Smaller fields are generally used for junior football; some are purpose-built, and some are temporarily marked out within the confines of full-sized oval; as for a senior match, there are no fixed dimensions for a junior-sized field.
12.
Since dimension is a local invariant ( i . e . the map sending each point to the dimension of its neighbourhood over which a chart is defined, is locally constant ), each connected component has a fixed dimension.
13.
Modularity as a means of measurement is intrinsic to certain types of building; for example, brick construction is by its nature modular insofar as the fixed dimensions of a brick necessarily yield dimensions that are multiples of the original unit.
14.
However, for every Euclidean space of fixed dimension, there are graphs that cannot be embedded greedily : whenever the number " n " is greater than the kissing number of the space, the graph " K " 1, " n " has no greedy embedding.
15.
Generally manifolds are taken to have a fixed dimension ( the space must be locally homeomorphic to a fixed " n "-ball ), and such a space is called an " "'n "-manifold "'; however, some authors admit manifolds where different points can have different dimensions.
16.
The " Print " button starts the " Photo Printing Wizard " which allows printing images with picture titles using various page layouts such as full page prints, wallet prints, contact / index sheets or certain fixed dimensions with the images cropped or rotated to fit the page.
17.
Barvinok's algorithm is always polynomial in the input size, for fixed dimension of the polytope and fixed degree of weights, whereas the " splintering " in Pugh's algorithm can grow with the coefficient values ( and thus exponentially in terms of input size, despite fixed dimension, unless there is some limit on coefficient sizes ).
18.
Barvinok's algorithm is always polynomial in the input size, for fixed dimension of the polytope and fixed degree of weights, whereas the " splintering " in Pugh's algorithm can grow with the coefficient values ( and thus exponentially in terms of input size, despite fixed dimension, unless there is some limit on coefficient sizes ).
19.
One can replace this stable isotopy class with an actual isotopy class by fixing the target space, either by using Hilbert space as the target space, or ( for a fixed dimension of manifold n ) using a fixed N sufficiently large, as " N " depends only on " n ", not the manifold in question.
20.
This can be seen intuitively in that the Euler class is a class whose degree depends on the dimension of the bundle ( or manifold, if the tangent bundle ) : it is always of top dimension, while the other classes have a fixed dimension ( the first Stiefel-Whitney class is in " H " 1, etc . ).
