For nonzero impulse functions J i, i = 1, …, p, this solution is discontinuous on [ a, b ] and, since discontinuity points τ i, i = 1, …, p, are not fixed and depend on the solution through (2), such a solution has to be searched in the space G L ( [ a, b ] ; R n ) ; see the notation below.
(39) where 0, 1, 2, 3 are primary discontinuity points.
The desired output (r(t) inmathbf{R}^{p} ) is piecewise differentiable with finite discontinuity points.
Hence, a0 is a P C function with discontinuity points {1, ı, -ı}.
The eventual discontinuity points of the piecewise continuous switching function, that is, (2.6).
The question is crucial of how to deal with the primary discontinuity points.
Let A = { t k : k ∈ N } be the set of its discontinuity points.
: has only a finite number of discontinuity points in every compact set of.
The set Q + of all rational numbers of R + is the set of discontinuity points g 0 (cf. [[14], (236 ]).
which is everywhere continuous in R + since the subset of its second-class discontinuity points is empty by hypothesis.
It is known that natural images do not simply include 1D piecewise scan-line, and have many discontinuity points.
