The phrase "at isolated points" is correct and usable in written English.
It can be used to describe occurrences or phenomena that happen at specific, separate locations rather than continuously or uniformly.
Example: "The temperature fluctuated at isolated points throughout the day, leading to unexpected weather changes."
Alternatives: "at specific locations" or "at distinct points".
Since the zeros of are isolated (because is analytic for ), the phase is unrestricted only at isolated points (the zeros of ).
It is satisfied, in particular, by differential inclusions exhibiting non-Lipschitz t-dependence at isolated points, governed, for example, by a fractional-power modulus of continuity.
Sequences of positive solutions to semilinear elliptic equations of critical exponential growth in the plane either are precompact in the Sobolev H1-topology or concentrate at isolated points of the domain.
In the example considered, such singularities cannot be of the Cantor type but are represented by Dirac's masses concentrated at isolated points, which are interpreted as localized rotations, similar-in-type to those corresponding to the formation of plastic hinges in the engineering theory of elastic-plastic beams.
Whereas a locus given by f x, y) = 0 may intersect itself only at isolated points, a locus given by an equation of the form f x, y, z) = 0 may intersect itself along curves, a problem that caused considerable difficulties.
Besides, tangent lines are not well defined at isolated points.
At this period, the northern coast of America was known at two isolated points only, viz., the mouth of the Copperrnine River, discovered by Hearne, but placed erroneously by him four degrees of latitude too much to the north; and the mouth of the Mackenzie, more correctly laid down by the very able traveller by whose name the river is now known.
We construct positive weak solutions of the problem Δu+up="0 in Ω, which vanish in a suitable trace sense on ∂Ω, but which are singular at prescribed isolated points if p is equal or slightly above N+1N−1.
Graphene is a semi-metal, or a zero-gap semiconductor because its conducting and valence π electron bands touch each other only at two isolated points in its two-dimensional (2D) Brillouin zone [12].
Such ''rational functions" are meromorphic, meaning that they are analytic for all except at a set of isolated points given by the zeros of the denominator polynomial.
Moreover, due to the simplified nature of the models used, continuous V̇/Q distributions could not be produced, and thus, the model outputs can only be compared to patient data at two or three isolated points on the V̇/Q curve.
