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absorbing set A convex set A ⊂ X in a vec- adduct formation) for the members of a series
tor space X is called absorbing if every x ∈ X of structurally similar indicator bases (or acids)
lies in tA for some t = t(x) > 0. of different strengths. The best known of these
functions is the Hammett acidity function H (for
0
acceleration The rate of change of velocity uncharged indicator bases that are primary aro-
with time. matic amines).

acceleration vector If v is the velocity vec- action (1) The action of a conservative
d v
tor, then the acceleration vector is a = ;or if
dt dynamical system is the space integral of the total
s is the vector specifying position relative to an momentum of the system, i.e.,
2
d s d s
origin, we have v = and hence a = 2 .
dt dt

d r i
P 2
acceptor A compound which forms a chem- m i dt · d r i
P 1 i
ical bond with a substituent group in a bimolecu-
lar chemical or biochemical reaction.
where m is the mass and r the position of the
i
i
Comment: The donor-acceptor formalism is
ith particle, t is time, and the system is assumed
necessarily binary, but reflects the reality that few
to pass from configuration P to P .
1
2
if any truly thermolecular reactions exist. The
(2) Action of a group: A (left) action of a
bonds are not limited to covalent. See also donor.
group G on a set M is a map ) : G×M −→ M
such that:
accumulation point Let {z } be a sequence
n
of complex numbers.An accumulation point of (i.) )(e, x) = x, for all x ∈ M, e is the
{z } is a complex number a such that, given any identity of G;
n
"> 0, there exist infinitely many integers n such (ii.) )(g, )(h, x)) = )(g · h, x), for all
that |z − a| <". x ∈ M and g, h ∈ G.(g · h denotes the group
n
operation (multiplication) in G.
accumulator In a computing machine, an
adder or counter that augments its stored number If G is a Lie group and M is a smooth mani-
by each successive number it receives. fold, the action is called smooth if the map ) is
smooth.
accuracy Correctness, usually referring to An action is said to be:
numerical computations.
(i.) free (without fixed points)if )(g, x) =
x, for some x ∈ M implies g = e;
acidity function Any function that meas-
ures the thermodynamic hydron-donating or (ii.) effective (faithful) if )(g, x) = x for all
-acceptingabilityofasolventsystem, oraclosely x ∈ M implies g = e;
related thermodynamic property, such as the ten- (iii.) transitive if for every x, y ∈ M there
dency of the lyate ion of the solvent system exists a g ∈ G such that )(g, x) = y.
to form Lewis adducts. (The term “basicity
See also left action, right action.
function” is not in common use in connection
with basic solutions.) Acidity functions are not
unique properties of the solvent system alone, action angle coordinates A system of gen-
but depend on the solute (or family of closely eralized coordinates (Q ,P ) is called action
i
i
related solutes) with respect to which the thermo- angle coordinates for a Hamiltonian system
dynamic tendency is measured. defined by a Hamiltonian function H if H
Commonly used acidity functions refer to depends only on the generalized momenta P but
i
concentrated acidic or basic solutions. Acidity not on the generalized positions Q . In these
i
functions are usually established over a range coordinates Hamilton’s equations take the form
of composition of such a system by UV/VIS
∂P ∂Q ∂H
spectrophotometric or NMR measurements of i = 0 , i =
the degree of hydronation (protonation or Lewis ∂t ∂t ∂P i
© 2003 by CRC Press LLC