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Let p be prime and r = r_mp^m+...+r_1p+r_0 (0<=r_i<p) (1) k = k_mp^m+...+k_1p+k_0 (0<=k_i<p), (2) then (r; k)=product_(i=0)^m(r_i; k_i) (mod p). (3) This is proved in Fine ...

Let rho(x) be an mth degree polynomial which is nonnegative in [-1,1]. Then rho(x) can be represented in the form {[A(x)]^2+(1-x^2)[B(x)]^2 for m even; ...

A necessary and sufficient condition for all the eigenvalues of a real n×n matrix A to have negative real parts is that the equation A^(T)V+VA=-I has as a solution where V is ...

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

A Lyndon word is an aperiodic notation for representing a necklace.

The Lyons group is the sporadic group Ly of order |Ly| = 51765179004000000 (1) = 2^8·3^7·5^6·7·11·31·37·67. (2) It is implemented in the Wolfram Language as LyonsGroupLy[].

If a sphere is covered by three closed sets, then one of them must contain a pair of antipodal points.

A robust estimation based on maximum likelihood arguments.

A tree not having the complete bipartite graph K_(1,2) with base at the vertex of degree two as a limb (Lu et al. 1993, Lu 1996).

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...