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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.
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 ...
Abeka Book, LLC, known as A Beka Book until 2017, is an American publisher affiliated with Pensacola Christian College (PCC) that produces K-12 curriculum materials that are used by Christian schools and homeschooling families around the world. [3] [4] [5] It is named after Rebekah Horton, wife of college president Arlin Horton.
Russell believed that dominant function is the driving force behind all harmonic motion. Russell focuses on the Lydian mode because it can be built with fifths. For instance, to construct a C Lydian scale one could list the first seven tones on the circle of fifths starting with C, the desired Lydian Tonic.
Riemann's "dualist" system for relating triads was adapted from earlier 19th-century harmonic theorists. The term "dualism" refers to the emphasis on the inversional relationship between major and minor, with minor triads being considered "upside down" versions of major triads; this "harmonic dualism" (harmonic polarity) is what produces the change-in-direction described above.
Elon Musk and Vivek Ramaswamy—two billionaire entrepreneurs and new Trump administration advisors—are making bold promises. Namely: This week, the duo told Congress that through their advisory ...
Santiago Felipe/Getty, Giles Keyte/Universal Pictures 'Wicked' director Jon M. Chu; 'Wicked' stars Cynthia Erivo and Ariana Grande
The mother of American journalist Austin Tice, who was taken captive during a reporting trip to Syria in August 2012, voiced hope that upheaval in Syria would lead to freedom for her son.. Debra ...