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Information × Registration Number 0212U008519, 0112U008075 , R & D reports Title Developing theory of discontinuous splines and its application for the decision of problems of a computer tomography for the purpose of improvement of quality of diagnosing popup.stage_title Head Pershina Yuliya Igorevna, Registration Date 11-01-2013 Organization Ukrainian Engineering-Pedagogic Academy popup.description2 Results of the theory of approach of functions by polynoms or splines which are continuous or differentiated to some order inclusive are well-known. At the same time practice shows that among multidimensional objects which need to be investigated, is considerable quantity is described by discontinuous functions. For example, in methods of a computer tomography the information on internal structure of a body of the person is insufficiently used. That is at body research it is useful to use its heterogeneity (different density in different parts of a body). All development of computing and applied mathematics says that use of each additional information on investigated object can lead to more exact and qualitative restoration of this object. In work the general theory for construction of discontinuous splines which have ruptures of the first sort between elements of triangular both rectangular forms and which special case are classical splines on a rectangular and triangular grid of knots develops. In work the new algorithm of an optimum finding of ruptures of function of one variable also is created. The received results are a theoretical basis of methodology of the decision of flat and spatial problems of a computer tomography. At the heart of methods of approach of discontinuous functions the idea of use of operators of interlineation for restoration of function of two variables is put. Operators of interlineation restore (probably, approximately) functions of two variables on their known traces on the given system of lines. That is integrals along such operators on the specified lines equal to integrals from the most restored function. In the given research the hypothesis is accepted to a basis: discontinuous functions in some points or on some lines of function are better for approaching discontinuous splines. Equally an approach appreciation in each element the splittings inherent in is continuous-differentiated splines thus turns out. Product Description popup.authors Драгун Сергій Володимирович Литвин Олег Миколайович Першина Юлія Ігорівна popup.nrat_date 2020-04-02 Close