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John Longeway notes that in the Middle Ages, the theory of demonstration, which developed the thinking in Aristotle's Posterior Analytics, was considered "the culmination of logic". [4] The modern scientific method often uses demonstrations that carefully describe certain processes and parts of nature in great detail. In science, often one ...
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.
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The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
Thomas Young and Hermann von Helmholtz assumed that the eye's retina consists of three different kinds of light receptors for red, green and blue.. The Young–Helmholtz theory (based on the work of Thomas Young and Hermann von Helmholtz in the 19th century), also known as the trichromatic theory, is a theory of trichromatic color vision – the manner in which the visual system gives rise to ...
Phillips resigned as president of Vision Forum on October 30, 2013 after acknowledging a "lengthy… relationship with a woman" which was "inappropriately affectionate and romantic." [ 12 ] [ 13 ] On November 11, 2013, Vision Forum Ministries' board of directors discontinued operations citing "serious sins" which prompted Phillips' resignation ...
Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. [1] The classic example is demonstrated with two similarly-tuned tuning forks. When one fork is struck and held near the other, vibrations are induced in the ...
A harmonic differential (one-form) is precisely the real part of an (analytic) complex differential. [1]: 172 To prove this one shows that u + iv satisfies the Cauchy–Riemann equations exactly when u + iv is locally an analytic function of x + iy. Of course an analytic function w(z) = u + iv is the local derivative of something (namely ∫w(z ...
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