Venn diagram

Summary

A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple closed curves drawn on a plane to represent sets. Very often, these curves are circles or ellipses. Similar ideas had been proposed before Venn such as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler (Letters to a German Princess) in 1768. The idea was popularised by Venn in Symbolic Logic, Chapter V "Diagrammatic Representation", published in 1881. Details A Venn diagram may also be called a set diagram or logic diagram. It is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed

Official source

https://en.wikipedia.org/wiki/Venn_diagram

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We extend the quasiparticle self-consistent approach beyond the GW approximation by using a range separated vertex function. The developed approach yields band gaps, dielectric constants, and band positions with an accuracy similar to highest-level electronic-structure calculations without exceeding the cost of regular quasiparticle self-consistent GW. We introduce an exchange-correlation kernel that accounts for the vertex over the full spatial range. In the long range it complies with the Ward identity, while it is approximated through the adiabatic local density functional in the short range. In this approach, the renormalization factor is balanced and the higher-order diagrams are effectively taken into account.

2021

Use cases are the modeling technique of UML for formalizing the functional requirements placed on systems. This technique has limitations in modeling the context of a system, in relating systems involved in a same business process, in reusing use cases, and in specifying various constraints such as execution constraints between use case occurrences. These limitations can be overcome to some extent by the realization of multiple diagrams of various types, but with unclear relationships between them. Thus, the specification activity becomes complex and error prone. In this paper, we show how to overcome the limitations of use cases by making the roles of actors explicit. Interestingly, our contributions not only make UML a more expressive specification language, they also make it simpler to use and more consistent.

2000