Topic
Bump function
About: Bump function is a research topic. Over the lifetime, 78 publications have been published within this topic receiving 1019 citations.
Papers published on a yearly basis
Papers
Journal Article•
TL;DR: Near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems is demonstrated and it is shown that the algorithm leads to smooth potential energy surfaces and yields large computational savings.
Abstract: We demonstrate near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. The theory behind our approach has been described previously, [J. Subotnik and M. Head-Gordon, J. Chem. Phys. 123, 064108 (2005)], and requires appropriately multiplying standard iterative amplitude equations by a bump function, creating local amplitude equations (which are smooth according to the implicit function theorem). Here, we provide an example that this theory works in practice: we show that our algorithm leads to smooth potential energy surfaces and yields large computational savings. As an example, we apply our LCCSD approach to measure the post-MP2 correction to the energetic gap between two different alanine tetrapeptide conformations.
119 citations
1 Dec 2006
TL;DR: Several Hardy-type inequalities with explicit constants for compactly supported smooth functions on open sets in the Euclidean space Ωn were proved in this article, where the constants were explicit constants.
Abstract: Several Hardy-type inequalities with explicit constants are proved for compactly supported smooth functions on open sets in the Euclidean space ℝn.
55 citations
55 citations
TL;DR: In this article, the authors established two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type, and proved the separation of the double and logarithmic bump conditions.
Abstract: We establish two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type. We do so first when the weights satisfy a double bump condition and then when the weights satisfy separated logarithmic bump conditions. Our results generalize recent work on the Euclidean case, but our proofs are simpler even in this setting. The other interesting feature of our approach is that we are able to prove the separated bump results (which always imply the corresponding double bump results) as a consequence of the double bump theorem.
43 citations
TL;DR: In this article, a generalization of Ekeland's ϵ-variational principle and its Borwein-Preiss smooth variant, replacing the distance and the norm by a "gauge-type" lower semi-continuous function, is presented.
34 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 2 |
| 2020 | 2 |
| 2019 | 4 |
| 2018 | 2 |
| 2017 | 1 |