzyme. contained set; otherwise it is denoted ⊃.
(2) (in chemistry) A chemical species, the Comment: The same idea can be applied to
reaction of which with some other chemical other types of collections, just considering parts
reagent is under observation (e.g., a compound of collections in the opposite sense. See also
that is transformed under the influence of a cat- bag, empty collection, list, parts of collections,
alyst). sequence, and set.
Comment: The term should be used with care.
Either the context or a specific statement should surface tension, γ, σ σ σ Work required to
γ, γ,
always make it clear which chemical species in increase a surface area divided by that area.
a reaction is regarded as the substrate. The dis- When two phases are studied it is often called
tinction is between the molecular material of a interfacial tension.
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC