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Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

Let P=p:q:r and U=u:v:w be points in trilinear coordinates, neither of which is on a side line of a reference triangle DeltaABC. Them the P-isoconjugate of U is the point ...

The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A=pir_A^2) with same perimeter (p=2pir_p) as the curve, Q = ...

Find the minimum number f(n) of subsets in a separating family for a set of n elements, where a separating family is a set of subsets in which each pair of adjacent elements ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...

Writing a Fourier series as f(theta)=1/2a_0+sum_(n=1)^(m-1)sinc((npi)/(2m))[a_ncos(ntheta)+b_nsin(ntheta)], where m is the last term, reduces the Gibbs phenomenon. The ...

Let F be the set of complex analytic functions f defined on an open region containing the closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each f in ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

Legion's number of the first kind is defined as L_1 = 666^(666) (1) = 27154..._()_(1871 digits)98016, (2) where 666 is the beast number. It has 1881 decimal digits. Legion's ...