Riesz spectral systems

In this paper we study systems in which the system operator, $A$, has a Riesz basis of (generalized) eigenvectors. We show that this class is subset of the class of spectral operators as studied by Dunford and Schwartz. For these systems we investigate several system theoretic properties, like stability and controllability. We apply our theory to Euler-Bernoulli beam with structural damping

Stability and boundedness of continuous- and discrete-time systems

In this paper we investigate the relation between discrete- and continuous-time systems. More precisely, we investigate the stability properties of the semigroup generated by A, and the sequence $A_d^n$, $n=1,2,...$, where $A_d = (I + A)(I - A)^{-1}$

On the Semigroup for Age Dependent Population Dynamics with Spatial Diffusion

AbstractWe continue a population model with age dependence and spatial diffusion in the semigroup framework, in which the assumptions of our previous paper [Manuscripta Math.66 (1990), 161-180] that birth and death rates are independent of spatial variables are removed. The infinitesimal generator is identified and its spectrum studied, and accordingly, by using a positive semigroup theory, we determine its dominant eigenvalue and hence the asymptotic expression is obtained

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

Nuclear effects in the Drell-Yan process at very high energies

We study Drell-Yan (DY) dilepton production in proton(deuterium)-nucleus and in nucleus-nucleus collisions within the light-cone color dipole formalism. This approach is especially suitable for predicting nuclear effects in the DY cross section for heavy ion collisions, as it provides the impact parameter dependence of nuclear shadowing and transverse momentum broadening, quantities that are not available from the standard parton model. For p(D)+A collisions we calculate nuclear shadowing and investigate nuclear modification of the DY transverse momentum distribution at RHIC and LHC for kinematics corresponding to coherence length much longer than the nuclear size. Calculations are performed separately for transversely and longitudinally polarized DY photons, and predictions are presented for the dilepton angular distribution. Furthermore, we calculate nuclear broadening of the mean transverse momentum squared of DY dileptons as function of the nuclear mass number and energy. We also predict nuclear effects for the cross section of the DY process in heavy ion collisions. We found a substantial nuclear shadowing for valence quarks, stronger than for the sea.Comment: 46 pages, 18 figures, title changed and some discussion added, accepted for publication in PR

Transverse Momentum Broadening in Semi-inclusive DIS on Nuclei

Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES energies, prehadron elastic scatterings contribute little to $p_\perp$-broadening. The acquired extra $\Delta p_\perp^2$ of hadrons can therefore be deduced entirely from the first stage of quasi free quark propagation with quark-nucleon collisions. We use this model to describe $\pi$-production on Ne, Kr, Xe and compare with the most recent HERMES preliminary data.Comment: 17 pages, 9 figures, Slightly modified plot legends to indicate that HERMES data are preliminar

The ARGO-YBJ Experiment Progresses and Future Extension

Gamma ray source detection above 30TeV is an encouraging approach for finding galactic cosmic ray origins. All sky survey for gamma ray sources using wide field of view detector is essential for population accumulation for various types of sources above 100GeV. To target the goals, the ARGO-YBJ experiment has been established. Significant progresses have been made in the experiment. A large air shower detector array in an area of 1km2 is proposed to boost the sensitivity. Hybrid detection with multi-techniques will allow a good discrimination between different types of primary particles, including photons and protons, thus enable an energy spectrum measurement for individual specie. Fluorescence light detector array will extend the spectrum measurement above 100PeV where the second knee is located. An energy scale determined by balloon experiments at 10TeV will be propagated to ultra high energy cosmic ray experiments

Measurement of the Atmospheric Muon Spectrum from 20 to 3000 GeV

The absolute muon flux between 20 GeV and 3000 GeV is measured with the L3 magnetic muon spectrometer for zenith angles ranging from 0 degree to 58 degree. Due to the large exposure of about 150 m2 sr d, and the excellent momentum resolution of the L3 muon chambers, a precision of 2.3 % at 150 GeV in the vertical direction is achieved. The ratio of positive to negative muons is studied between 20 GeV and 500 GeV, and the average vertical muon charge ratio is found to be 1.285 +- 0.003 (stat.) +- 0.019 (syst.).Comment: Total 32 pages, 9Figure