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

Partial Derivatives and Gas Laws01:26

Partial Derivatives and Gas Laws

186
In functions with multiple variables, partial derivatives describe how a function changes with respect to one variable while keeping the others constant. A partial derivative is calculated from the ordinary derivative of the function with respect to the desired variable, while treating the other variables as constants. Consider the function z = f(x, y). The partial derivative of the function z with respect to x at constant y is written as (∂z/∂x)y, using 'curly d'. It...
186
Partial Fractions01:28

Partial Fractions

389
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
389
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

775
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
775
Introduction to Differential Equations01:20

Introduction to Differential Equations

550
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
550
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.4K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.4K
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

291
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
291

You might also read

Related Articles

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

Sort by
Same author

Multiomics reveals fatty acid metabolism and immune remodeling in retinal artery occlusion.

iScience·2026
Same author

Correlated clustering and projection for dimensionality reduction.

Machine learning: science and technology·2026
Same author

Knowledge Discovery and Drug-Repurposing Framework for Pancreatic Ductal Adenocarcinoma: Molecular Networking and Computational Docking.

Computational and structural biotechnology journal·2026
Same author

Editorial Expression of Concern: Nociceptive neurons promote gastric tumour progression via a CGRP-RAMP1 axis.

Nature·2026
Same author

VARIANT: Web Server for Decoding and Analyzing Viral Mutations at Genome and Protein Levels.

ArXiv·2026
Same author

Manifold topological deep learning for biomedical data.

Nature communications·2026

Related Experiment Video

Updated: May 4, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
09:43

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

8.5K

High-order fractional partial differential equation transform for molecular surface construction.

Langhua Hu1, Duan Chen2, Guo-Wei Wei3

  • 1Department of Mathematics Michigan State University, MI 48824, USA.

Molecular Based Mathematical Biology
|December 24, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces high-order fractional partial differential equations (PDEs) for advanced modeling and protein surface generation. The novel fractional PDE transform offers enhanced control over data analysis for signals and surfaces.

Keywords:
Fractional PDE transformFractional calculusHigh order fractional derivativesMolecular surface generation

More Related Videos

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

14.1K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.6K

Related Experiment Videos

Last Updated: May 4, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
09:43

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

8.5K
Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

14.1K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

7.6K

Area of Science:

  • Applied Mathematics
  • Computational Physics
  • Biophysics

Background:

  • Fractional calculus is vital for modeling, but high-order derivatives are underutilized.
  • Existing methods for high-order fractional derivatives present challenges in application and numerical stability.

Purpose of the Study:

  • To introduce arbitrarily high-order fractional partial differential equations (PDEs) for fractional hyperdiffusion modeling.
  • To develop a numerical method for solving these high-order fractional PDEs efficiently.
  • To apply these methods to biomolecular surface generation and analysis.

Main Methods:

  • Construction of high-order fractional PDEs using a fractional variational principle.
  • Development of a fast fractional Fourier transform (FFFT) for numerical integration.
  • Application to protein surface generation and analysis, including fractional PDE transform development.

Main Results:

  • Validated high-order fractional PDEs and FFFT in 2D and 3D settings for surface generation.
  • Demonstrated the fractional PDE transform's ability for time-frequency localization, spectral control, and spatial resolution regulation.
  • Showcased robust, stable, and efficient biomolecular surface generation, validated against benchmark indicators and MSMS.

Conclusions:

  • Arbitrarily high-order fractional PDEs provide a powerful framework for advanced modeling and data analysis.
  • The proposed methods are robust, stable, and computationally efficient for biomolecular surface generation.
  • The fractional PDE transform enables advanced mode decomposition and analysis of complex data.