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Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

The term "isomorphic" means "having the same form" and is used in many branches of mathematics to identify mathematical objects which have the same structural properties. ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

Two partially ordered sets are said to be isomorphic if their "structures" are entirely analogous. Formally, partially ordered sets P=(X,<=) and Q=(X^',<=^') are isomorphic ...

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

Let a plane figure have area A and perimeter p. Then Q=(4piA)/(p^2)<=1, where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...