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antibody A protein (immunoglobulin) pro- approximate solution Consider the differ-
duced by the immune system of an organism in ential equation (*) x = f(x, t) , x ∈ ; ⊂

n
response to exposure to a foreign molecule (anti- R ,t ∈ [a, b]. The vector valued function y(t)

gen) and characterized by its specific binding to is an "-approximate solution of (*) if y (t) −
a site of that molecule (antigenic determinant or f(t, y(t)) R n <", for all t ∈ [a, b].
epitope).
arc (1) A segment, or piece, of a curve.
anticommutator If A, B are two linear (2) The image of a closed interval [a, b] under
a one-to-one, continuous map.
operators, their anticommutator is {A, B}=
AB + BA.
n
arc length Let σ :[a, b] → R be a C 1
antiderivation A linear operator T on a curve. The arc length l(σ) of σ is defined as
graded algebra (A, ·) satisfying T(a · b) = Ta · b
b + (−1) (degree of b) a · Tb for all a, b ∈ A. l(σ) = σ (t) dt.

a
antiderivative A function F(x) is called an
arccosecant The inverse trigonometric

antiderivative of a function f(x) if F (x) =
function of cosecant. The arccosecant of a
f(x).
number x is a number y whose cosecant is x,
−1
written as y = csc (x) = arc csc(x), i.e.,
antigen A substance that stimulates the
x = csc(y).
immune system to produce a set of specific
antibodies and that combines with the antibody
arccosine The inverse trigonometric func-
through a specific binding site or epitope.
tion of cosine. The arccosine of a number x
is a number y whose cosine is x, written as
antimatter Matter composed of antipar- −1
y = cos (x) = arc cos(x), i.e., x = cos(y).
ticles.
arccotangent The inverse trigonometric
antiparticle A subatomic particle identical
function of cotangent. The arccotangent of a
to another subatomic particle in mass but oppos-
number x is a number y whose cotangent is
ite to it in the electric and magnetic properties. −1 −1
x, written as y = cot (x) = ctn (x) =
antiselfdual A gauge field F such that F = arc cot(x), i.e., x = cot(y).
−∗ F, where ∗ is the Hodge-star operator.
arcsecant The inverse trigonometric func-
aphelion The point in the path of a celestial tion of secant. The arccosecant of a number x
is a number y whose secant is x, written as
body (as a planet) that is farthest from the sun. −1
y = sec (x) = arc sec(x), i.e., x = sec(y).
apogee The point in the orbit of an object (as
arcsine The inverse trigonometric function
a satellite) orbiting the earth that is the greatest
of sine. The arcsine of a number x is a number
distance from the center of the earth. −1
y whose sine is x, written as y = sin (x) =
applied potential The difference of poten- arc sin(x), i.e., x = sin(y).
tial measured between identical metallic leads
arctangent The inverse trigonometric func-
to two electrodes of a cell. The applied poten-
tion of tangent. The arctangent of a number x
tial is divided into two electrode potentials, each
is a number y whose tangent is x, written as
of which is the difference of potential existing −1
y = tan (x) = arc tan(x), i.e., x = tan(y).
between the bulk of the solution and the interior
of the conducting material of the electrode, an
area of surface Consider thesurfaceS given
iR or ohmic potential drop through the solution, by z = f (x, y) that projects onto the bounded
and another ohmic potential drop through each region D in the xy-plane. The area A(S) of the
electrode. surface S is given by
In the electroanalytical literature this quan-

tity has often been denoted by the term voltage, A(S) = f + f + 1 dD.
2
2
y
x
whose continued use is not recommended. D
© 2003 by CRC Press LLC