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Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4 相似文献
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Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions. 相似文献
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Alfred Wünsche 《Annalen der Physik》1992,504(3):181-197
The eigenvalue problem for arbitrary linear combinations kα + μα? of a boson annihilation operator α and a boson creation operator α? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter. 相似文献
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Timur Seidel Alfred Golloch Hans Beerwald Günther Böhm 《Fresenius' Journal of Analytical Chemistry》1993,347(3-4):92-102
Summary A new analytical radiation source combined with fiber optics linked to a diode array detection device with modified software is described. The direct-reading spectrometer simultaneously covers the wavelength range 185–510 nm with a spectral resolution of <1.5 nm. Intense optical emission is observed when positionally stable high-current surface sparks supplied by a pulse-generator with definite discharge parameters (max. 800 Ampere/pulse) are sliding over compact non-conductive materials such as plastics, glasses, quartz filters or powder pellets. Substrate vaporization, ionization and excitation processes in the surface discharge plasma channel generate emission corresponding to neutral and ionic states. The spectra are essentially composed of lines emitted by the electrode material (e.g. copper, silver), from the substrate under investigation, radiation continuum as well as structured background from the surrounding air atmosphere. Due to the occurrence of emission lines of reactive fillers, inorganic pigments and stabilizers, a rapid multi-element screening method is demonstrated. A rapid identification system (mix-up test) of PVC or fire-retardant thermoplastics within one second has been realized from the atomic emission line intensity originating from the sputtered copper electrode material according to its increased volatility in the presence of chlorine (modified Beilstein test).Puls-Plasma-Technik GmbH, Dortmund 相似文献