If a sequence of points is chosen along these directions, the quotient in the definition of the Fr�chet derivative, which considers all directions at once, may not converge.
12.
For example, the path in hyperspace may not be smooth but a sequence of points, and the time change from jumping from one point to another may be abrupt.
13.
:The obvious ( to me ) definition of closeness is the angle between the two vectors, so that you want a sequence of points lying within successively thinner cones.
14.
In some mathematical frameworks, a given point process may be considered as a sequence of points with each point randomly positioned in " d "-dimensional Euclidean space "'R " "'d"
15.
Explicitly, this means that for every sequence of points from the domain of such that and, it holds that belongs to the domain of and " y " } }.
16.
Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can tend to the missing point, thereby not getting arbitrarily close to any point " within " the space.
17.
One such generalization is that a space is " sequentially " compact if any infinite sequence of points sampled from the space must frequently ( infinitely often ) get arbitrarily close to some point of the space.
18.
The notation, as well as the terminology, of point processes depends on their setting and interpretation as mathematical objects which under certain assumptions can be interpreted as a random sequences of points, random sets of points or random counting measures.
19.
For any constant " ? ", a fractal construction resembling a flattened version of the Koch snowflake can be used to define a sequence of point sets whose " ? "-skeletons are paths of arbitrarily large length within a unit square.
20.
Newton's method constructs a sequence of points that under certain conditions will converge to a solution x of an equation f ( x ) = 0 or a vector solution of a system of equation F ( x ) = 0.
