Let F (z) = z − H(z) with o(H(z)) ≥ 2 be a formal map from Cn to Cn and G(z) the formal inverse of F (z). In this paper, we give two recurrent formulas for the formal inverse G(z). The first formula not only provides an efficient method for the calculation of G(z), but also reduces the inversion problem to a Cauchy problem of a partial differential equation. The second one is differential free ...

In the study of integrable systems of ODE’s arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. Many of these systems are algebraically completely integrable in that they linearize on the Jacobian of a spectral curve. In an earlier paper the authors gave a classification of the spectral curves in terms of the Weyl group and arranged the spectral curve...

which has a simple zero at (0, . . . , 0) residually: we have not only fi(0, . . . , 0) = 0 residually but also the Jacobian of this system J(0, . . . , 0) is in A×. We are going to associate, in an explicit way, to such a system a unitary polynomial f of degre m which is of the form Xm−1(X − 1) residually. To this polynomial we can associate the extension Af of A obtained by forcing f(z) = 0 a...

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then End(J(C)) = Z. Notice that it easily follows that the ring of K-endomorphisms of J(C) coincides with Z and the real pro...

background co-infection with human immunodeficiency virus (hiv) and hepatitis b virus (hbv) is common due to shared routes of transmission, as reported approximately 10% of 33 million hiv-infected patients worldwide are chronically infected with hbv. mutations of hbsag especially within the “a” determinant could alter the antigenicity of the protein, causing failure of hbsag neutralization and ...

The problem taken up in the study is the management of the company in terms of costs incurred on the implementation of the concept of sustainable development. The problem is important and topical in view of the possibility of increasing the efficiency of management in companies organizing their activities in the perspective of sustainable development. As a consequence of the formulated research...

Recently, significant technological changes, greater customer demand and the rise of new business models have triggered a rapid increase in electronic service (e-service) innovations. Now, innovation in the provision of e-services has become one of the priorities of managers in order to gain a competitive advantage. However, few studies so far have explored the determinant factors needed in the...