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A number n for which a shortest chain exists (which is also a Hansen chain) is called a Hansen number.

The Harada-Norton group is the sporadic group HN of order |HN| = 273030912000000 (1) = 2^(14)·3^6·5^6·7·11·19. (2) It is implemented in the Wolfram Language as ...

Let omega(n) be the number of distinct prime factors of n. If Psi(x) tends steadily to infinity with x, then lnlnx-Psi(x)sqrt(lnlnx)<omega(n)<lnlnx+Psi(x)sqrt(lnlnx) for ...

Let alpha_(n+1) = (2alpha_nbeta_n)/(alpha_n+beta_n) (1) beta_(n+1) = sqrt(alpha_nbeta_n), (2) then H(alpha_0,beta_0)=lim_(n->infty)a_n=1/(M(alpha_0^(-1),beta_0^(-1))), (3) ...

The statistical index P_H=(sumv_0)/(sum(v_0p_0)/(p_n))=(sump_0q_0)/(sum(p_0^2q_0)/(p_n)), where p_n is the price per unit in period n, q_n is the quantity produced in period ...

Let D=D(z_0,R) be an open disk, and let u be a harmonic function on D such that u(z)>=0 for all z in D. Then for all z in D, we have 0<=u(z)<=(R/(R-|z-z_0|))^2u(z_0).

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

The partial differential equation u_t=u_(xxx)u^3.

Let F be a finite field with q elements, and let F_s be a field containing F such that [F_s:F]=s. Let chi be a nontrivial multiplicative character of F and chi^'=chi ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...