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step in the computation where the output pro- symmetries; the associated conserved current is
duced is not a function of the input presented, given by
even though all inputs and outputs exist with ∂L λ
E = X
probability one. See deterministic and stochastic ∂u λ
computations. λ λ
where (x ,u ) are local coordinates on the tan-
gent bundle TM.
nonenzymaticdegree Thedegreeofareact-
ive conjunction node excluding the macro-
nuclear decay A spontaneous nuclear trans-
molecular catalyst.
formation.
nonlinear optical effect An effect brought
nuclear fission The division of a nucleus
about by electromagnetic radiation the magni- into two or more parts with masses of equal order
tude of which is not proportional to the irradi- of magnitude, usually accompanied by the emis-
ance. Nonlinear optical effects of importance sion of neutrons, gamma radiation, and, rarely,
to photochemistry are harmonic frequency small charged nuclear fragments.
generation, lasers, Raman shifting, upconver-
sion, and others. nucleic acids Macromolecules, the major
organic matter of the nuclei of biological cells,
norm (of a vector) See angle between vec- made up of nucleotide units, and hydrolyzable
tors, normed space. into certain pyrimidine or purine bases (usually
adenine, cytosine, guanine, thymine, or uracil),
normal Perpendicular, as a vector to a sur- d-ribose or 2-deoxy-d-ribose, and phosphoric
face or to another vector. acid.
See deoxyribonucleic acids.
normedspace AvectorspaceX withanorm
||x|| defined, for x ∈ X, satisfying
nucleosides Ribosyl or deoxyribosyl de-
(i.) ||x|| ≥ 0 and equality only when x = 0, rivatives (rarely, other glycosyl derivatives) of
certain pyrimidine or purine bases. They are
(ii.) ||x + y||≤||x||+||y||, and
thus glycosylamines or N-glycosides related to
(iii.) ||λx||=|λ|||x||.
nucleotides by the lack of phosphorylation. It has
alsobecomecustomarytoincludeamongnucleo-
N¨other’s theorem (1)Ifthe Lie algebra
sides analogous substances in which the glycosyl
g acts canonically on the Poisson manifold P ,
group is attached to carbon rather than nitrogen
admits a momentum map J : P → g , and
∗
(“C-nucleosides”). See also nucleic acids.
H ∈ C (P) is g-invariant, i.e., ξ (H) = 0 for
∞
P
all ξ ∈ g, then J is a constant of the motion for
nucleotides Compounds formally obtained
H, i.e.,
by esterification of the 3 or 5 hydroxy group of

J ◦ ϕ = J nucleosides with phosphoric acid. They are the
t
where ϕ is the flow of the Hamiltonian vector monomers of nucleic acids and are formed from
t
field X . them by hydrolytic cleavage.
H
(2) (of a Lagrangian system) A map between
1-parameter families of Lagrangian symmetries nuclide A species of atom, characterized by
and conserved currents. For example, let (M, its mass number, atomic number, and nuclear
L) be a time-independent Lagrangian system energy state, provided that the mean life in that
λ
and X = X ∂ an infinitesimal generator of state is long enough to be observable.
λ

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