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analog In contrast to digital, analog means a analytical function A function which
dynamic variable taking a continuum of values, relates the measure value C to the instrument

a
e.g., a timepiece having hour and minute hands. reading, X, with the value of all interferants, C ,
i
remaining constant. This function is expressed
by the following regression of the calibration
analog computation Instead of using
results:
binary computation as in a digital computer, one
C = f(X)

uses a device which has continuous dynamic a
variables such as current (or voltage) in an elec- The analytical function is taken as equal to the
trical circuit, or displacement in a mechanical inverse of the calibration function.
device.
analytical index The analytical index of an
analog computer A device that computes elliptic complex {D ,E } is defined as
p
p
using analog computation. A computer that

p
operates with numbers represented by directly index{D ,E }= (−1) dim ker ,
p
p
p
measurable quantities (e.g., voltage). p
where p = dδ + δd is the Laplacian on p-
analog multiplier Using analog computa- forms.
tion to obtain the product, as output, of two
(input) quantities. analytical unit (analyser) An assembly of
subunits comprising: suitable apparatus permit-
analog variable See analog and analog ting the introduction and removal of the gas,
computation. liquid, or solid to be analyzed and/or calibration
materials; a measuring cell or other apparatus
which, from the physical or chemical properties
analytic dynamics A dynamical system is
of the components of the material to be analyzed,
called analytic if the coefficients of the vector
gives signals allowing their identification and/or
field are analytic functions.
measurement; signal processing devices (ampli-
fication, recording)or, ifneedbe, dataprocessing
analytic function A function f(x) is called devices.
analytic at x = a if it can be represented by a
power series angle A system of two rays extending from
the same point. The numerical measure of an
∞
n angle is the degree (measured as a fraction of
f(x) = c (x − a) ,
n
◦
360 , the entire angle from a line to itself ) or the
n=0
radian (= 180/π degrees).
convergent for |x| <r, for some r> 0.
angle between curves Let c (t) and c (t)
2
1
analytic geometry A part of geometry in be two curves intersecting at t , i.e., c (t ) =
1
0
0
which algebraic methods are used to solve geo- c (t ) = p. The angle between c and c at p
2
1
2
0
metric problems. is given by the angle between the two tangent
vectors ˙c (t ) and ˙c (t ).
0
0
1
2
analytic manifold A manifold M such that
angle between lines Let L and L be two
1
2
its coordinate transition functions are analytic.
nonvertical lines in the plane with slopes m and
1
See chart.
m , respectively. If θ, the angle from L to L ,
1
2
2
is not a right angle, then
analytic structure The set (atlas) of coor-
m − m
dinate patches on an analytic manifold M. See 2 1
tan θ = .
chart. 1 + m m 2
1
© 2003 by CRC Press LLC