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A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

Let {a_i}_(i=0)^(N-1) be a periodic sequence, then the autocorrelation of the sequence, sometimes called the periodic autocorrelation (Zwillinger 1995, p. 223), is the ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

Ramanujan's Dirichlet L-series is defined as f(s)=sum_(n=1)^infty(tau(n))/(n^s), (1) where tau(n) is the tau function. Note that the notation F(s) is sometimes used instead ...

A complex polynomial is a polynomial with complex coefficients.