Abstract:
We present an algorithm which computes the Hilbert depth of a graded module based on a theorem of Uliczka. Connected to a Herzog's question we see that the Hilbert depth of a direct sum of modules can be strictly bigger than the Hilbert depth of all the summands.

Abstract:
In this paper we show that the depth and the Stanley depth of the factor of two monomial ideals is invariant under taking a so called canonical form. It follows easily that the Stanley Conjecture holds for the factor if and only if it holds for its canonical form. In particular, we construct an algorithm which simplifies the depth computation and using the canonical form we massively reduce the run time for the sdepth computation.

Abstract:
Let $I$ be an intersection of three monomial prime ideals of a polynomial algebra $S$ over a field. We give a special Stanley decomposition of $I$ which provides a lower bound of the Stanley depth of $I$, greater than or equal to $\depth\ (I)$, that is, Stanley's Conjecture holds for $I$.

Abstract:
Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.

Abstract:
An algorithmic proof of General Neron Desingularization is given here for one dimensional local domains and it is implemented in \textsc{Singular}. Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional Cohen-Macaulay local rings.

Abstract:
In the last years the Space Science community was confronted to a continuous increasing interest in Martian missions, extra-solar planet search and multi-satellite missions. The presented T.I.P.O. mission is a proposal for a research program dedicated to study, by space borne interferometric methods, the radio emissions generated in the atmospheres and magnetospheres of planets, both solar and extra-solar.

Abstract:
In the Dimension Embedded in Unified Symmetry (Adrian Sabin Popescu, D.E.U.S. (Dimension Embedded in Unified Symmetry), p. 221-247, Ed. Cartea Universitara, Bucuresti, ISBN 978-973-731-519-9 (arXiv:0704.2670) (2007)) book we made a qualitative description of the way in which we can construct the Large Scale Structure of the Universe from the knot-particle equivalence. Even that we are limited by the lack of computational power implemented on a nonlinear computational architecture needed to conduct this study to its finish, we are still able to give the algorithm to be used in a future simulation, on a, let say, quantum computer.

Abstract:
The fortress of Noviodunum on the lower Danube guarded the border of both the Roman and the Byzantine empires. The Noviodunum Archaeological Project, based in the Institute of Archaeology, is an international collaborative project with the primary aim of investigating the changing economic relations between the fortress, its hinterland and the wider Mediterranean world. The project began in 2000 and the final season of fieldwork will take place in 2009. In this article the directors describe the work of the last four seasons and present preliminary conclusions.

Abstract:
It is shown that the current-induced torques between a ferromagnetic layer and an antiferromagnetic layer with a compensated interface vanish when the ferromagnet is aligned with an axis of spin-rotation symmetry of the antiferromagnet. For properly chosen geometries this implies that the current induced torque can stabilize the out-of-plane (or hard axis) orientation of the ferromagnetic layer. This current-induced torque relies on phase coherent transport, and we calculate the robustness of this torque to phase breaking scattering. From this it is shown that the torque is not linearly dependent on applied current, but has an absolute maximum.