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Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

If f:[a,b]->[a,b] (where [a,b] denotes the closed interval from a to b on the real line) satisfies a Lipschitz condition with constant K, i.e., if |f(x)-f(y)|<=K|x-y| for all ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

The grouping of data into bins (spaced apart by the so-called class interval) plotting the number of members in each bin versus the bin number. The above histogram shows the ...

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits of its distinct prime factors (excluding 1). ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Let 1/p+1/q=1 (1) with p, q>1. Then Hölder's inequality for integrals states that int_a^b|f(x)g(x)|dx<=[int_a^b|f(x)|^pdx]^(1/p)[int_a^b|g(x)|^qdx]^(1/q), (2) with equality ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...