Let M be an n-manifold, and let A be a space with a partial sum behaving as an n-fold loop sum. We define the space C(M ;A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled configuration spaces, and spaces of rational curves. We show that C(In, ∂In;A) is an n-fold classifying space of C(In;A), and for n = 1 it is homeomorphic to ...

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...

We study theoretically and numerically the bending-driven levelling of thin viscous films within lubrication approximation. derive Green’s function linearized thin-film equation further show that it represents a universal self-similar attractor at long times. As such, rescaled perturbation film profile converges in time towards function, for any summable initial profile. In addition, stepped ax...

We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.