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resolvent See spectrum. Ricci scalar On a manifold M with a con-
nection N and a metric g the contraction of the
resonance effect See mesomeric effect. Ricci tensor of N with the inverse metric
µν
R = g R .
µν
responsivity (in detection of radiation), R R R
Detector input can be, e.g., radiant power, irradi-
Riccitensor ThecontractionoftheRiemann
ation, orradiantenergy. Itproducesameasurable
tensor defined by
detector output which may be, e.g., an electri-
cal charge, an electrical current or potential or R βν = R α · βαν = −R α · βνα .
a change in pressure. The ratio of the detector
output to the detector input is defined as the It is symmetric in the indices (β, ν).
responsivity. It is given in, e.g., ampere/watt,
volt/watt. The responsivity is a special case of Riemannian manifold A pair (M, g)
the general term sensitivity. formed by a manifold M of dimension m and
Dark current is the term for the electrical out- a Riemannian metric g on it. If the metric is
put of a detector in the absence of input. This is a positive definite (i.e., of signature (m, 0)) then
special case of the general term dark output. For it is called strictly Riemanniann; if the metric is
photoconductive detectors the term dark resist- indefinite then it is called pseudo-Riemannian.
ance is used.
If the responsivity is normalized with regard
Riemannian metric A positive definite
to that obtained from a reference radiation, the
inner product on the tangent space to a manifold
resulting ratio is called relative responsivity. For
at x, for each point x of the manifold, varying
measurements with monochromatic radiation at
continuously with x.
a given wavelength λ the term spectral responsiv-
ity R(λ) is used. In some cases the relative spec-
tral responsivity, where the spectral responsivity right action (of a group on a space X ) A
is normalized with respect to the responsivity at map ρ : X × G → X such that:
somegivenwavelength, isused. Thedependence
(i.) ρ(x, e) = x;
of the spectral responsivity on the wavelength is
(ii.) ρ(x, g · g ) = ρ(ρ(x, g ), g );
described by the spectral responsivity function. 1 2 1 2
The useful spectral range of the detector should
where G is a group, e its neutral element, ·
be given as the wavelength range where the rela- the product operation in G, and X a topologi-
tive responsivity does not fall below a specified cal space. The maps ρ : X → X defined by
g
value.
ρ (x) = ρ(x, g) are required to be homeomor-
g
phisms.If X has a further structure one usually
rest point (of a balance) The position of the requires ρ to preserve the structure. If ρ is a right
pointer with respect to the pointer scale when the action, then one can define a left action by setting
motion of the beam has ceased. λ(g, x) = ρ(x, g ). See also left action.
−1
retinoids Oxygenated derivatives of 3,7-
right invariance The property that an object
dimethyl-1-(2,6,6-trimethylcyclohex-1-enyl)
on a manifold M is invariant with respect to a
nona-1,3,5,7-tetraene and derivatives thereof.
right action of a group on M. For example, a
vector field X ∈ X(M) is right invariant with
reversibility In chemistry and biochemistry,
respect to the right action ρ : M → M if and
g
the notion that any reaction can proceed in
only if:
both directions, at least to some extent. See
T ρ X(x) = X(x · g).
also dextralateral, direction, dynamic equilib- x g
rium, formal reaction equation, microscopic
reversibility, product, rate constant, sinistra- right translations (on a group G) The right
lateral, and substrate. action of G onto itself defined byρ(h, g) =

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