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A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

Let p_i denote the ith prime, and write m=product_(i)p_i^(v_i). Then the exponent vector is v(m)=(v_1,v_2,...).

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)

An inscribed angle is an angle ∠ABC formed by points A, B, and C on a circle's circumference as illustrated above. For an inscribed angle ∠ABC and central angle ∠AOC with the ...

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...

The continued fraction ((x+1)^n-(x-1)^n)/((x+1)^n+(x-1)^n)=n/(x+)(n^2-1)/(3x+)(n^2-2^2)/(5x+...).

The second-order ordinary differential equation y^('')-[(m(m+1)+1/4-(m+1/2)cosx)/(sin^2x)+(lambda+1/2)]y=0.

The vector field N_f(z)=-(f(z))/(f^'(z)) arising in the definition of the Newtonian graph of a complex univariate polynomial f (Smale 1985, Shub et al. 1988, Kozen and ...

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.