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A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

Let P_i=x_i:y_i:z_i be trilinear points for i=1, 2, 3. The A-vertex of the unary cofactor triangle is then defined as the point y_2z_3-z_2y_3:z_2x_3-x_2z_3:x_2y_3-y_2x_3, and ...

A triangular matrix U of the form U_(ij)={a_(ij) for i<=j; 0 for i>j. (1) Written explicitly, U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... a_(nn)]. ...

For a second-order ordinary differential equation, y^('')+p(x)y^'+q(x)y=g(x). (1) Assume that linearly independent solutions y_1(x) and y_2(x) are known to the homogeneous ...

The Weibull distribution is given by P(x) = alphabeta^(-alpha)x^(alpha-1)e^(-(x/beta)^alpha) (1) D(x) = 1-e^(-(x/beta)^alpha) (2) for x in [0,infty), and is implemented in ...

Let all of the functions f_n(z)=sum_(k=0)^inftya_k^((n))(z-z_0)^k (1) with n=0, 1, 2, ..., be regular at least for |z-z_0|<r, and let F(z) = sum_(n=0)^(infty)f_n(z) (2) = (3) ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...