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The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

A generalization of calculus of variations which draws the relationship between the stationary points of a smooth real-valued function on a manifold and the global topology ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

Iofinova and Ivanov (1985) showed that there exist exactly five bipartite cubic semisymmetric graphs whose automorphism groups preserves the bipartite parts and acts ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

The path graph P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2. A path graph is therefore a graph that can be drawn so that all of ...

The resistance distance between vertices i and j of a graph G is defined as the effective resistance between the two vertices (as when a battery is attached across them) when ...

There are at least two graphs associated with H. Walther. A graph on 25 vertices which appears somewhat similar to Tutte's fragment is implemented without discussion or ...

Delta_hf(x)=(f(x+h)-f(x))/h=(Deltaf)/h. It gives the slope of the secant line passing through f(x) and f(x+h). In the limit h->0, the difference quotient becomes the partial ...