Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for each 0 6= d ∈ D, there exists an n = n(d) with dn = st where s ∈ S and t is v-coprime to each element of S. An integral domain D is an almost GCD (AGCD) domain if for every x, y ∈ D, there exists a positive integer n = n(x, y) such that xnD ∩ ynD is a principal ideal. We prove that the polynomial ring D[X...

in a bounded domain. In the case f (u)= p(x)uγ, a > 0, and γ >max(1,a), Lair and Wood [7] dealt with the above equation in bounded domain and the whole space. They proved the existence of entire large solution under the condition ∫∞ 0 rmax|x|=r p(x)dr <∞ when the domain is RN . Recall that u is a large solution on a bounded domain Ω in RN , if u(x) → +∞ as dist(x,∂Ω) → 0, and u is called an ent...

In terms of a multiscale approach based on the Landau-Ginzburg expansion and on ab initio parameters evaluated by means of the fully relativistic screened Korringa-Kohn-Rostoker method, the width of domain walls is evaluated for the whole range of concentration in NixFe1 x. It is found that domain-wall formation occurs only for x < 20% and x > 55%; i.e., in the neighborhood of the structural ph...

Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...

Pattern-based signal/noise separation is a common technique to suppress multiples. It can be formulated in the t x domain using non-stationary Prediction Error Filters (PEF). One can obtain a kinematically correct model of the multiples by downward continuation. The CMP gather and the corresponding multiple estimate are characterized by a space varying PEF. After applying a simple separation te...

Antoine Rousse,∗1 Christian Rischel,∗2 Sylvain Fourmaux,∗1 Ingo Uschmann,∗3 Eckhart Förster,∗3 Jean-Claude Gauthier,∗4 and Danièle Hulin∗1 ∗1 Laboratoire d’Optique Appliquee-ENSTA, CNRS UMR7639, Ecole Polytechnique, Chemin de la Huniere, France ∗2 Niels Bohr Institute, The Royal Veterinary and Agricultural University, Denmark ∗3 X-ray Optics Group, Institute of Optics and Quantum Electronics, F...