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Let R be a ring. If phi:R->S is a ring homomorphism, then Ker(phi) is an ideal of R, phi(R) is a subring of S, and R/Ker(phi)=phi(R).

The following table gives the centers of the first Yff circles triangle in terms of the centers of the reference triangle for Kimberling centers X_n with n<=100. X_n center ...

The first Yff triangle is the Cevian triangle DeltaA^'B^'C^' of the first Yff point. The area of the first Yff triangle is Delta=(u^3)/(2R), where R is the circumradius of ...

The statistical index P_B=sqrt(P_LP_P), where P_L is Laspeyres' index and P_P is Paasche's index.

A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information only in the signs of the differences ...

A balanced incomplete block design (v, k, lambda, r, b) exists only for b>=v (or, equivalently, r>=k).

Given T an unbiased estimator of theta so that <T>=theta. Then var(T)>=1/(Nint_(-infty)^infty[(partial(lnf))/(partialtheta)]^2fdx), where var is the variance.

Let A be a sum of squares of n independent normal standardized variates X_i, and suppose A=B+C where B is a quadratic form in the x_i, distributed as chi-squared with h ...

Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group H, denoted F(H). In the case of a finite group, the subgroup generated will itself ...