Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Forced Transdifferentiation01:28

Forced Transdifferentiation

2.2K
Transdifferentiation, also known as lineage reprogramming, was first discovered by Selman and Kafatos in 1974 in silkmoths. They observed that the moths’ cuticle-producing cells transformed into salt-producing cells. Many such cases of natural transdifferentiation occur in organisms. In humans, pancreatic alpha cells can become beta cells. In newts, the loss of the eye’s lens causes the pigmented epithelial cells to transdifferentiate into the lens cells.
Artificial...
2.2K
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

2.6K
Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
2.6K
Curvilinear Motion: Normal and Tangential Components01:27

Curvilinear Motion: Normal and Tangential Components

708
When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
708
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

459
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
459
Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

389
The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
389
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.5K
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.
Consider a scalar function. The curl of its...
2.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Ellipticity and the problem of iterates in Denjoy-Carleman classes.

Collectanea mathematica (Barcelona, Spain)·2026
Same author

The Kotake-Narasimhan theorem in general ultradifferentiable classes.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A, Matematicas·2024
See all related articles

Related Experiment Video

Updated: Dec 16, 2025

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

10.8K

Ultradifferentiable CR Manifolds.

Stefan Fürdös1,2

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Journal of Geometric Analysis
|July 7, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces ultradifferentiable CR manifolds and proves regularity for CR mappings using Denjoy-Carleman classes. It also investigates the regularity of infinitesimal CR automorphisms on these manifolds.

Keywords:
CR mappingsInfinitesimal CR automorphismsUltradifferentiable CR manifoldsUltradifferentiable regularity

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.5K
Author Spotlight: An Efficient and Robust Software for Automated Fusion of Multiple Preclinical Imaging Modalities
07:13

Author Spotlight: An Efficient and Robust Software for Automated Fusion of Multiple Preclinical Imaging Modalities

Published on: October 27, 2023

1.6K

Related Experiment Videos

Last Updated: Dec 16, 2025

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

10.8K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.5K
Author Spotlight: An Efficient and Robust Software for Automated Fusion of Multiple Preclinical Imaging Modalities
07:13

Author Spotlight: An Efficient and Robust Software for Automated Fusion of Multiple Preclinical Imaging Modalities

Published on: October 27, 2023

1.6K

Area of Science:

  • Differential Geometry
  • Complex Analysis
  • Harmonic Analysis

Background:

  • The study of CR manifolds is a significant area in differential geometry.
  • Understanding regularity properties of mappings between manifolds is crucial for geometric analysis.
  • Denjoy-Carleman classes provide a framework for analyzing ultradifferentiable functions.

Purpose of the Study:

  • To introduce the concept of ultradifferentiable CR manifolds.
  • To establish an ultradifferentiable regularity result for finitely nondegenerate CR mappings.
  • To investigate the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds.

Main Methods:

  • Introduction of ultradifferentiable CR manifolds based on Denjoy-Carleman classes.
  • Proof of an ultradifferentiable regularity result for CR mappings.
  • Analysis of the regularity of infinitesimal CR automorphisms.

Main Results:

  • The notion of ultradifferentiable CR manifold is formally introduced.
  • An ultradifferentiable regularity result for finitely nondegenerate CR mappings is established.
  • The regularity of infinitesimal CR automorphisms on these manifolds is investigated.

Conclusions:

  • The study extends the understanding of regularity in the context of CR manifolds.
  • The findings contribute to the theory of ultradifferentiable functions and geometric analysis.
  • This work opens avenues for further research into the properties of CR manifolds and their associated mappings.