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An intensity-duration-frequency curve (IDF curve) is a mathematical function that relates the intensity of an event (e.g. rainfall) with its duration and frequency of occurrence. [1] Frequency is the inverse of the probability of occurrence. These curves are commonly used in hydrology for flood forecasting and civil engineering for urban ...
The equation loses accuracy for gaps under about 10 μm in air at one atmosphere [9] and incorrectly predicts an infinite arc voltage at a gap of about 2.7 μm. Breakdown voltage can also differ from the Paschen curve prediction for very small electrode gaps, when field emission from the cathode surface becomes important.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
More commonly used is the power spectral density (PSD, or simply power spectrum), which applies to signals existing over all time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The PSD then refers to the spectral energy distribution ...
In astronomy, a light curve is a graph of the light intensity of a celestial object or region as a function of time, typically with the magnitude of light received on the y-axis and with time on the x-axis. The light is usually in a particular frequency interval or band.
The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
Schwarzschild's equation is the formula by which you may calculate the intensity of any flux of electromagnetic energy after passage through a non-scattering medium when all variables are fixed, provided we know the temperature, pressure, and composition of the medium.