The counterarguments are meant to build up the willingness to consider the less radical proposal that I made, which follows naturally from my work on singularities
in standard general relativity ( and references therein) and is discussed in Section 7.
By any measure, First-Person Singularities
is grade-A reading fodder.
We further assume that X has only rational singularities
. Then [X.sup.+] has only rational singularities
 Nemethi,A.: Some topological invariants of isolated hypersurface singularities
, EMS summer schoolEger (Hungary), 29 July-9 August (1996).
The number of singularities
is defined by the right-hand sides of the (1) and the locations of the singularities
(coordinates, see Table II) are given by the system of algebraic equations
The two mathematical techniques avoiding transformation singularities
are proposed in the case of [z.sub.2] > 0 as in the following section.
France-Japanese Symposium on Singularities
(5th: 2009: Strasbourg, France) Ed.
in mathematics in 1986 for his results in the area of complex analytic singularities
Stiffness maps of both 5R and 6-RUS manipulators show that highest values of stiffness occur in poses where crank-connecting rod systems reach inverse singularities
. Taking advantage of this fact, an approach to motion planning is devised which makes use of inverse singularities
to obtain stiffer trajectories.
Then the only finite singularities
of a solution f (z) which can occur are the zeroes of the leading coefficient [p.sub.0](z); notice in particular that there are no movable singularities
, that is, singularities
which depend on the initial conditions.
Because we do not limit the solution by that the metric must be regular, the obtained metric has two singularities
: 1) collapse by [g.sub.00] = 0, and 2) break of the space by [g.sub.11] [right arrow] [infinity].
One of the "wrinkles" in the mathematical model of cloaking is that the transformations that define the required material parameters have singularities
, that is, points at which the transformations fail to exist or fail to have properties such as smoothness or boundness that are required to demonstrate cloaking.