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Ramanujan's two-variable theta function f(a,b) is defined by f(a,b)=sum_(n=-infty)^inftya^(n(n+1)/2)b^(n(n-1)/2) (1) for |ab|<1 (Berndt 1985, p. 34; Berndt et al. 2000). It ...

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The ...

Bridge is a card game played with a normal deck of 52 cards. The number of possible distinct 13-card hands is N=(52; 13)=635013559600, (1) where (n; k) is a binomial ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...