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

Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

312
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
312
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

433
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
433
Slant Asymptotes01:27

Slant Asymptotes

231
A function's behavior is often guided by asymptotic constraints, where one term dominates another, defining a limiting trend. In the given scenario, the mathematical pattern follows a rational function: a cubic term in the numerator is divided by a squared term in the denominator. This results in a function with distinct characteristics, including an oblique asymptote, critical points, and undefined regions.The function's validity is determined by the denominator, which must be nonzero. This...
231
Introduction to Nonlinear Inequalities01:25

Introduction to Nonlinear Inequalities

299
Linear and nonlinear inequalities are fundamental for analyzing variable relationships and identifying ranges satisfying specific conditions. A linear inequality involves variables raised only to the first power, resulting in a straight-line graph. This line partitions the coordinate plane into two distinct regions: one that satisfies the inequality and one that does not. Each region represents a set of solutions where the linear relationship holds true under the specified constraint.Nonlinear...
299
One-Way ANOVA01:18

One-Way ANOVA

14.7K
One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
14.7K
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

428
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...
428

You might also read

Related Articles

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

Sort by
Same author

Photoelectrochemical Dehydrogenative Cross-Coupling of Aliphatic C-H Bonds via an In-Situ-Generated Hypervalent Iodine Mediator.

Organic letters·2026
Same author

Practical and regioselective halonitrooxylation of olefins to access β-halonitrates.

Nature communications·2024
Same author

Enantioselective copper-catalyzed azidation/click cascade reaction for access to chiral 1,2,3-triazoles.

Nature communications·2024
Same author

HMGB1-Promoted Neutrophil Extracellular Traps Contribute to Cardiac Diastolic Dysfunction in Mice.

Journal of the American Heart Association·2022
Same author

Proton Conductive Lanthanide-Based Metal-Organic Frameworks: Synthesis Strategies, Structural Features, and Recent Progress.

Topics in current chemistry (Cham)·2022
Same author

Spatiotemporal evolution of NO<sub>2</sub> diffusion in Beijing in response to COVID-19 lockdown using complex network.

Chemosphere·2022

Related Experiment Video

Updated: Apr 2, 2026

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

10.2K

[Study on Error Analysis of Nonlinear Function Coefficient of FAIMS].

Le-hua Zhang, Chi-lai Chen, You-jiang Liu

    Guang Pu Xue Yu Guang Pu Fen Xi = Guang Pu
    |September 30, 2015
    PubMed
    Summary

    This study optimizes High Field Asymmetric waveform Ion Mobility Spectrometry (FAIMS) by developing a method to accurately solve nonlinear coefficients α2 and α4. This improves substance identification and enables faster, more precise field detection.

    More Related Videos

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
    09:01

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

    Published on: April 4, 2017

    9.2K
    ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
    07:11

    ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

    Published on: August 19, 2021

    3.1K

    Related Experiment Videos

    Last Updated: Apr 2, 2026

    Experimental Methods to Study Human Postural Control
    08:12

    Experimental Methods to Study Human Postural Control

    Published on: September 11, 2019

    10.2K
    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
    09:01

    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

    Published on: April 4, 2017

    9.2K
    ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
    07:11

    ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

    Published on: August 19, 2021

    3.1K

    Area of Science:

    • Analytical Chemistry
    • Spectroscopy

    Context:

    • High Field Asymmetric waveform Ion Mobility Spectrometry (FAIMS) relies on accurate nonlinear function coefficients (α2 and α4) for substance identification.
    • Current methods for determining α2 and α4 lack established error evaluation standards and prior information.
    • Variations in dispersion voltage significantly influence the spectral characteristics and thus the calculated α2 and α4 values.

    Purpose:

    • To develop a robust method for solving nonlinear function coefficients α2 and α4 in FAIMS.
    • To investigate the influence of dispersion voltage parameters on the accuracy of α2 and α4 determination.
    • To establish a reliable error evaluation standard for the solved coefficients.

    Summary:

    • Acetone, isopropanol, and 1, 2-dichlorobenzene were analyzed using a homemade FAIMS device across various dispersion voltages.
    • Analysis of spectral data revealed that α2 and α4 conform to a normal distribution (goodness of fit > 0.96), allowing standard deviation to serve as an error metric.
    • Optimized data acquisition strategies, focusing on specific dispersion voltage points, significantly reduce errors and improve the efficiency of solving α2 and α4.

    Impact:

    • The study establishes a reliable method for error evaluation of α2 and α4 coefficients, crucial for accurate substance identification in FAIMS.
    • Findings demonstrate that optimizing the number and selection method of dispersion voltage points can reduce detection frequency, enabling faster field analysis.
    • The research provides a foundation for enhanced rapid field detection and precise spectral analysis using FAIMS technology.