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Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

The pentanacci numbers are a generalization of the Fibonacci numbers defined by P_0=0, P_1=1, P_2=1, P_3=2, P_4=4, and the recurrence relation ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

Let p={a_1,a_2,...,a_n} be a permutation. Then i is a permutation ascent if a_i<a_(i+1). For example, the permutation {1,2,3,4} is composed of three ascents, namely {1,2}, ...

Polynomials s_k(x;lambda,mu) which are a generalization of the Boole polynomials, form the Sheffer sequence for g(t) = (1+e^(lambdat))^mu (1) f(t) = e^t-1 (2) and have ...

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value, |x|={-x for x<0; 0 for x=0; x for x>0. (1) Piecewise ...

A plaindrome is a number whose hexadecimal digits are in nondecreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, ...