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Given a short exact sequence of modules 0->A->B->C->0, (1) let ...->P_2->^(d_2)P_1->^(d_1)P_0->^(d_0)A->0 (2) ...->Q_2->^(f_2)Q_1->^(f_1)Q_0->^(f_0)C->0 (3) be projective ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then every even function h(rho) analytic in ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

Let a distribution to be approximated be the distribution F_n of standardized sums Y_n=(sum_(i=1)^(n)(X_i-X^_))/(sqrt(sum_(i=1)^(n)sigma_X^2)). (1) In the Charlier series, ...

The 34 distinct convergent hypergeometric series of order two enumerated by Horn (1931) and corrected by Borngässer (1933). There are 14 complete series for which ...

Wynn's epsilon-method is a method for numerical evaluation of sums and products that samples a number of additional terms in the series and then tries to extrapolate them by ...

The extension of a, an ideal in commutative ring A, in a ring B, is the ideal generated by its image f(a) under a ring homomorphism f. Explicitly, it is any finite sum of the ...

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

An amicable pair (m,n) consists of two integers m,n for which the sum of proper divisors (the divisors excluding the number itself) of one number equals the other. Amicable ...