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

¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

1.9K
The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
1.9K
Structures of Aldehydes and Ketones01:04

Structures of Aldehydes and Ketones

9.7K
Vanillin—a flavoring agent in vanilla, cinnamaldehyde—a molecule responsible for the distinct smell of cinnamon, and acetone—a strong-smelling ingredient in nail polish removers, all belong to a class of carbonyl compounds called aldehydes and ketones (Figure 1). Although both aldehydes and ketones contain the characteristic carbonyl (C=O) bond, their chemical structures vary with respect to the groups directly attached to the carbonyl carbon.
In aldehydes (Figures 1a and 1b),...
9.7K
Structure of Benzene: Molecular Orbital Model01:18

Structure of Benzene: Molecular Orbital Model

10.0K
According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
10.0K
SFG Algebra01:16

SFG Algebra

176
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
176
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.4K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.4K
Structures of Carboxylic Acid Derivatives01:28

Structures of Carboxylic Acid Derivatives

2.9K
Structure of Carboxylic Acid Derivatives
Carboxylic acid derivatives contain an acyl group attached to a heteroatom such as chlorine, oxygen, or nitrogen. The carbonyl carbon and oxygen are both sp2-hybridized with an unhybridized p orbital.
The three sp2 orbitals of the carbonyl carbon form three σ bonds, one each with the carbonyl oxygen, the α carbon, and the heteroatom, whereas the other two sp2 orbitals of the carbonyl oxygen are occupied by the lone pairs. Further, the...
2.9K

You might also read

Related Articles

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

Sort by
Same author

T-Fuzzy Structure on JU-Algebra.

F1000Research·2025
Same author

On <i>t</i>-derivations of PMS-algebras.

F1000Research·2025
Same author

Pythagorean  fuzzy deductive system of BCL-algebra.

F1000Research·2025
Same author

Bipolar Fuzzy Pseudo-UP Ideal Of Pseudo-UP Algebra.

F1000Research·2025
Same journal

Exploring potential strategies to enhance memory and cognition in aging mice.

F1000Research·2026
Same journal

Construction an Implicit Block Multi-Steps Approach for Solving Sixth-Order Fractional Differential Equations.

F1000Research·2026
Same journal

Kansei Engineering in the Evolving Service Sector: A Decade of Insights.

F1000Research·2026
Same journal

A Safety-First Mindset:  Role of Patient Safety Culture in Enhancing Healthcare Workers' Emotional Intelligence.

F1000Research·2026
Same journal

Decoding Decisions: Personality-Interest Motivational Sequences as Predictors of Career Paths.

F1000Research·2026
Same journal

Beyond the Transparent Barrier: A Domain Visualization and Integrative Review of Contemporary Research on Gender-Based Professional Stasis.

F1000Research·2026
See all related articles

Related Experiment Video

Updated: Sep 17, 2025

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

8.2K

Group Structures and Derivations on  PMS-algebras.

Nibret Melese Kassahun1,2, Berhanu Assaye Alaba1, Yohannes Gedamu Wondifraw1

  • 1Mathematics, Bahir Dar University, Bahir Dar, Amhara, 6000, Ethiopia.

F1000Research
|July 4, 2025
PubMed
Summary
This summary is machine-generated.

The set of derivations in P MS-algebras forms a semigroup. This study analyzes generalized derivations, d-invariant ideals, and fixed sets in these algebraic structures.

Keywords:
P MS-algebrasderivationsgeneralized derivationsemigrouptorsion free P MS-algebra

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Curation of Computational Chemical Libraries Demonstrated with Alpha-Amino Acids
08:21

Curation of Computational Chemical Libraries Demonstrated with Alpha-Amino Acids

Published on: April 13, 2022

2.7K

Related Experiment Videos

Last Updated: Sep 17, 2025

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

Published on: February 15, 2016

8.2K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Curation of Computational Chemical Libraries Demonstrated with Alpha-Amino Acids
08:21

Curation of Computational Chemical Libraries Demonstrated with Alpha-Amino Acids

Published on: April 13, 2022

2.7K

Area of Science:

  • Abstract Algebra
  • Mathematical Structures

Background:

  • PMS-algebras generalize BCK-algebras.
  • Focus on group structure and derivations within PMS-algebras.

Purpose of the Study:

  • Analyze properties of derivations in PMS-algebras.
  • Investigate derivations in specific subcategories like torsion-free PMS-algebras.

Main Methods:

  • Employs rigorous mathematical techniques.
  • Examines characteristics and behavior of derivations.

Main Results:

  • The set of derivations forms a semigroup.
  • Comprehensive analysis of generalized derivations, d-invariant ideals, fixed sets, and torsion-free PMS-algebras.

Conclusions:

  • Deepens understanding of PMS-algebraic structure and derivations.
  • Implications for abstract algebra research.