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

Base Excision Repair01:54

Base Excision Repair

26.2K
One of the common DNA damages is the chemical alteration of single bases by alkylation, oxidation, or deamination. The altered bases cause mispairing and strand breakage during replication. This type of damage causes minimal change to the DNA double helix structure and can be repaired by the base excision repair (BER) pathways. BER corrects damaged DNA sequences by removing the damaged base and restoring the original base sequence using the complementary strand as a template.
The first step of...
26.2K
DNA Base Pairing02:27

DNA Base Pairing

33.1K
Erwin Chargaff’s rules on DNA equivalence paved the way for the discovery of base pairing in DNA. Chargaff’s rules state that in a double-stranded DNA molecule,
33.1K
Lewis Acids and Bases02:33

Lewis Acids and Bases

48.3K
In 1923, G. N. Lewis proposed a generalized definition of acid-base behavior in which acids and bases are identified by their ability to accept or to donate a pair of electrons and form a coordinate covalent bond.
A coordinate covalent bond (or dative bond) occurs when one of the atoms in the bond provides both bonding electrons. For example, a coordinate covalent bond occurs when a water molecule combines with a hydrogen ion to form a hydronium ion. A coordinate covalent bond also results when...
48.3K
Weak Base Solutions03:21

Weak Base Solutions

24.9K
Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
24.9K
Ions as Acids and Bases02:54

Ions as Acids and Bases

26.3K
Salts with Acidic Ions
Salts are ionic compounds composed of cations and anions, either of which may be capable of undergoing an acid or base ionization reaction with water. Aqueous salt solutions, therefore, may be acidic, basic, or neutral, depending on the relative acid-base strengths of the salt’s constituent ions. For example, dissolving the ammonium chloride in water results in its dissociation, as described by the equation:
26.3K
Acid–Base Equilibria: Activity-Based Definition of pH01:10

Acid–Base Equilibria: Activity-Based Definition of pH

1.2K
For an ideal solution, the pH is defined as the negative logarithm of the hydrogen ion concentration. For a non-ideal solution, an accurate measurement of the pH must consider the negative logarithm of the hydrogen ion activity rather than concentration. In such a solution, the pH can be more accurately defined as the negative logarithm of a product of the hydrogen ion concentration and its activity coefficient.
In solutions of very low ionic strength—for example, pure water—the...
1.2K

You might also read

Related Articles

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

Sort by
Same author

Protocol for a cluster randomized trial to evaluate a faith-based breast cancer screening navigation model.

Trials·2026
Same author

Probing linewidth dynamics with short-time delayed linear interferometer in integrated frequency microcombs.

Optics express·2025
Same author

Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings.

Acta crystallographica. Section A, Foundations and advances·2022
Same author

Frequency comb-to-comb stabilization over a 1.3-km free-space atmospheric optical link.

Light, science & applications·2022
Same author

The Effects of Switching from Sevoflurane to Short-Term Desflurane prior to the End of General Anesthesia on Patient Emergence and Recovery: A Randomized Controlled Trial.

BioMed research international·2022
Same author

Pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings.

Acta crystallographica. Section A, Foundations and advances·2020

Related Experiment Video

Updated: Jan 25, 2026

Workflow and Tools for Crystallographic Fragment Screening at the Helmholtz-Zentrum Berlin
06:29

Workflow and Tools for Crystallographic Fragment Screening at the Helmholtz-Zentrum Berlin

Published on: March 3, 2021

6.0K

Gröbner-Shirshov bases for non-crystallographic Coxeter groups.

Jeong Yup Lee1, Dong Il Lee2

  • 1Department of Mathematics Education, Catholic Kwandong University, Gangneung 25601, Korea.

Acta Crystallographica. Section A, Foundations and Advances
|May 2, 2019
PubMed
Summary

This study constructs the Gröbner-Shirshov basis and standard monomials for the H4 Coxeter group algebra. This provides a clear description of symmetries for the 120-cell and an operation table for its 14400 elements.

Keywords:
Coxeter groupsGröbner–Shirshov basisstandard monomials

More Related Videos

Sample Preparation using a Lipid Monolayer Method for Electron Crystallographic Studies
04:22

Sample Preparation using a Lipid Monolayer Method for Electron Crystallographic Studies

Published on: November 20, 2021

4.9K
Lectin-based Isolation and Culture of Mouse Embryonic Motoneurons
09:25

Lectin-based Isolation and Culture of Mouse Embryonic Motoneurons

Published on: September 15, 2011

18.5K

Related Experiment Videos

Last Updated: Jan 25, 2026

Workflow and Tools for Crystallographic Fragment Screening at the Helmholtz-Zentrum Berlin
06:29

Workflow and Tools for Crystallographic Fragment Screening at the Helmholtz-Zentrum Berlin

Published on: March 3, 2021

6.0K
Sample Preparation using a Lipid Monolayer Method for Electron Crystallographic Studies
04:22

Sample Preparation using a Lipid Monolayer Method for Electron Crystallographic Studies

Published on: November 20, 2021

4.9K
Lectin-based Isolation and Culture of Mouse Embryonic Motoneurons
09:25

Lectin-based Isolation and Culture of Mouse Embryonic Motoneurons

Published on: September 15, 2011

18.5K

Area of Science:

  • Algebraic Combinatorics
  • Group Theory
  • Geometric Group Theory

Background:

  • The H4 Coxeter group is a finite non-crystallographic group with significant geometric and algebraic properties.
  • Understanding the structure of group algebras is crucial for studying symmetries and combinatorial objects.

Purpose of the Study:

  • To construct the Gröbner-Shirshov basis for the group algebra of the H4 Coxeter group.
  • To determine the standard monomials associated with this basis.
  • To explicitly describe the symmetries of the 120-cell and generate its operation table.

Main Methods:

  • Utilizing Gröbner-Shirshov bases theory for constructing algebraic structures.
  • Applying computational methods to derive standard monomials.
  • Analyzing the geometric interpretation of the algebraic results in relation to the 120-cell.

Main Results:

  • A Gröbner-Shirshov basis for the H4 Coxeter group algebra has been successfully constructed.
  • The corresponding standard monomials are identified, providing a basis for the algebra.
  • Explicit descriptions of symmetries acting on the 120-cell are obtained.
  • A natural operation table for the 14400 elements of the H4 group is generated.

Conclusions:

  • The Gröbner-Shirshov basis and standard monomials offer a comprehensive algebraic framework for the H4 Coxeter group.
  • This work provides new insights into the symmetries of the 120-cell and its underlying group structure.
  • The generated operation table facilitates further computational and theoretical studies of this group.