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

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

49.9K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than...
49.9K
Ladder Diagrams: Complexation Equilibria01:07

Ladder Diagrams: Complexation Equilibria

686
Ladder diagrams are useful for evaluating equilibria involving metal-ligand complexes. The vertical scale of the ladder diagram represents the concentration of unreacted or free ligand, pL. The horizontal lines on the scale depict the log of stepwise formation constants for metal-ligand complexes and indicate the dominant species in all the regions.
The formation constant, K1, for the formation of Cd(NH3)2+ complex from cadmium and ammonia is 3.55 × 102. Log K1 (i.e. pNH3) is 2.55, and...
686
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

32.0K
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
32.0K
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

452
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
452
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

2.0K
Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
2.0K
Fischer Projections02:18

Fischer Projections

18.0K
Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.
18.0K

You might also read

Related Articles

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

Sort by
Same author

Stability of a model of human granulopoiesis using continuous maturation.

Journal of mathematical biology·2004
Same journal

Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator.

Numerical methods for partial differential equations·2022
Same journal

Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel.

Numerical methods for partial differential equations·2020
Same journal

Mathematical modeling for novel coronavirus (COVID-19) and control.

Numerical methods for partial differential equations·2020
Same journal

Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport.

Numerical methods for partial differential equations·2019
Same journal

Dynamic Data-Driven Finite Element Models for Laser Treatment of Cancer.

Numerical methods for partial differential equations·2011
See all related articles

Related Experiment Video

Updated: Apr 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Double complexes and local cochain projections.

Richard S Falk1, Ragnar Winther2

  • 1Department of Mathematics, Rutgers University Piscataway, New Jersey, 08854.

Numerical Methods for Partial Differential Equations
|April 28, 2015
PubMed
Summary
This summary is machine-generated.

Researchers developed new local bounded cochain projections for finite element exterior calculus. This advances stability analysis by overcoming the nonlocality of previous methods.

Keywords:
cochain projectionsfinite element exterior calculusstability analysis

More Related Videos

Preparation of SNS CobaltII Pincer Model Complexes of Liver Alcohol Dehydrogenase
06:31

Preparation of SNS CobaltII Pincer Model Complexes of Liver Alcohol Dehydrogenase

Published on: March 19, 2020

7.8K
Versatile CO2 Transformations into Complex Products: A One-pot Two-step Strategy
07:36

Versatile CO2 Transformations into Complex Products: A One-pot Two-step Strategy

Published on: November 9, 2019

8.5K

Related Experiment Videos

Last Updated: Apr 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K
Preparation of SNS CobaltII Pincer Model Complexes of Liver Alcohol Dehydrogenase
06:31

Preparation of SNS CobaltII Pincer Model Complexes of Liver Alcohol Dehydrogenase

Published on: March 19, 2020

7.8K
Versatile CO2 Transformations into Complex Products: A One-pot Two-step Strategy
07:36

Versatile CO2 Transformations into Complex Products: A One-pot Two-step Strategy

Published on: November 9, 2019

8.5K

Area of Science:

  • Mathematical analysis
  • Computational mathematics
  • Topology

Background:

  • Bounded cochain projections are crucial for stability analysis in finite element exterior calculus.
  • Current methods combine smoothing operators with canonical projections, resulting in nonlocal operators.
  • Nonlocality in these projections is an undesirable property hindering certain applications.

Purpose of the Study:

  • To present an alternative construction of bounded cochain projections.
  • To develop bounded cochain projections that are local, unlike existing methods.
  • To enhance the applicability of finite element exterior calculus in stability analysis.

Main Methods:

  • Utilizing a double complex structure, analogous to the Čech-de Rham double complex.
  • Developing a novel approach to construct bounded cochain projections.
  • Ensuring the constructed projections commute with the exterior derivative and are bounded in Sobolev spaces.

Main Results:

  • A new construction for bounded cochain projections has been established.
  • These newly constructed projections exhibit locality, a significant improvement over prior methods.
  • The double complex structure provides a powerful framework for this construction.

Conclusions:

  • The development of local bounded cochain projections offers a significant advancement.
  • This new construction is expected to improve stability analysis in finite element exterior calculus.
  • The use of double complex structures opens new avenues for theoretical and computational advancements.