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Airy equation The equation y − xy = 0. almost K¨ahler An almost K¨ahler manifold
is an almost Hermitian manifold (M,J,g) such
AKNS method A procedure developed by that the fundamental two-form ; defined by
Ablowitz, Kaup, Newell, and Segur (1973) that ;(u, v) = g(u, Jv) is closed.
allows one, given a suitable scattering problem,
to derive the nonlinear evolution equations solv- almost periodic A function f(t) is called
able by the inverse scattering transform. almost periodic if there exists T(") such that for
any " and every interval I = (x, x + T(")),
"
algebra An algebra over a field F is a ring there is x ∈ I such that, |f(t + x) − f(t)| <".
"
R which is also a finite dimensional vector space
over F, satisfying (ax)(by) = (ab)(xy) for all α α α-limit set Consider a dynamical system
a, b ∈ F and all x, y ∈ R. u(t) in a metric space (M, d) which is described
by a semigroup S(t), i.e., u(t) = S(t)u(0),
n
algebraic equation Let f(x) = a x + S(t + s) = S(t) · S(s) and S(0) = I. The α-
n
a x n−1 + ...+ a x + a be a polynomial in limit set, when it exists, of u ∈ M,or A ⊂ M,
n−1 1 0 0
R[x], where R is a commutative ring with unity. is defined as
n
The equation a x + a n−1 x n−1 + ... + a x + −1
1
n
a = 0 is called an algebraic equation. α(u ) = S(−t) u ,
0
0
0
s≤0 t≤s
ALGOL A programming language. or

−1
α(A) = S(−t) A.
algorithm A process consisting of a specific
s≤0 t≤s
sequence of operations to solve certain types of
problems. Notice, φ ∈ α(A) if and only if there exists
a sequence ψ converging to φ in M and a
n
alignment In dealing with sequence data sequence t →+∞, such that φ = S(t )ψ ∈
n
n
n
such as DNAs and proteins, one compares two A, for all n.
such molecules by matching the sequences.
alphabet A set of letters or other characters
Sequence alignment means finding optimal
with which one or more languages are written.
matching, defined by some criteria usually called
“scores.” Between two binary sequences, for
alternating series A series that alternates
example, the Hamming distance is a widely used n
signs, i.e., of the form (−1) a , a ≥ 0.
n
n
score function. n
alternation For any covariant tensor field
almost complex manifold A manifold with
K on a manifold M the alternation A is defined
an almost complex structure.
as
almost complex structure A manifold M is 1
(AK)(X , ..., X ) = (sign π)
r
1
said to possess an almost complex structure if it r!
π
carries a real differentiable tensor field J of type
2
(1, 1) satisfying J =−I. K(X π(1) , ..., X π(r) )
where the summation is taken over all r! permu-
almosteverywhere Apropertyholdsalmost
tations π of (1, 2, ..., r).
everywhere (a.e.) if it holds everywhere except
on a set of measure zero.
amplitude of a complex number The angle
θ is called the amplitude of the complex number
almost Hermitian A manifold M with a iθ
z = re = r(cos θ + i sin θ).
Riemannian metric g invariant by the almost
complex structure J, i.e., g and J satisfy amplitude of oscillation The simplest equa-
2
tion of a linear oscillator is m d x 2 =−kx. It has
g(Ju, Jv) = g(u, v) √
dt
the solution x(t) = A cos(t k/m − c). A is
for any tangent vectors u and v. called the amplitude.
© 2003 by CRC Press LLC