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addition reaction A chemical reaction of Comment: Note that in this version any node
twoormorereactingmolecularentities, resulting is present at least twice: as the key to each sublist
in a single reaction product containing all atoms (X−[... ] and as a member of some other sublist
of all components, with formation of two chem- (−[X]). This representation is a more compact
ical bonds and a net reduction in bond multipli- version of the connection tables often used to
city in at least one of the reactants. The reverse represent compound structures.
process is called an elimination reaction. If the
reagent or the source of the addends of an add-
adjacent For any graph G(V, E), two nodes
ition are not specified, then it is called an addition
v , v are adjacent if they are both incident to
i
i
transformation.
the same edge (share an edge); that is, if the edge
See also [addition, α-addition, cheletropic
(v ,v ) ∈ E. Similarly, two edges (v ,v ),
reaction, cycloadition.] i i i i
(v ,v ) are adjacent if they are both incident to
i i
adduct Anew chemical species AB, each the same vertex; that is if {v ,v }∩{v ,v } = ∅.
i
i
i
i
molecular entity of which is formed by direct Comment: Two atoms are said to be adjacent
combination of two separate molecular entities if they share a bond; two reactions (compounds)
A and B in such a way that there is change in are said to be adjacent if they share a compound
connectivity, but no loss, of atoms within the (reaction).
moieties A and B. Stoichiometries other than 1:1
are also possible, e.g., a bis-adduct (2:1). An
adjoint representations (on a [Lie] group G)
intramolecularadductcanbeformedwhenAand
(1) The action of any group G onto itself defined
B are groups contained within the same molecu-
by ad : G → Hom(G) : g → ad . The
g
lar entity.
group automorphism ad : G → G is defined
g
This is a general term which, whenever appro- −1
by ad (h) = g · h · g .
g
priate, should be used in preference to the less
(2) On a Lie algebra. If G is a Lie group
explicit term complex. It is also used specifically
the adjoint representation above induces by deri-
for products of an addition reaction.
vation the adjoint representation of G on its Lie
algebra g. It is defined by T ad : g → g where
adiabatic lapse rate (in atmospheric chemistry) e g
T denotes the tangentmap (see tangentlift). If G
The rate of decrease in temperature with increase e
is a matrix group, then the adjoint representation
in altitude of an air parcel which is expanding
−1
is given by T ad (ξ) = g · ξ · g .
slowly to a lower atmospheric pressure without e g
exchange of heat; for a descending parcel it is the (3) Also defined is the adjoint representa-
rate of increase in temperature with decrease in tion Ad : g → Hom(g) of the Lie algebra
altitude. Theorypredictsthatfordryairitisequal g onto itself. For ξ, ζ ∈ g, the Lie algebra
to the acceleration of gravity divided by the spe- homomorphism Ad ξ : g → g is defined by
cific heat of dry air at constant pressure (approx- commutators Ad (ζ) = [ξ, ζ].
ξ
−1
imately 9.8 Ckm ). The moist adiabatic lapse
◦
rate is less than the dry adiabatic lapse rate and adsorbent A condensed phase at the surface
depends on the moisture content of the air mass. of which adsorption may occur.
adjacency list A list of edges of a graph G
of the form adsorption An increase in the concentration
of a dissolved substance at the interface of a con-
[v − [v ,v ,...,v ],v − [v ,v ,...,v ]],
i j k n j i l m
densed and a liquid phase due to the operation of
...,v − [v ,v ,...v ], surface forces. Adsorption can also occur at the
n i p q
where interface of a condensed and a gaseous phase.
E ={(v ,v ), (v ,v ),...,(v ,v ), (v ,v ),
i j i k i n j l
adsorptive The material that is present in
...,(v ,v ),...,(v ,v ),...,(v ,v )}, one or other (or both) of the bulk phases and
m
n
p
q
j
n
and i, j, k, l, m, n, p, and q are indices. capable of being adsorbed.
© 2003 by CRC Press LLC