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mass spectrometer An instrument in which Maxwell-Vlasov equations Let f(x, v,t)
beams of ions are separated (analyzed) according denote the plasma density and E(x, t), B(x, t)
tothequotientmass/charge, andinwhichtheions the electric and magnetic fields, respectively.
are measured electrically. This term should also The equations for a collisionless plasma of a sin-
beusedwhenascintillationdetectorisemployed. gle species of charged particles with charge e
and mass m are described by the Maxwell-Vlasov
matrix (1) (in analysis) A rectangular array
equations
of scalars. A matrix with n rows and m columns
represents a linear operator from an m dimen-  ∂f ∂f e 1 ∂f
+ v · + (E + v × B) · = 0,

sional vector space to an n dimensional vector  ∂t ∂x m c ∂v



space. 
 1 ∂B
 =−curl E,

(2) (in analytical chemistry) The components c ∂t
of the sample other than the analyte.
1
 1 ∂E =−curl B − j ,


 c ∂t c f


matrix effect (1) (in analytical chemistry) 


The combined effect of all components of the div E = ρ f and divB = 0
sample other than the analyte on the measure-
ment of the quantity. If a specific component where the current of f is given by j f =

can be identified as causing an effect then this is e vf (x, v, t)dv, and the charge density by

referred to as interference. See matrix. ρ = e f (x, v, t)dv.
f
(2) (in surface analysis) Effects which cause
changes in Auger-electron, photoelectron, sec- measurable set A measure on a set S is fre-
ondary ion yield, or scattered ion intensity, the quently defined only on certain subsets of S,
energy or shape of the signal of an element in forming a σ algebra (closed under countable
any environment as compared to these quantities unions and differences of its members). Sets in
in a pure element. this σ algebra are called measurable sets.
(a) Chemical matrix effects: changes in the
chemical composition of the solid which affect measure (1) A numerical determination of
the signals as described above. size. For example, the cardinality, if x is a set;
(b) Physical matrix effects: topographical and/or or the length, if x is a sequence; or the absolute
crystalline properties which affect the signal as value, if x is a number.
described above. (2) A nonnegative, real valued function µ
defined on certain subsets of a set S and satis-
maximal common subgraph Two graphs,
fying
G and G ,have a maximal common subgraph
1
2
if there exists a graph, G , which is the largest (i.) µ()) = 0

subgraph common to G and G .
1
2
(ii.) µ(∪U ) = µ(U ) when {U } is a
n
n
n
maximal element (in a partially ordered set pairwise disjoint, countable sequence of sets.
[A, ]) Referring to an element m ∈ A such
that there is no element a ∈ A except a = m such mechanism (of a reaction) A detailed
that a m. See ordering and minimum. description of the process leading from the reac-
tants to the products of a reaction, including a
maximum (in a partially ordered set [A, ]) characterization as complete as possible of the
Referring to an element m ∈ A such that ∀a ∈ A, composition, structure, energy, and other prop-
m a. See ordering.
erties of reaction intermediates, products, and
transition states. An acceptable mechanism of a
Maxwell’s equations In electrodynamics,
for an electric field E(x, t) and magnetic field specified reaction (and there may be a number of
B(x, t) Maxwell’s equations in the vacuum are such alternative mechanisms not excluded by the
evidence) must be consistent with the reaction

 E = curl B stoichiometry, the rate law, and with all other
t
B =−curl E available experimental data, such as the stereo-
t

div B = div E = 0. chemical course of the reaction. Inferences
© 2003 by CRC Press LLC