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A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

Use the definition of the q-series (a;q)_n=product_(j=0)^(n-1)(1-aq^j) (1) and define [N; M]=((q^(N-M+1);q)_M)/((q;q)_m). (2) Then P. Borwein has conjectured that (1) the ...

y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...

A complemented lattice is an algebraic structure (L, ^ , v ,0,1,^') such that (L, ^ , v ,0,1) is a bounded lattice and for each element x in L, the element x^' in L is a ...

A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...

If the sampling of an interferogram is modulated at a definite frequency instead of being uniformly sampled, spurious spectral features called "ghosts" are produced (Brault ...

A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...