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The theorem is also useful on a more microscopic scale, in biology. Living systems, such as cells, can be analyzed thermodynamically. They are rather complex systems, where many energy transformations occur, and they often waste heat. Hence, the Gouy-Stodola theorem may be useful, in certain situations, to perform exergy analysis on such systems.
Littlewood's three principles are quoted in several real analysis texts, for example Royden, [2] Bressoud, [3] and Stein & Shakarchi. [4] Royden [5] gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a ...
The Poisson–Boltzmann equation describes a model proposed independently by Louis Georges Gouy and David Leonard Chapman in 1910 and 1913, respectively. [3] In the Gouy-Chapman model, a charged solid comes into contact with an ionic solution, creating a layer of surface charges and counter-ions or double layer. [4]
Schematic diagram of Gouy balance. The Gouy balance, invented by the French physicist Louis Georges Gouy, is a device for measuring the magnetic susceptibility of a sample. . The Gouy balance operates on magnetic torque, by placing the sample on a horizontal arm or beam suspended by a thin fiber, and placing either a permanent magnet or electromagnet on the other end of the arm, there is a ...
Louis Georges Gouy. Louis Georges Gouy (February 19, 1854 – January 27, 1926) [1] was a French physicist.He is the namesake of the Gouy balance, the Gouy–Chapman electric double layer model (which is a relatively successful albeit limited model that describes the electrical double-layer which finds applications in vast areas of studies from physical chemistry to biophysics) and the Gouy phase.
Geometric group theory grew out of combinatorial group theory that largely studied properties of discrete groups via analyzing group presentations, which describe groups as quotients of free groups; this field was first systematically studied by Walther von Dyck, student of Felix Klein, in the early 1880s, [2] while an early form is found in the 1856 icosian calculus of William Rowan Hamilton ...
While this example is simple, compare to the Nash embedding theorem, specifically the Nash–Kuiper theorem, which says that any short smooth embedding or immersion of in + or larger can be arbitrarily well approximated by an isometric -embedding (respectively, immersion). This is also a dense h-principle, and can be proven by an essentially ...
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.