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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.
Informally, G has the above presentation if it is the "freest group" generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R. As a simple example, the cyclic group of order n has the ...
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.
Although Burnside [7] attributes the theorem to Jordan, [8] Eric Nummela [9] nonetheless argues that the standard name—"Cayley's Theorem"—is in fact appropriate. Cayley, in his original 1854 paper, [10] showed that the correspondence in the theorem is one-to-one, but he failed to explicitly show it was a homomorphism (and thus an embedding ...
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization.
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 ...
The Poisson–Boltzmann equation can be applied to biomolecular systems. One example is the binding of electrolytes to biomolecules in a solution. This process is dependent upon the electrostatic field generated by the molecule, the electrostatic potential on the surface of the molecule, as well as the electrostatic free energy. [13]