Family of Curves


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family of curves

[‚fam·lē əv ′kərvz]
(mathematics)
A set of curves whose equations can be obtained by varying a finite number of parameters in a particular general equation.

Family of Curves

 

a set of curves that depend in a continuous manner on one or more parameters. In the plane, for example, a family of curves can be specified by an equation of the form

(*) F(x, y, C1, C2,…, Cn = 0

where C1,C2,…, Cn are parameters. If the parameters are assigned particular numerical values, then equation (*) defines a single curve. A family of curves on a surface is defined in a similar way. In this case, the Cartesian coordinates x and y in equation (*) are replaced by the intrinsic coordinates u and v on the surface.

It is usually assumed that F is a continuous function with respect to the set of its arguments and has a continuous partial derivative with respect to each argument. The concept of an envelope plays an important role in the study of one-parameter families in the plane or on an arbitrary surface.

References in periodicals archive ?
Different Finsler metrics and their geodesics resulting from selection H([alpha], [beta]) and E(x, y) arbitrary functions are discussed in the next section for family of curves that has two-parameter Weibull distribution.
According to the methodology, the family of curves that was obtained for the first group of simulations was the following: In figure 1, a decline is observed both for the glucose and insulin levels with the pass of time, and these levels trend to the reference values.
Family of curves is divided into several groups according to [[gamma].sub.[DELTA]], [epsilon] or [[gamma].sub.[DELTA]], [[gamma].sub.c].
The modulus of a family of curves. For a family of curves [GAMMA] in the plane, we use the notation M([GAMMA]) for its modulus [17].
Formula 3 predicts a barrel-shaped family of curves, and statistically, this implies that the interaction is concentrated in the linear-by-quadratic interaction components (Anderson & Farkas, 1975).
For compressors with inlet guide vanes, compressor map is represented by a new family of curves that do not depend on suction conditions either.
The family of curves corresponding to different area ratios evidently collapsed to a single straight line by plotting the quantity [C.sub.b]/[([A.sub.b]/[A.sub.c]).sup.n] as a function of ([Q.sub.b]/[Q.sub.c]).
that which have behavior into of the family of curves, [sigma](t) = [[sigma].sub.0][e.sup.-[gamma]t].
We shall see that the solution to the two questions stated above is essentially based on the idea of considering the values of a function along various curves from a given family of curves.
Let us remind that all secantoptics of a curve C for a fixed [beta] [member of] [0, [pi]), fixed [gamma] [member of] [0, [pi] - [beta]) and various [alpha] [member of] ([beta] + [gamma], [pi]) form two parameters family of curves [F.sub.[beta], [gamma]] ([alpha], t) (see [8]).
Now consider the family of curves that represent the effect of changing system pressures on pump performance.
It should be noted that Equation 4 does not apply to the family of curves for disks, but only for the more spherical particles as noted above.

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