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The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

The Earls sequence gives the starting position in the decimal digits of pi (or in general, any constant), not counting digits to the left of the decimal point, at which a ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

For any Abelian group G and any natural number n, there is a unique space (up to homotopy type) such that all homotopy groups except for the nth are trivial (including the ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

The empire problem, also known as the m-pire problem) asks for the maximum number of colors needed to color countries such that no two countries sharing a common border have ...