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A transpose of a doubly indexed object is the object obtained by replacing all elements a_(ij) with a_(ji). For a second-tensor rank tensor a_(ij), the tensor transpose is ...

The biharmonic operator, also known as the bilaplacian, is the differential operator defined by del ^4=(del ^2)^2, where del ^2 is the Laplacian. In n-dimensional space, del ...

An orthogonal projection of a cross onto a three-dimensional subspace. It is said to be normalized if the cross vectors are all of unit length.

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

Unit vectors which are orthogonal are said to be orthonormal.

The scalar |v|=ds/dt, where s is the arc length, equal to the magnitude of the velocity v.

A number n with prime factorization n=product_(i=1)^rp_i^(a_i) is called k-almost prime if it has a sum of exponents sum_(i=1)^(r)a_i=k, i.e., when the prime factor ...

The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n=product_(j=0)^(n-1)((3j+1)!)/((n+j)!). This ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

The Barnes-Wall lattice is a d-dimensional lattice that exists when d is a power of 2. It is implemented in the Wolfram Language as LatticeData[{"BarnesWall", n}]. Special ...