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: Complex Splitting01:13

¹H NMR: Complex Splitting

1.9K
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...
1.9K
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

6.9K
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...
6.9K
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

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

2.6K
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...
2.6K
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

1.8K
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
1.8K
NMR Spectroscopy: Chemical Shift Overview01:15

NMR Spectroscopy: Chemical Shift Overview

3.3K
The position of the absorption signal of a sample is reported relative to the position of the signal of tetramethylsilane (TMS), which is added as an internal reference while recording spectra. The difference between the absorption frequencies of the sample and TMS (in Hz) is divided by the spectrometer operating frequency (in MHz) to obtain a dimensionless quantity called the chemical shift. It is reported on the δ (delta) scale and expressed in parts per million.
For instance, the proton...
3.3K
Proton (¹H) NMR: Chemical Shift01:07

Proton (¹H) NMR: Chemical Shift

3.5K
Organic molecules primarily contain carbon and hydrogen atoms. While all the hydrogen isotopes are NMR-active, protium or hydrogen-1 is the most abundant. It has a significant energy separation between its nuclear spin states due to its large gyromagnetic ratio. As per Boltzmann's distribution, an increase in the energy separation implies a greater excess population of nuclei available for excitation, resulting in a strong NMR absorption signal.
Absorption signals of all the protium nuclei...
3.5K

You might also read

Related Articles

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

Sort by
Same author

Identification of Lipid Metabolism-Related Gene <i>GM2A</i> as a Potential Biomarker in Atopic Dermatitis by Combining Weighted Gene Co-Expression Network Analysis and Machine Learning.

DNA and cell biology·2026
Same author

Targeted Next-Generation Sequencing for Etiologic Diagnosis of Cutaneous Mycobacterium marinum Infection.

JAMA dermatology·2025
Same author

Six cases of collective lightning-induced arc explosion injuries: A case report.

The American journal of emergency medicine·2025
Same author

[Retracted] CIP2A, an oncoprotein, is associated with cell proliferation, invasion and migration in laryngeal carcinoma cells.

Oncology reports·2025
Same author

Na(C<sub>2</sub>H<sub>10</sub>N<sub>2</sub>)<sub>2</sub>[Zn<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub>(H<sub>0.5</sub>PO<sub>4</sub>)]<sub>2</sub>: A Short-Wave Ultraviolet Open-Framework Zincophosphate Exhibiting Substantial Optical Dispersion Ability.

Inorganic chemistry·2024
Same author

Ethoxyquin mediates lung fibrosis and cellular immunity in BLM-CIA mice by inhibiting HSP90.

Advances in clinical and experimental medicine : official organ Wroclaw Medical University·2024
Same journal

Modeling the impact of budget limitation on the screening and treatment pathway of HPV-induced precancerous cervical lesions.

Mathematical biosciences and engineering : MBE·2026
Same journal

Modeling the effects of trait-mediated dispersal on coexistence of two species: Competition and non-consumptive predator-prey.

Mathematical biosciences and engineering : MBE·2026
Same journal

A close look at the viral reduction rate in target cell limited models.

Mathematical biosciences and engineering : MBE·2026
Same journal

A stochastic agent-based model for simulating tumor-immune dynamics and evaluating therapeutic strategies.

Mathematical biosciences and engineering : MBE·2026
Same journal

Addressing domain shift via imbalance-aware domain adaptation in embryo development assessment.

Mathematical biosciences and engineering : MBE·2026
Same journal

Effect of drug resistance on an HIV epidemic in heterogeneous populations.

Mathematical biosciences and engineering : MBE·2026
See all related articles

Related Experiment Video

Updated: Jan 27, 2026

An Engineered Split-TET2 Enzyme for Chemical-inducible DNA Hydroxymethylation and Epigenetic Remodeling
08:34

An Engineered Split-TET2 Enzyme for Chemical-inducible DNA Hydroxymethylation and Epigenetic Remodeling

Published on: December 18, 2017

7.0K

A parameterized shift-splitting preconditioner for saddle point problems.

Li-Tao Zhang1, Chao-Qian Li, Yao-Tang Li

  • 1College of Science, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450015, P. R. China.

Mathematical Biosciences and Engineering : MBE
|March 14, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a new parameterized shift-splitting preconditioner for solving large sparse augmented systems. This method ensures unconditional convergence for fixed-point iterations, improving upon existing generalized shift-splitting techniques.

Keywords:
Eigenvalueconvergenceparameterized shift-splittingpreconditionersaddle point problem

More Related Videos

Investigating Long-Distance Transport of Perfluoroalkyl Acids in Wheat via a Split-Root Exposure Technique
07:06

Investigating Long-Distance Transport of Perfluoroalkyl Acids in Wheat via a Split-Root Exposure Technique

Published on: September 28, 2022

2.0K
A Porcine Corneal Endothelial Organ Culture Model Using Split Corneal Buttons
08:36

A Porcine Corneal Endothelial Organ Culture Model Using Split Corneal Buttons

Published on: October 6, 2019

7.5K

Related Experiment Videos

Last Updated: Jan 27, 2026

An Engineered Split-TET2 Enzyme for Chemical-inducible DNA Hydroxymethylation and Epigenetic Remodeling
08:34

An Engineered Split-TET2 Enzyme for Chemical-inducible DNA Hydroxymethylation and Epigenetic Remodeling

Published on: December 18, 2017

7.0K
Investigating Long-Distance Transport of Perfluoroalkyl Acids in Wheat via a Split-Root Exposure Technique
07:06

Investigating Long-Distance Transport of Perfluoroalkyl Acids in Wheat via a Split-Root Exposure Technique

Published on: September 28, 2022

2.0K
A Porcine Corneal Endothelial Organ Culture Model Using Split Corneal Buttons
08:36

A Porcine Corneal Endothelial Organ Culture Model Using Split Corneal Buttons

Published on: October 6, 2019

7.5K

Area of Science:

  • Numerical Analysis
  • Scientific Computing
  • Linear Algebra

Background:

  • Saddle point problems are common in scientific computing and often require efficient solution methods.
  • Existing generalized shift-splitting preconditioners have shown promise for symmetric positive definite (1,1)-block saddle point problems.
  • Solving large sparse augmented systems efficiently remains a challenge in various computational fields.

Purpose of the Study:

  • To develop and analyze a novel parameterized shift-splitting preconditioner for large sparse augmented systems.
  • To establish the unconditional convergence of the fixed-point iteration associated with the proposed preconditioner.
  • To demonstrate the effectiveness of the new preconditioner through numerical examples.

Main Methods:

  • A parameterized shift-splitting strategy is applied to the saddle point matrix.
  • A fixed-point iteration scheme is derived based on the parameterized splitting.
  • The convergence properties of the iteration are analyzed theoretically.
  • Numerical experiments are conducted to validate the performance.

Main Results:

  • A parameterized shift-splitting preconditioner is successfully established for augmented systems.
  • The proposed preconditioner leads to a fixed-point iteration with unconditional convergence.
  • The new method shows intersections with previously developed generalized shift-splitting preconditioners.
  • A numerical example confirms the practical effectiveness of the approach.

Conclusions:

  • The parameterized shift-splitting preconditioner offers an effective and unconditionally convergent method for solving large sparse augmented systems.
  • This work extends existing shift-splitting preconditioner techniques for saddle point problems.
  • The findings contribute to the development of more efficient numerical solvers in computational mathematics.