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The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
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The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
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Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
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Related Experiment Video

Updated: Feb 23, 2026

Inducible LAP-tagged Stable Cell Lines for Investigating Protein Function, Spatiotemporal Localization and Protein Interaction Networks
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Erratum: Localization of Laplacian eigenvectors on random networks.

Shigefumi Hata1, Hiroya Nakao2

  • 1Department of Physics and Astronomy, Kagoshima University, Kagoshima, 890-0065, Japan. sighata@sci.kagoshima-u.ac.jp.

Scientific Reports
|September 8, 2017
PubMed
Summary

A correction has been published for this article, but the original error remains unfixed in the paper. Further details are available via the HTML version link.

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Area of Science:

  • Scientific publishing standards
  • Article errata and corrections

Background:

  • A published article contains an error.
  • A correction notice has been issued for the article.

Purpose of the Study:

  • To inform readers about a published correction.
  • To clarify the status of an error in a scientific paper.

Main Methods:

  • Issuance of a formal correction notice.
  • Linking the correction to the original article's HTML version.

Main Results:

  • A correction has been published.
  • The original error persists in the article text.

Conclusions:

  • Readers should be aware of the published correction.
  • The original article contains an unrectified error.