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Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

The third-order ordinary differential equation 2y^(''')+yy^('')=0. This equation arises in the theory of fluid boundary layers, and must be solved numerically (Rosenhead ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

The Borwein integrals are the class of definite integrals defined by I_n=1/piint_0^inftyx^(-(n+1)/2)product_(k=1,3,...)^nsin(x/k)dx for odd n. The integrals are curious ...

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded ...

A roll of two 6s (the highest roll possible) on a pair of 6-sided dice. The probability of rolling boxcars in a single roll of two dice is 1/36, or 2.777...%. In order to ...

The area of the shadow of a body on a plane, also called the "outer quermass."

Let p_n/q_n be the sequence of convergents of the continued fraction of a number alpha. Then a Brjuno number is an irrational number such that ...

The nth root of the content of the set sum of two sets in n-dimensional Euclidean space is greater than or equal to the sum of the nth roots of the contents of the individual ...

A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...