Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Real modeReal mode, also called real address mode, is an operating mode of all x86-compatible CPUs. The mode gets its name from the fact that addresses in real mode always correspond to real locations in memory. Real mode is characterized by a 20-bit segmented memory address space (giving 1 MB of addressable memory) and unlimited direct software access to all addressable memory, I/O addresses and peripheral hardware. Real mode provides no support for memory protection, multitasking, or code privilege levels.
Canonical coordinatesIn mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details.
Protected modeIn computing, protected mode, also called protected virtual address mode, is an operational mode of x86-compatible central processing units (CPUs). It allows system software to use features such as segmentation, virtual memory, paging and safe multi-tasking designed to increase an operating system's control over application software. When a processor that supports x86 protected mode is powered on, it begins executing instructions in real mode, in order to maintain backward compatibility with earlier x86 processors.
Canonical commutation relationIn quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example, between the position operator x and momentum operator px in the x direction of a point particle in one dimension, where [x , px] = x px − px x is the commutator of x and px , i is the imaginary unit, and ħ is the reduced Planck's constant h/2π, and is the unit operator.
Virtual 8086 modeIn the 80386 microprocessor and later, virtual 8086 mode (also called virtual real mode, V86-mode, or VM86) allows the execution of real mode applications that are incapable of running directly in protected mode while the processor is running a protected mode operating system. It is a hardware virtualization technique that allowed multiple 8086 processors to be emulated by the 386 chip. It emerged from the painful experiences with the 80286 protected mode, which by itself was not suitable to run concurrent real-mode applications well.
