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A von Neumann architecture scheme. The von Neumann architecture—also known as the von Neumann model or Princeton architecture—is a computer architecture based on the First Draft of a Report on the EDVAC, [1] written by John von Neumann in 1945, describing designs discussed with John Mauchly and J. Presper Eckert at the University of Pennsylvania's Moore School of Electrical Engineering.
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC.
Von Neumann describes a detailed design of a "very high speed automatic digital computing system." He divides it into six major subdivisions: a central arithmetic part, CA; a central control part, CC; memory, M; input, I; output, O; and (slow) external memory, R, such as punched cards, Teletype tape, or magnetic wire or steel tape.
Von Neumann's model of an expanding economy considered the matrix pencil A − λB with nonnegative matrices A and B; von Neumann sought probability vectors p and q and a positive number λ that would solve the complementarity equation () = along with two inequality systems expressing economic efficiency.
The Schrödinger equation or, actually, the von Neumann equation, is a special case of the GKSL equation, which has led to some speculation that quantum mechanics may be productively extended and expanded through further application and analysis of the Lindblad equation. [2]
Therefore, the axiom of limitation of size holds for the model V κ. The theorem stating that V κ has a well-ordering can be proved directly. Since κ is an ordinal of cardinality κ and |V κ | = κ, there is a one-to-one correspondence between κ and V κ. This correspondence produces a well-ordering of V κ. Von Neumann's proof is indirect.
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
can be thought of as being built in "stages" resembling the construction of the von Neumann universe, . The stages are indexed by ordinals . In von Neumann's universe, at a successor stage, one takes V α + 1 {\displaystyle V_{\alpha +1}} to be the set of all subsets of the previous stage, V α {\displaystyle V_{\alpha }} .