Asymptotics of large eigenvalues for a class of band matrices

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in $l^2$

Estimating the NEMA characteristics of the J-PET tomograph using the GATE package

The novel whole-body PET system based on plastic scintillators is developed by the {J-PET} Collaboration. It consists of plastic scintillator strips arranged axially in the form of a cylinder, allowing the cost-effective construction of the total-body PET. In order to determine properties of the scanner prototype and optimize its geometry, advanced computer simulations using the GATE software were performed. The spatial resolution, the sensitivity, the scatter fraction and the noise equivalent count rate were estimated according to the NEMA norm as a function of the length of the tomograph, number of the detection layers, diameter of the tomographic chamber and for various types of the applied readout. For the single-layer geometry with the diameter of 85 cm, strip length of 100 cm, cross-section of 4 mm x 20 mm and silicon photomultipliers with the additional layer of wavelength shifter as the readout, the spatial resolution (FWHM) in the centre of the scanner is equal to 3 mm (radial, tangential) and 6 mm (axial). For the analogous double-layer geometry with the same readout, diameter and scintillator length, with the strip cross-section of 7 mm x 20 mm, the NECR peak of 300 kcps was reached at 40 kBq/cc activity concentration, the scatter fraction is estimated to about 35% and the sensitivity at the centre amounts to 14.9 cps/kBq. Sensitivity profiles were also determined

Asymptotic Completeness for Multiparticle Dispersive Charge Transfer Models

AbstractWe prove the asymptotic completeness of wave operators associated with the scattering of a quantum particle in a field of classical particles in the dispersive case when the free hamiltonian has the formH0=p(D) withpelliptic of degreem⩾1 and satisfying some convexity hypotheses