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Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

In the IEEE 754-2008 standard (referred to as IEEE 754 henceforth), a quiet NaN or qNaN is a NaN which is quiet in the sense of rarely signaling a floating-point exception. ...

Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

A problem also known as the points problem or unfinished game. Consider a tournament involving k players playing the same game repetitively. Each game has a single winner, ...

Given a reference triangle DeltaABC and a point P, the triple (x,y,z), with x=PA, y=PB and z=PC representing the distances from P to the vertices of the reference triangle, ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

A knot property, also called the twist number, defined as the sum of crossings p of a link L, w(L)=sum_(p in C(L))epsilon(p), (1) where epsilon(p) defined to be +/-1 if the ...

The series h_q(-r)=sum_(n=1)^infty1/(q^n+r) (1) for q an integer other than 0 and +/-1. h_q and the related series Ln_q(-r+1)=sum_(n=1)^infty((-1)^n)/(q^n+r), (2) which is a ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p). An s-cluster is an isolated group of s adjacent (i.e., horizontally ...

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...