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

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Stereoisomerism of Cyclic Compounds02:33

Stereoisomerism of Cyclic Compounds

In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...

You might also read

Related Articles

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

Sort by
Same journal

Howe Duality and Dynamical Weyl Group.

Transformation groups·2026
Same journal

On an Equivalence of Divisors on <math><msub><mrow><mover><mrow><mi>M</mi></mrow> <mo>¯</mo></mover></mrow> <mrow><mn>0</mn> <mo>,</mo> <mi>n</mi></mrow></msub></math> from Gromov-Witten Theory and Conformal Blocks.

Transformation groups·2026
Same journal

Automorphism Groups of Deformations and Quantizations of Kleinian Singularities.

Transformation groups·2026
Same journal

Rational Singularities for Moment Maps of Totally Negative Quivers.

Transformation groups·2026
Same journal

Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic.

Transformation groups·2025
Same journal

A Remark on Torsors under Affine Group Schemes.

Transformation groups·2025

Related Experiment Video

Updated: May 26, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Multi-centered Dilatations, Congruent Isomorphisms and Rost Double Deformation Space.

Arnaud Mayeux1

  • 1Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401 Israel.

Transformation Groups
|May 25, 2026
PubMed
Summary

This study introduces multi-centered dilatations for rings, schemes, and algebraic spaces. This new algebraic concept aids in understanding structures and formulating congruent isomorphisms.

Keywords:
Algebraic dilatationsArtin spacesCongruent isomorphismsDilatations of algebraic spacesDilatations of ringsDilatations of schemesEffective Cartier divisorsGrothendieck schemesRost double deformation space

More Related Videos

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Measuring the Complete-arch Distortion of an Optical Dental Impression
06:51

Measuring the Complete-arch Distortion of an Optical Dental Impression

Published on: May 30, 2019

Related Experiment Videos

Last Updated: May 26, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Measuring the Complete-arch Distortion of an Optical Dental Impression
06:51

Measuring the Complete-arch Distortion of an Optical Dental Impression

Published on: May 30, 2019

Area of Science:

  • Algebraic Geometry
  • Commutative Algebra

Background:

  • The concept of dilatations is fundamental in algebraic geometry.
  • Existing methods primarily focus on mono-centered dilatations.

Purpose of the Study:

  • Introduce and define multi-centered dilatations for rings, schemes, and algebraic spaces.
  • Extend the understanding of dilatations to multi-centered scenarios.
  • Explore applications in algebraic structures and geometric spaces.

Main Methods:

  • Development of a novel formalism for multi-centered dilatations.
  • Analysis of dilatations on schemes with inherent structures (monoid, group, Lie algebra).
  • Application of the new formalism to specific problems in algebraic geometry.

Main Results:

  • Established a new framework for multi-centered dilatations.
  • Demonstrated that dilatations of structured schemes often preserve the structure.
  • Provided new insights into mono-centered dilatations.
  • Formulated and deduced multi-centered congruent isomorphisms.
  • Interpreted Rost's double deformation space as a double-centered dilatation.

Conclusions:

  • The multi-centered dilatation formalism offers a powerful tool for algebraic geometry.
  • This approach unifies and extends existing concepts.
  • Opens new avenues for research in algebraic structures and geometric spaces.