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Geometrical Product Specification and Verification (GPS&V) [1] is a set of ISO standards developed by ISO Technical Committee 213. [2] The aim of those standards is to develop a common language to specify macro geometry (size, form, orientation, location) and micro-geometry (surface texture) of products or parts of products so that the language can be used consistently worldwide.
Partitions of a 4-element set ordered by refinement. A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that ...
ASME Y14.41 is a standard published by American Society of Mechanical Engineers (ASME) which establishes requirements and reference documents applicable to the preparation and revision of digital product definition data (also known as model-based definition), which pertains to CAD software and those who use CAD software to create the product definition within the 3D model.
A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). [4] One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be ...
A generalization for partition into r sets was given by Helge Tverberg and is now known as Tverberg's theorem. It states that for any set of (+) + points in Euclidean d-space, there is a partition into r subsets whose convex hulls intersect in at least one common point.
Cylinder sets over topological vector spaces are the core ingredient in the [citation needed] definition of abstract Wiener spaces, which provide the formal definition of the Feynman path integral or functional integral of quantum field theory, and the partition function of statistical mechanics.
In the sense of universal algebra, a pointed set is a set together with a single nullary operation:, [a] which picks out the basepoint. [7] Pointed maps are the homomorphisms of these algebraic structures. The class of all pointed sets together with the class of all based maps forms a category.
A split graph may have more than one partition into a clique and an independent set; for instance, the path a–b–c is a split graph, the vertices of which can be partitioned in three different ways: the clique {a, b} and the independent set {c} the clique {b, c} and the independent set {a} the clique {b} and the independent set {a, c}
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