weak transitivity - meaning and definition. What is weak transitivity
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  3. weak transitivity

What (who) is weak transitivity - definition

GENERALIZATION OF TOTAL ORDERINGS ALLOWING TIES, AXIOMATIZED AS STRICT WEAK ORDERS, TOTAL PREORDERS, OR ORDERED PARTITIONS
Total preorder; Ordered partition of a set; Ordered partition; Strict weak order; Weak order; Strict weak ordering; Preferential arrangement; Transitivity of incomparability
  • The permutohedron on four elements, a three-dimensional [[convex polyhedron]]. It has 24 vertices, 36 edges, and 14 two-dimensional faces, which all together with the whole three-dimensional polyhedron correspond to the 75 weak orderings on four elements.
  • A weak order on the set <math>\{a, b, c, d\}</math> where <math>a</math> is ranked below <math>b</math> and <math>c, b</math> and <math>c</math> are of equal rank, and <math>d</math> is ranked above <math>b</math> and <math>c</math> <br/>I) representation as a strict weak order <math>\,<\,</math> where <math>x < y</math> is shown as an arrow from <math>x</math> to <math>y</math>; <br/>II) representations as a total preorder <math>\,\leq,</math> shown using arrows; <br/>III) representation as an ordered partition, with the sets of the partition as dotted ellipses and the total order on these sets shown with arrows.

Weak interaction         
  • electron antineutrino]].
  • W boson-}}}}).
  • Pion+}} decay through the weak interaction
  • spin]]. Note the lack of reflective symmetry between the states.
  • A diagram depicting the decay routes due to the charged weak interaction and some indication of their likelihood. The intensity of the lines is given by the [[CKM parameters]].
FUNDAMENTAL INTERACTION RESPONSIBLE FOR BETA DECAY AND NUCLEAR FISSION
Weak force; Weak nuclear interaction; Weak decay; Weak interactions; Weak Interaction; Weak Force; Quantum flavordynamics; Flavordynamics; Weak nuclear force; Weak nuclear interactions; Weak Law of Action and Reaction; Weak-Nuclear Force; Weak Nuclear Force; Nuclear weak force; Flavodynamics; Weak Nuclear Forces; Wesak force; V-A theory; W boson exchange; V–A theory; V−A theory
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion.
https://en.wikipedia.org/wiki/Weak_interaction
Weak inflection         
INFLECTION SYSTEM
Weak (grammatical term)
In grammar, the term weak (originally coined in German: schwach) is used in opposition to the term strong (stark) to designate a conjugation or declension when a language has two parallel systems. The only constant feature in all the grammatical usages of the word "weak" is that it forms a polarity with "strong"; there is not necessarily any objective "weakness" about the forms so designated.
https://en.wikipedia.org/wiki/Weak_inflection
weak interaction         
  • electron antineutrino]].
  • W boson-}}}}).
  • Pion+}} decay through the weak interaction
  • spin]]. Note the lack of reflective symmetry between the states.
  • A diagram depicting the decay routes due to the charged weak interaction and some indication of their likelihood. The intensity of the lines is given by the [[CKM parameters]].
FUNDAMENTAL INTERACTION RESPONSIBLE FOR BETA DECAY AND NUCLEAR FISSION
Weak force; Weak nuclear interaction; Weak decay; Weak interactions; Weak Interaction; Weak Force; Quantum flavordynamics; Flavordynamics; Weak nuclear force; Weak nuclear interactions; Weak Law of Action and Reaction; Weak-Nuclear Force; Weak Nuclear Force; Nuclear weak force; Flavodynamics; Weak Nuclear Forces; Wesak force; V-A theory; W boson exchange; V–A theory; V−A theory
(also weak force)
¦ noun Physics a short-range interaction between particles which is very much weaker than the electromagnetic and the strong interactions and conserves neither strangeness, parity, nor isospin.

Wikipedia

Weak ordering

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.

There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible.

Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library.

https://en.wikipedia.org/wiki/Weak ordering
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