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second derivative function  (OriginLab corp)


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    OriginLab corp second derivative function
    Second Derivative Function, supplied by OriginLab corp, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/second+derivative/second+derivative+function/pm26854427-59-6-35
    Average 90 stars, based on 1 article reviews
    second derivative function - by Bioz Stars, 2026-10
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    Article Title: Investigating the influence of drug aggregation on the percutaneous penetration rate of tetracaine when applying low doses of the agent topically to the skin.
    Article Snippet: The first method employed a second derivative function that was applied to a Gaussian distribution function to determine the critical points, which could then be used to define the CAC with OriginPro (OriginPro version 8.6, Origin Lab Corporation, US).



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    a – e Conventional solitons can form in the presence of quadratic dispersion. a Equivalence of the dispersion operator in the time and frequency domains. b The dispersion (red) and (inverse) group velocity (dashed green) vary smoothly with frequency ω . The dot dashed vertical line marks the soliton central frequency ω 0 . c At low intensities I , dispersion stretches pulses in time. Solitons can form at high intensities with smooth ( d ) spectral and ( e ) temporal profiles that decay exponentially. f Corresponding dispersion operator for Hilbert-NLS solitons. g The dispersion relation Eq. has a discontinuous (disc.) derivative (red) and associated discontinuous (inverse) group velocity (dashed green) as a function of frequency; h At low intensities, the dispersion causes input pulses to split in two. At high intensities, solitons form, which have ( i ) a spectrum with discontinuous derivative, and ( k ) non-exponential decay in time. The units are arbitrary, and the intensity profiles in ( d , e , i ) and ( k ) are on logarithmic scales.

    Journal: Nature Communications

    Article Title: Nonlinear wave propagation governed by a fractional derivative

    doi: 10.1038/s41467-025-60625-4

    Figure Lengend Snippet: a – e Conventional solitons can form in the presence of quadratic dispersion. a Equivalence of the dispersion operator in the time and frequency domains. b The dispersion (red) and (inverse) group velocity (dashed green) vary smoothly with frequency ω . The dot dashed vertical line marks the soliton central frequency ω 0 . c At low intensities I , dispersion stretches pulses in time. Solitons can form at high intensities with smooth ( d ) spectral and ( e ) temporal profiles that decay exponentially. f Corresponding dispersion operator for Hilbert-NLS solitons. g The dispersion relation Eq. has a discontinuous (disc.) derivative (red) and associated discontinuous (inverse) group velocity (dashed green) as a function of frequency; h At low intensities, the dispersion causes input pulses to split in two. At high intensities, solitons form, which have ( i ) a spectrum with discontinuous derivative, and ( k ) non-exponential decay in time. The units are arbitrary, and the intensity profiles in ( d , e , i ) and ( k ) are on logarithmic scales.

    Article Snippet: To understand how a fractional Laplacian is represented in our optical experiment, we first consider the conventional case of the nonlinear Schrödinger equation, in which a second derivative operator (∣ β 2 ∣/2)(∂ 2 /∂ t 2 ), where β 2 is the dispersion coefficient, in the time domain, corresponds to a parabolic dispersion relation in frequency.

    Techniques: Dispersion