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  2. Classification of discontinuities - Wikipedia

    en.wikipedia.org/wiki/Classification_of...

    With the same purpose, Walter Rudin [4] and Karl R. Stromberg [5] study also removable and jump discontinuities by using different terminologies. However, furtherly, both authors state that is always a countable set (see [6] [7]). The term essential discontinuity has evidence of use in mathematical context as early as 1889. [8]

  3. Oscillation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Oscillation_(mathematics)

    in a removable discontinuity, the distance that the value of the function is off by is the oscillation; in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits from the two sides); in an essential discontinuity, oscillation measures the failure of a limit to exist.

  4. Kuramoto model - Wikipedia

    en.wikipedia.org/wiki/Kuramoto_model

    In the work from Dörfler and colleagues, several theorems provide rigorous conditions for phase and frequency synchronization of this model. Further studies, motivated by experimental observations in neuroscience, focus on deriving analytical conditions for cluster synchronization of heterogeneous Kuramoto oscillators on arbitrary network ...

  5. Wave function - Wikipedia

    en.wikipedia.org/wiki/Wave_function

    Panels (E–F) show two different wave functions that are solutions of the Schrödinger equation but not standing waves. The wave function of an initially very localized free particle. In quantum physics , a wave function (or wavefunction ) is a mathematical description of the quantum state of an isolated quantum system .

  6. List of equations in wave theory - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_wave...

    The following may be deduced by applying the principle of superposition to two sinusoidal waves, using trigonometric identities. The angle addition and sum-to-product trigonometric formulae are useful; in more advanced work complex numbers and fourier series and transforms are used.

  7. Discontinuities of monotone functions - Wikipedia

    en.wikipedia.org/wiki/Discontinuities_of...

    Let be a real-valued monotone function defined on an interval. Then the set of discontinuities of the first kind is at most countable.. One can prove [5] [3] that all points of discontinuity of a monotone real-valued function defined on an interval are jump discontinuities and hence, by our definition, of the first kind.

  8. Gibbs phenomenon - Wikipedia

    en.wikipedia.org/wiki/Gibbs_phenomenon

    Since the Gibbs phenomenon comes from undershooting, it may be eliminated by using kernels that are never negative, such as the Fejér kernel. [12] [13]In practice, the difficulties associated with the Gibbs phenomenon can be ameliorated by using a smoother method of Fourier series summation, such as Fejér summation or Riesz summation, or by using sigma-approximation.

  9. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

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