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Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

A square n×n matrix A=a_(ij) is called reducible if the indices 1, 2, ..., n can be divided into two disjoint nonempty sets i_1, i_2, ..., i_mu and j_1, j_2, ..., j_nu (with ...

A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of ...

R(X_1,...X_n)=sum_(i=1)^nH(X_i)-H(X_1,...,X_n), where H(x_i) is the entropy and H(X_1,...,X_n) is the joint entropy. Linear redundancy is defined as ...

A reference triangle is a triangle relative to which trilinear coordinates, exact trilinear coordinates, derived triangle, or other objects are defined in triangle geometry ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

Let X be a normed space and X^(**)=(X^*)^* denote the second dual vector space of X. The canonical map x|->x^^ defined by x^^(f)=f(x),f in X^* gives an isometric linear ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...