Sentence examples for the graph of a function from inspiring English sources

Specifically, we optimize the wave profile of a two dimensional channel containing a Navier Stokes fluid with no assumption on the wave profile other than it is a traveling wave (e.g. we do not assume it is the graph of a function).

Locally, such surfaces are the graph of a function (y = phi x, t)) satisfying (1).

The graph of a function F is the set (operatorname{Gr}(F ={ (x,y in Xtimes Y: yin F x)} ) [29].

We define the graph of a function G to be the set (operatorname{Gr}(G)={ (x,y in Xtimes Y, yin G x)}) and recall two results for closed graphs and upper semicontinuity.

Then the IFS W is contractive with (unique) attractor A = G ( f ), the graph of a function f : [ 0, 1 ] → R such that f ( x n ) = y n for all n ∈ [ N ].

In this case, a section is the graph of a function (f :Omega rightarrow {mathbb C}), and the metric for the trivial line bundle is given by begin{aligned} langle f, g rangle (z) := f z) overline{g z)} e^{-varphi (z)}, quad zin Omega.

By the Inverse Function Theorem, (beta _{i}) is the graph of a holomorphic function (x=phi y)) where (phi :mathbb{D}_{r}rightarrow U').

Notice that (pr_{2} C_{t}rightarrowmathbb{D} _{r}), (pr_{2} x,z =z) is a degree one covering map, hence (C_{t}) is the graph of a holomorphic function (x=varphi^{1}_{t} z)).

We consider the disintegration of the Lebesgue measure on the graph of a convex function f Rn→R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure on the k-dimensional face on which it is concentrated.

The graph of a continuous function  f : Pω  →  Pω is defined by graph( f) = { (n, m) :   m∈ f en) }.

The attractor G ( p = 0.8 ) is the graph of a fractal function f ( p = 0.8 ) whose graph has Minkowski dimension ( 2 − ln ( 5 / 4 ) / ln 2 ).