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The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist ...

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...

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 ...

The representation, beloved of engineers and physicists, of a complex number in terms of a complex exponential x+iy=|z|e^(iphi), (1) where i (called j by engineers) is the ...

A mathematical problem, usually not requiring advanced mathematics, to which a solution is desired. Puzzles frequently require the rearrangement of existing pieces (e.g., 15 ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...