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Comment: This is one of two standard total ion current (in mass spectrometry)
definitions. Common examples are smooth (1) (after mass analysis) The sum of the separate
deformation of a triangle into a circle; a sphere ion currents carried by the different ions con-
into a beaker (a cup without a handle); and a tributing to the spectrum. This is sometimes
trefoil knot into a circle. In the last case, the called the reconstructed ion current.
transformation is allowed to cut the perimeter of (2) (before mass analysis) The sum of all the
the figure so long as the cut ends are rejoined in separate ion currents for ions of the same sign
their original manner. Note that expansions and before mass analysis.
contractions of the network are not topological
totallyunimodularmatrix Seeunimodular
transformations.
matrix.
topology (1) (of a network) The topology of toxicity (1) Capacity to cause injury to a
a network G(V, E) is the set of nodes V and their living organism defined with reference to the
incidence relations in the network, E. quantity of substance administered or absorbed,
Comment: Specified here are two particular the way in which the substance is administered
topologicalpropertieswhicharetoremaininvari- (inhalation, ingestion, topical application, injec-
ant under a topological transformation, such as a tion) and distributed in time (single or repeated
continuous deformation. The standard definition doses), the type and severity of injury, the time
requires only that the edges remain invariant to needed to produce the injury, the nature of the
transformation. This is perfectly reasonable for organism(s) affected and other relevant condi-
networks derived from mathematics, but does tions.
not fit the biological case as well. Many net- (2) Adverse effects of a substance on a living
works will include singleton nodes which are organism defined with reference to the quantity
important, but whose edges are not yet known. of substance administered or absorbed, the way
Hence the standard definition is here augmented in which the substance is administered (inhala-
to cover this case as well. There are a number of tion, ingestion, topicalapplication, injection)and
other important senses of the word which are not distributed in time (single or repeated doses), the
type and severity of injury, the time needed to
directly relevant here.
produce the injury, the nature of the organism(s)
(2) (on a set X ) A set τ(X) of subsets of
affected, and other relevant conditions.
X, called open sets, which satisfy the following
(3) Measure of incompatibility of a substance
axioms:
with life. This quantity may be expressed as the
(i.) the empty set ∅ and the whole space X reciprocal of the absolute value of median lethal
are elements in τ(X); dose (1/LD ) or concentration (1/LC ).
50
50
(ii.) the intersection of a finite number of ele-
trace element Any element having an aver-
ments in τ(X) is still in τ(X); and
age concentration of less than about 100 parts per
(iii.) the union of a (possibly infinite) family million atoms (ppma) or less than 100 µg per g.
of elements in τ(X) is still in τ(X).
trajectory (in reaction dynamics) A path
torque, T T T Sum of moments of forces not taken by a reaction system over a potential-
energy surface, or a diagram or mathematical
acting along the same line.
description that represents that path. A trajec-
tory can also be called a reaction path.
torsion tensor Let N α be a (linear)
βµ
connection on a manifold M. The torsion of transfer Movement of a component within
α
α
the connection is the tensor T βµ = N α βµ − N . a system or across its boundary. It may be
µβ
Despite the fact that the connection is not a ten- expressed using different kinds of quantities,
sor, the torsion is a tensor since nonhomogeneous e.g., rates of change dQ/dt or Q/ t.
terms in the transformation rules of connections Examples are mass rate, dm /dt or m / t;
B B
cancel out. substance rate, dn /dt or n / t.
B B

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