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

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

1.4K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.4K
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.3K
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...
1.3K
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

5.3K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
5.3K
Second Uniqueness Theorem01:16

Second Uniqueness Theorem

1.1K
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...
1.1K
Singularity Functions for Shear01:26

Singularity Functions for Shear

168
In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
168
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

2.6K
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
2.6K

You might also read

Related Articles

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

Sort by
Same journal

Combining Higher-Order Logic with Set Theory Formalizations.

Journal of automated reasoning·2023
Same journal

Synthesising Programs with Non-trivial Constants.

Journal of automated reasoning·2023
Same journal

First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems: Automation, Formalization, Certification.

Journal of automated reasoning·2023
Same journal

A Formalization of SQL with Nulls.

Journal of automated reasoning·2022
Same journal

A Comprehensive Framework for Saturation Theorem Proving.

Journal of automated reasoning·2022
Same journal

A Formalization of the Smith Normal Form in Higher-Order Logic.

Journal of automated reasoning·2022
See all related articles

Related Experiment Video

Updated: Jul 31, 2025

A Visual Guide to Sorting Electrophysiological Recordings Using 'SpikeSorter'
10:31

A Visual Guide to Sorting Electrophysiological Recordings Using 'SpikeSorter'

Published on: February 10, 2017

11.2K

Unifying Splitting.

Gabriel Ebner1, Jasmin Blanchette1,2,3, Sophie Tourret2,3

  • 1Vrije Universiteit Amsterdam, Amsterdam, The Netherlands.

Journal of Automated Reasoning
|May 3, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a unifying framework for clause splitting in saturation provers, analyzing the refutational completeness of the AVATAR architecture and related methods using SAT solvers.

Keywords:
AVATARAutomated theorem provingCompletenessSplitting

More Related Videos

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
08:51

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

10.4K
Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

8.3K

Related Experiment Videos

Last Updated: Jul 31, 2025

A Visual Guide to Sorting Electrophysiological Recordings Using 'SpikeSorter'
10:31

A Visual Guide to Sorting Electrophysiological Recordings Using 'SpikeSorter'

Published on: February 10, 2017

11.2K
Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
08:51

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

10.4K
Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

8.3K

Area of Science:

  • Automated reasoning
  • Mathematical logic
  • Computer science

Background:

  • Clause splitting is crucial for efficient saturation provers.
  • The AVATAR architecture effectively splits clauses using SAT solvers.
  • Questions remain about AVATAR's refutational completeness and its relation to other splitting methods.

Purpose of the Study:

  • To present a unifying framework for clause splitting in saturation provers.
  • To analyze the refutational completeness of splitting architectures.
  • To investigate the relationship between different splitting strategies.

Main Methods:

  • Developed a unifying framework extending saturation calculi with splitting.
  • Integrated the framework into a SAT solver-guided prover.
  • Introduced and studied 'locking', a model-based subsumption mechanism.

Main Results:

  • The framework encompasses various splitting architectures, including AVATAR and labeled splitting.
  • The study provides a basis for analyzing the refutational completeness of these architectures.
  • The 'locking' mechanism offers a new approach to subsumption.

Conclusions:

  • The proposed framework offers a comprehensive view of splitting architectures in automated reasoning.
  • It clarifies the properties of AVATAR and related methods.
  • The framework facilitates the development and analysis of advanced provers.