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The height of a tree g is defined as the vertex height of its root vertex, where the vertex height of a vertex v in a tree g is the number of edges on the longest downward ...
The ratio X_1/X_2 of uniform variates X_1 and X_2 on the interval [0,1] can be found directly as P_(X_1/X_2)(u) = int_0^1int_0^1delta((x_1)/(x_2)-u)dx_1dx_2 (1) = ...
Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...
The constant polynomial P(x)=0 whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. ...
Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...
The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...
The inverse hyperbolic tangent tanh^(-1)z (Zwillinger 1995, p. 481; Beyer 1987, p. 181), sometimes called the area hyperbolic tangent (Harris and Stocker 1998, p. 267), is ...
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 ...
Let B={b_1,b_2,...} be an infinite Abelian semigroup with linear order b_1<b_2<... such that b_1 is the unit element and a<b implies ac<bc for a,b,c in B. Define a Möbius ...
A general class of means introduced by Italian mathematician Oscar Chisini (pronounced keeseenee) in 1929. Given a function of n variables f(x_1,...,x_n), the Chisini mean of ...
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