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A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

A strong Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a strong pseudo-Riemannian metric and positive definite. In a very precise way, the ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

A weak Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a weak pseudo-Riemannian metric and positive definite. In a very precise way, the ...

The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

The Moser spindle is the 7-node unit-distance graph illustrated above (Read and Wilson 1998, p. 187). It is sometimes called the Hajós graph (e.g., Bondy and Murty 2008. p. ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...