Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 25 min ago
PreprintCC BY 4.0arXiv

A least-squares lower bound for capacity

  • Thomas Ransford
Open at sourcePDFDOICite

Abstract

We establish a least-squares lower bound for the logarithmic capacity of an arbitrary compact plane set, extending an inequality previously known for connected sets. The bound generalizes classical inequalities involving area and moment of inertia. It is sharp for disks, and asymptotically sharp for compact sets whose capacity coincides with that of their interior. We further show that asymptotic sharpness holds for general compact sets if we replace logarithmic capacity by minimal carrier capacity.

Related

  1. An improved lower bound for maximal partial Room squares
    Peter Horak, Dongryul Kim
    arXivPreprintCC BY-NC-SA 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. Improved lower bound for the two-way-assisted quantum capacity of the bosonic thermal-loss channel
    Matthew Barber, Stefano Pirandola
    arXivPreprintarXiv licenceFull textMathematical physicsComputational physicsarXiv
  3. An Improved Lower Bound on Support Size of Capacity-Achieving Inputs for the Binomial Channel: Extended version
    Mohammadamin Baniasadi, Antonino Favano, Luca Barletta +1
    arXivPreprintCC BY 4.0Full textGeneral mathematicsarXiv
  4. A COVID-19 transmission model with optimal control integrating BERT with LHS and least-squares fitting for real-world consistency
    Yinghui Chen, Chairat Modnak
    Scientific ReportsPeer-reviewedCC BY-NC-ND 4.0Full textGeneral mathematicsCrossref
  5. A comparison of artificial neural networks and partial least squares modelling for the rapid detection of the microbial spoilage of beef fillets based on Fourier transform infrared spectral fingerprints
    Efstathios Panagou, Fady Mohareb, Anthoula Argyri +2
    Food MicrobiologyPeer-reviewedLicence not statedFull text76 citedGeneral biologyStatisticsHAL

Cite

BibTeXRIS
BibTeX
@misc{ransford2026leastsquares,
  title = {{A least-squares lower bound for capacity}},
  author = {Thomas Ransford},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24702},
  eprint = {2610.24702},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24702},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A least-squares lower bound for capacity
AU  - Thomas Ransford
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24702
UR  - https://arxiv.org/abs/2610.24702
AB  - We establish a least-squares lower bound for the logarithmic capacity of an arbitrary compact plane set, extending an inequality previously known for connected sets. The bound generalizes classical inequalities involving area and moment of inertia. It is sharp for disks, and asymptotically sharp for compact sets whose capacity coincides with that of their interior. We further show that asymptotic sharpness holds for general compact sets if we replace logarithmic capacity by minimal carrier capacity.
ER  -