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Hilbert Spaces And Fourier Analysis
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that defines a distance function for which the space is a complete metric space. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer), and ergodic theory (which forms the mathematical underpinning of thermodynamics). John von Neumann coined the term ''Hilbert space'' for the abstract concept th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standing Waves On A String
Standing, also referred to as orthostasis, is a position in which the body is held in an ''erect'' ("orthostatic") position and supported only by the feet. Although seemingly static, the body rocks slightly back and forth from the ankle in the sagittal plane. The sagittal plane bisects the body into right and left sides. The sway of quiet standing is often likened to the motion of an inverted pendulum. Standing at attention is a military standing posture, as is stand at ease, but these terms are also used in military-style organisations and in some professions which involve standing, such as modeling. ''At ease'' refers to the classic military position of standing with legs slightly apart, not in as formal or regimented a pose as standing at attention. In modeling, ''model at ease'' refers to the model standing with one leg straight, with the majority of the weight on it, and the other leg tucked over and slightly around. Control Standing posture relies on dynamic rather than s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
