Search Results for ""

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

The n-roll mill curve is given by the equation x^n-(n; 2)x^(n-2)y^2+(n; 4)x^(n-4)y^4-...=a^n, where (n; k) is a binomial coefficient.

If the fourth moment mu_4!=0, then P(|x^_-mu_4|>=lambda)<=(mu_4+3(N-1)sigma^4)/(N^3lambda^4), where sigma^2 is the variance.

A sequence of real numbers {x_n} is equidistributed on an interval [a,b] if the probability of finding x_n in any subinterval is proportional to the subinterval length. The ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

Another "beta function" defined in terms of an integral is the "exponential" beta function, given by beta_n(z) = int_(-1)^1t^ne^(-zt)dt (1) = ...