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characteristicpolynomial Seecharacteris- chemical equation A balanced elementary
tic equation. reaction equation, bimolecular or less on one
side, which describes the organic chemistry of
characteristic set The characteristic set of
the noncatalytic species of an overall biochem-
a pseudodifferential operator P is the subset
ical reaction by one of five fundamental organic
∗
Char(P ) ⊂ T M − 0 defined by p(x, ξ) = 0,
mechanisms (substitution, addition, elimina-
where p(x, ξ) : T M − 0 → R is the principal tion, rearrangement, and oxidation-reduction).
∗
symbol of P .
Equally, a set of such reaction equations which
characteristic x-ray emission X-ray emis- sums to the overall biochemical reaction.
sion originates from the radiative decay of Comment: These mechanisms distinguish
electronically highly excited states of matter. all the various subtypes (nucleophilic, elec-
Excitation by electrons is called primary excita- trophilic, free-radical; heterolytic, homolytic,
tion and by photons, secondary or fluorescence pericyclic; direct electron, hydride, hydrogen
excitation. Particle induced x-ray emission atom transfer, ester intermediates, displacement,
(PIXE) is produced by the excitation of heav- and addition-elimination reactions).
ier particles such as protons, deuterons, or heavy
atoms in varying degrees of ionization. Emis- chemical measurement process (CMP) An
sion of photons in the x-ray wavelength region analytical method of defined structure that has
occurs from ionized gases or plasmas at high been brought into a state of statistical control,
temperatures, nuclear processes (low-energy end such that its imprecision and bias are fixed,
of the gamma-ray spectrum) and from radiative given the measurement conditions. This is
transitions between muonic states. prerequisite for the evaluation of the performing
Characteristic x-ray emission consists of a characteristics of the method, or the development
series of x-ray spectral lines with discrete fre- of meaningful uncertainty statements concerning
quencies, characteristic of the emitting atom. analytical results.
Other features are emission bands from transi-
tions to valence levels. In a spectrum obtained chemical motif A motif describing a chem-
with electron or photon excitation the most ical relationship between two compounds in the
intense lines are called diagram lines or normal donor-acceptor formalism.
x-ray lines. They are dipole allowed transitions Comment: The constraint for bimolecular
between normal x-ray diagram levels. relationship permits use of the common donor-
acceptor language. A reaction may have more
chargeconjugation ForaDiracspinorψ =
than one such relationship. See also biochem-
ψ L the charge conjugate spinor is ψ c ical, dynamical, functional, kinetic, mechanistic,
ψ R =
2 phylogenetic, regulatory, thermodynamic, and
σ ψ R ∗ topological motives.
2
−σ ψ ∗ , where ∗ means the complex con-
L

0 −i
2 chemical potential In thermodynamics, the
jugate and σ = is the secomd Pauli
i 0 partial molar Gibbs free energy. In a thermal
spin matrix. Note that (ψ ) = ψ. equilibrium with many chemical reactions, all
∗ ∗
components have to have the same chemical
chart A chart on a manifold M is a pair
potential.
(U, φ) where U is an open subset of M and φ
n
is bijection form U onto an open subset of R .
−1 chemical reaction A process that results in
U is called a coordinate patch, φ φ are coor-
i j
dinate transition functions. the interconversion of chemical species. Chem-
ical reactions may be elementary reactions or
p
Chebyshev’s inequality If f ∈ (L ,µ) stepwise reactions. (It should be noted that
(0 <p < ∞), then for any α> 0 this definition includes experimentally observ-
able interconversions of conformers.)
p
f p
µ{x : |f(x)| >α}≤ . Detectable chemical reactions normally
α involve sets of molecular entities, as indicated
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC