Abstract. For any given set of angles θ 0 < . . . < θ n in [0, π), we show that a set of n+2 2Radon projections, consisting of k parallel X-ray beams in each direction θ k , k = 0, . . . , n, determines uniquely algebraic polynomials of degree n in two variables. Introduction.Most of the methods for approximate reconstruction of a univariate function f are based on sampling values of f at a finite number of points, and the tools used are usually those of interpolation. This is a natural approach to approximation of univariate functions since a table of function values is a standard type of information about f that comes as output in practical problems and processes described by functions in one variable, and in addition, the Lagrange interpolation problem by polynomials is always solvable. In the multivariate case, such an approach encounters serious difficulties. For example, it is well known that pointwise interpolation by multivariate polynomials is no more possible for every choice of nodes. Moreover, there are a lot of practical problems in which information about the relevant function comes as a set of functionals different from point evaluations. In tomography, electronic microscopy, and technics, the data often consists of values of linear integrals over segments. In many situations, a table of mean values of a function of d variables on (d − 1)-dimensional hyperplanes is considered to be the most natural type of data for multivariate functions. Hakopian's famous interpolation formula [6] (see also [7]) is an important reason to take this approach.Hakopian proved that for any given n + 2 distinct points X 0 , . . . , X n+1 on the boundary of a convex body D (say, a disk), the set of integrals of f over all the linear segments [X i , X j ] determines uniquely every polyno-

One of the pathological hallmarks of Alzheimer’s disease (AD) associated with its progression that contributes to β-amyloid (Aβ) generation is oxidative stress (OS). Clinical data suggest that melatonin is a potent antioxidant that might be effective in the adjunctive therapy of this neurodegenerative disease. The present study aimed to explore the role of melatonin on behavioral changes and markers of OS in three rat models, namely, pinealectomy (pin) model of melatonin deficit, intracerebroventricular (icv)Aβ1-42 model of AD, and combination of both pin and Aβ1-42 model (pin+icvAβ1-42). The chronic injection with vehicle/melatonin (50 mg/kg, i.p. for 40 days) started on the same day of sham/pin and icv vehicle/Aβ1-42 infusion procedures. Anxiety in the open field and the elevated plus-maze test and cognitive responses in the object recognition test were tested between the 30th–35th day after the surgical procedures. Markers of OS in the frontal cortex (FC) and hippocampus were detected by the ELISA method. Melatonin treatment corrected the exacerbated anxiety response only in the pin+icvAβ1-42 model while it alleviated the cognitive impairment in the three models. Pinealectomy disturbed the antioxidant system via enhanced SOD activity and decreased GSH levels both in the FC and hippocampus. The Aβ1-42 model decreased the SOD activity in the FC and elevated the MDA level in the two brain structures. The pin+icvAβ1-42 model impaired the antioxidant system and elevated lipid peroxidation. Melatonin supplementation restored only the elevated MDA level of icvAβ1-42 and pin+icvAβ1-42 model in the hippocampus. In conclusion, our study reveals that the pin+icvAβ1-42 rat model triggers more pronounced anxiety and alterations in markers of OS that may be associated with melatonin deficit concomitant to icvAβ1-42-induced AD pathology.

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