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A tree-like curve with finitely many marked double points In mathematics , particularly in differential geometry , a tree-like curve is a generic immersion c : S 1 → R 2 {\displaystyle c:S^{1}\to \mathbb {R} ^{2}} with the property that removing any double point splits the curve into exactly two disjoint connected components .
Tree topology, a topology based on a hierarchy of nodes in a computer network; Tree diagram (physics), an acyclic Feynman diagram, pictorial representations of the mathematical expressions governing the behavior of subatomic particles; Outliners, a common software application that is used to generate tree diagrams; Network diagram; Tree ...
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves , space curves , polyhedra , ordinary differential equations , partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films ...
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear operators acting upon these spaces and respecting these structures in a suitable sense.
There are eight ways that signs can be assigned to the sides of a triangle. An odd number of negative signs makes an unbalanced triangle, according to Fritz Heider's theory. In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign.
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
Euler tour of a tree, with edges labeled to show the order in which they are traversed by the tour. The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge