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Example A column scaling A row scaling
10x+100y=500 .333x+y=500 x+10y =50
30x +.3y =.2 x+.003y =.2 300x +3y =2

n
Another method is logarithmic scaling, which Schr¨odinger equation Let U ⊂ R be open
scales by the logarithm of the greatest magnitude. and u : U × R → R. The Schr¨odinger equation
More sophisticated methods are algorithmic, tak- for u is
ing both row and column extremes into account. iu + u = 0.
t
scintillators Materials used for the mea-
scaling argument (homogeneity argument)
surement of radioactivity, by recording the
The idea is to exploit the behavior of norms
radioluminescence. They contain compounds
of functions or vector fields under pull-backs
(chromophores) which combine a high fluores-
related to scaling transformations x → δx,
cence quantum efficiency, a short fluorescence
δ> 0. Very closely related to techniques relying
lifetime, and a high solubility. These compounds
on parametric equivalence.
are employed as solutes in aromatic liquids and
polymers to form organic liquid and plastic scin-
scatter search A population-based meta- tillators, respectively.
heuristic, starting with a collection of reference
points, usually obtained by the application of search tree The tree formed by a branch and
some heuristic. A new point is created by tak- bound algorithm strategy. It is a tree because
ing combinations of points in the population, and at each (forward) branching step the problem is
rounding elements that must be integer valued. It partitioned into a disjunction. A common one is
bears some relation to a genetic algorithm, except to dichotomize the value of some variable, x ≤ v
that scatter search uses linear combinations of or x ≥ v + 1. This creates two nodes from the
the population, while the GA crossover operation parent:
can be nonlinear.
[parent node]
x ≤ v x ≥ v + 1
scheduling (e.g., jobs) A schedule for a
8 9
sequence of jobs, say j ,...,j , is a specifica-
1 n [left child] [right child]
tion of start times, say t ,...,t , such that cer-
1
n
tain constraints are met. A schedule is sought secant The function
that minimizes cost and/or some measure of time,
1
like the overall project completion time (when the sec(x) =
last job is finished) or the tardy time (amount by cos x
which the completion time exceeds a given dead- See cosine.
line). There are precedence constraints, such as
in the construction industry, where a wall cannot secant method A method to find a root of a
be erected until the foundation is laid. univariate function, say F. The iterate is
There is a variety of scheduling heuristics.
k
k
Two of these for scheduling jobs on machines (k+1) k F(x )[x − x (k−1) ]
x = x − .
k
are list heuristics: the Shortest Processing Time F(x ) − F(x (k−1) )
(SPT) and the Longest Processing Time ( LPT).
2

If F is in C and F (x) = 0, the order of con-
These rules put jobs on the list in non-decreasing
and non-increasing order of processing time, vergence is the golden mean, say, g (approx. =
1.618), and the limiting ratio is:
respectively.
Other scheduling problems, which might not , , (g−1)

, 2F (x) ,
involve sequencing jobs, arise in production , , .

, F (x) ,
planning.
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC