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A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

A graph in which individual nodes have no distinct identifications except through their interconnectivity. Graphs in which labels (which are most commonly numbers) are ...

The fractal-like two-dimensional function f(x,y)=((x^2-y^2)sin((x+y)/a))/(x^2+y^2). The function is named for the appearance of a butterfly-like pattern centered around the ...

An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram. The plot above shows 1/x, which has a vertical ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...

A point where a curve intersects itself along four arcs. The above plot shows the quadruple point at the origin of the quadrifolium (x^2+y^2)^3-4x^2y^2=0.

The vertical axis of a two-dimensional plot in Cartesian coordinates. Physicists and astronomers sometimes call this axis the ordinate, although that term is more commonly ...

A p-element x of a group G is semisimple if E(C_G(x))!=1, where E(H) is the commuting product of all components of H and C_G(x) is the centralizer of G.

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

A plot of the cumulative frequency against the upper class boundary with the points joined by line segments. Any continuous cumulative frequency curve, including a cumulative ...