Dy namic of Abelia n Subgroups of GL( n, $$\mathbb{C}$$): A Structure Theorem

In this paper, we characterize the dynamic of every Abelian subgroups of , or . We show that there exists a -invariant, dense open set U in saturated by minimal orbits with a union of at most n -invariant vector subspaces of of dimension n−1 or n−2 over . As a consequence, has height at most n and in particular it admits a minimal set in . This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15     

pH-Metric study of gamma-irradiated table sugar for dosimetry purpose

Table sugar has been studied for a long time as a dosimeter in radiation accident and in high-dose dosimetry by using different analytical techniques especially electron paramagnetic resonance (EPR) and optical absorption spectrometry (OA). In this work, we report the results obtained by pH-metry on gamma-irradiated sugar. Table sugar samples were exposed to gamma radiation with doses of 0.1–58 kGy. Aqueous solutions of sugar were prepared with different concentrations ranged from 1% to 60% (w/w). It was found that sugar solutions showed strong decrease of pH up to concentration of 10% (w/w) followed by a slow decrease for the concentrations between 10 and 60% (w/w). Two possible mechanisms are proposed to explain the acidity increasing of the sugar solutions based on the existence of a carbonyl radical induced by gamma irradiation in solid table sugar with an open ring structure. Results for radiation response, post-irradiation change, reading temperature, dose-rate effect and repeatability are presented in this study. The results showed that pH-metric/sugar solution is an adequate high-dose dosimetric system in the dose range of 0.1–10 kGy.     

Modeling wave-induced pore pressure and effective stress in a granular seabed

The response of a sandy seabed under wave loading is investigated on the basis of numerical modeling using a multi-scale approach. To that aim, the discrete element method is coupled to a finite volume method specially enhanced to describe compressible fluid flow. Both solid and fluid phase mechanics are upscaled from considerations established at the pore level. Model’s predictions are validated against poroelasticity theory and discussed in comparison with experiments where a sediment analog is subjected to wave action in a flume. Special emphasis is put on the mechanisms leading the seabed to liquefy under wave-induced pressure variation on its surface. Liquefaction is observed in both dilative and compactive regimes. It is shown that the instability can be triggered for a well-identified range of hydraulic conditions. Particularly, the results confirm that the gas content, together with the permeability of the medium are key parameters affecting the transmission of pressure inside the soil.     

EPR study of table sugar rod and powder as high dose dosimeters

In order to improve the ease of sample handling, the reproducibility of signal detection and quantification, simple methods of incorporating a homogeneous mixture containing sugar powder (30%) with wax (35%) and rubber (35%) into rods has been adopted. The dose response, the time stability of the free radicals produced in table sugar dosimeters (in both rod and powder form) by gamma radiation and the effect of the temperature during irradiation were studied by EPR (Electron Paramagnetic Resonance). The peak-to-peak height (PPH) measurement of the EPR signal is studied as a function of the absorbed gamma dose in the range 0.1–58 kGy. For the two forms, a linear dependency is found between 0.1 and 26 kGy. At higher doses the EPR signal amplitude continues to grow but non-linear up to 58 kGy. The dependence of temperature during irradiation has been investigated in the temperature range 25–40 °C and the calculated correction coefficients were found (2.7 ± 0.2)% °C^?1 and (1.5 ± 0.3)% °C^?1, respectively, for powder and rod forms. The time stability of the stored sugar samples was investigated for 34 days at room temperature, a rapid decrease of EPR signal was showed immediately after irradiation followed by slowly decrease.     

Supercyclic abelian semigroups of matrices on \mathbb {C}^{n}

We give a complete characterization of a supercyclic abelian semigroup of matrices on \(\mathbb {C}^{n}\) . For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over \(\mathbb {C}\) that form a supercyclic abelian semigroup on \({\mathbb {C}}^{n}\) . In particular, no abelian semigroup generated by \(n-1\) matrices on \(\mathbb {C}^{n}\) can be supercyclic.     

On Morse Conjecture for Flows on Closed Surfaces

Let M be a closed orientable surface and let ϕ be a C¹‐flow on M with set of singularities compact countable. In this paper, we prove the Morse conjecture for ϕ: if ϕ is topologically transitive then it is metrically transitive.     

On a Morse conjecture for analytic flows on compact surfaces

The aim of this paper is to prove a Morse conjecture; in particular it is shown that a topologically transitive analytic flow on a compact surface is metrically transitive. We also build smooth topologically transitive flows on surfaces which are not metrically transitive.     

Area preserving analytic flows with dense orbits

The aim of this paper is to give sufficient conditions on area-preserving flows that guarantee the existence of dense orbits. We also answer a question by M.D. Hirsch [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545-1553]. The results of this work are a generalization of the ones in [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545-1553] and [H. Marzougui, Area preserving flows with a dense orbit, Nonlinearity 15 (2002) 1379-1384].