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A Münchhausen number (sometimes spelled Münchausen number, with a single 'h') is a number equal to the sum of its digits raised to each digit's power. Münchhausen numbers ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication (Wolfram 2002, pp. 5 and 716-717). More specifically, the ...

Surrogate data are artificially generated data which mimic statistical properties of real data. Isospectral surrogates have identical power spectra as real data but with ...

The average power of a complex signal f(t) as a function of time t is defined as <f^2(t)>=lim_(T->infty)1/(2T)int_(-T)^T|f(t)|^2dt, where |z| is the complex modulus (Papoulis ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

The whole neighborhood of any point y_i of an algebraic curve may be uniformly represented by a certain finite number of convergent developments in power series, ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...