Sentence examples for unbounded variation from inspiring English sources

We give a representation formula for this extension showing the appearance of an additional "Lavrentiev" term which gives the energy necessary for the creation of a singularity with unbounded variation.

In both situations, the function f is allowed to be discontinuous and the function g is only regulated (possibly with unbounded variation).

We will prove a general theorem (Theorem 1) encompassing this situation as well as the more interesting case when the RSI exists, namely when the integrand and the integrator have a possibly unbounded variation, but they have finite p-variation and q-variation, respectively, with (p>1), (q>1) and (p^{-1}+q^{-1}>1).

end{aligned} (12) Also, when X has paths of unbounded variation, the proof of exist problems often relies on an approximation idea, which has already appeared in various papers; see Albrecher and Ivanovs [3], Czarna [9] and Baurdoux et al. [10].

In order to build a scale of efficiency, we select a few algorithms that solve the TOL efficiently in different conditions (a priori information or not, bounded vs. unbounded memory) and we determine their patterns of variation.

(2) Let q be bounded, but not of bounded variation on [ 0, ∞ ). Then (3) can have unbounded oscillatory solutions, see, e.g., [[17], Chapter VI-5, Theorem 3].

Unbounded chatter begets unbounded despair.

Unbounded problems.

His generosity seemed unbounded.

The possibilities seem unbounded.

And his ambition is unbounded.