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Every request received by a non-failing node in the system must result in a response. This is the definition of availability in CAP theorem as defined by Gilbert and Lynch. [1] Note that availability as defined in CAP theorem is different from high availability in software architecture. [5] Partition tolerance
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap ...
Pitot theorem (plane geometry) Pizza theorem ; Pivot theorem ; Planar separator theorem (graph theory) Plancherel theorem (Fourier analysis) Plancherel theorem for spherical functions (representation theory) Poincaré–Bendixson theorem (dynamical systems) Poincaré–Birkhoff–Witt theorem (universal enveloping algebras)
The tradeoff between availability, consistency and latency, as described by the PACELC theorem. In database theory, the PACELC theorem is an extension to the CAP theorem.It states that in case of network partitioning (P) in a distributed computer system, one has to choose between availability (A) and consistency (C) (as per the CAP theorem), but else (E), even when the system is running ...
A convex cap, also known as a convex floating body [1] or just floating body, [2] is a well defined structure in mathematics commonly used in convex analysis for approximating convex shapes. In general it can be thought of as the intersection of a convex Polytope with a half-space .
In affine geometry, a cap set is a subset of the affine space (the -dimensional affine space over the three-element field) where no three elements sum to the zero vector. The cap set problem is the problem of finding the size of the largest possible cap set, as a function of n {\displaystyle n} . [ 1 ]
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In analogy with the interpretation of the cup product in terms of the Künneth formula, we can explain the existence of the cap product in the following way.Using CW approximation we may assume that is a CW-complex and () (and ()) is the complex of its cellular chains (or cochains, respectively).