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A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. [1] But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data points of ...
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives ...
Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński but appeared as a decorative pattern many centuries before the work of Sierpiński.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
For those who are feeling "stuck" or overwhelmed while striving for work-life balance, some experts recommend adopting a "pendulum lifestyle.". Coined by Dr. Jeffrey Karp, Ph.D, a professor of ...
In another class, he filled out a worksheet asking him to identify his favorite color and other favorite things that might help him relate to other addicts. Despite the story the records tell of Patrick’s generally happy disposition and his willingness to role-play his way to sobriety, he still hadn’t shed the self-doubt he had carried with ...
Diffraction geometry, showing aperture (or diffracting object) plane and image plane, with coordinate system. If the aperture is in x ′ y ′ plane, with the origin in the aperture and is illuminated by a monochromatic wave, of wavelength λ, wavenumber k with complex amplitude A(x ′,y ′), and the diffracted wave is observed in the unprimed x,y-plane along the positive -axis, where l,m ...
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