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A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

Let |sum_(n=1)^pa_n|<K, (1) where K is independent of p. Then if f_n>=f_(n+1)>0 and lim_(n->infty)f_n=0, (2) it follows that sum_(n=1)^inftya_nf_n (3) converges.

Not continuous. A point at which a function is discontinuous is called a discontinuity, or sometimes a jump.

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

Johnson solid J_(90).

If lim_(k->infty)u_k!=0, then the series {u_n} diverges.

A divergent sequence is a sequence that is not convergent.

This statement seems incomplete. Locate a reference and complete statement of the condition. For any group of k men out of N, there must be at least k jobs for which they are ...