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A relation R on a set S is symmetric provided that for every x and y in S we have xRy iff yRx. The symmetric relations on n nodes are isomorphic with the rooted graphs on n ...

The second-order ordinary differential equation y^('')-[(M^2-1/4+K^2-2MKcosx)/(sin^2x)+(sigma+K^2+1/4)]y=0.

A quartic surface which is the locus of zeros of the determinant of a symmetric 4×4 matrix of linear forms. A general symmetroid has 10 ordinary double points (Jessop 1916, ...

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

Symmetric points are preserved under a Möbius transformation. The Schwarz reflection principle is sometimes called the symmetry principle (Needham 2000, p. 252).

A map T:(M_1,omega_1)->(M_2,omega_2) between the symplectic manifolds (M_1,omega_1) and (M_2,omega_2) which is a diffeomorphism and T^*(omega_2)=omega_1, where T^* is the ...

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 pair (M,omega), where M is a manifold and omega is a symplectic form on M. The phase space R^(2n)=R^n×R^n is a symplectic manifold. Near every point on a symplectic ...

Informally, a symplectic map is a map which preserves the sum of areas projected onto the set of (p_i,q_i) planes. It is the generalization of an area-preserving map. ...

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...