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The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...

A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2. Alternatively ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...

Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...

The Schrödinger equation describes the motion of particles in nonrelativistic quantum mechanics, and was first written down by Erwin Schrödinger. The time-dependent ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...