2019
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/40562
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Документ Optimal choice of planes for placing tomograms in computed tomography(Національний технічний університет "Харківський політехнічний інститут", 2019) Pershyna, Iuliia Igorivna; Tokmakova, Iryna AnatoliyivnaThe solution of the problem of reconstructing the internal structure of a three-dimensional body by the known tomograms produced by a computer to-mograph using interflatation of functions and blending approximation is proposed. The known methods ofapproximating functions of one and two variables by interpolation type piecewise constant splines using means and medians are also considered. The paper presents an algorithm for optimizing the choice of the planes in which the tomogramsproduced by a computer tomograph are placed. The case is considered when all the tomograms are parallel to each other. The algorithm developeduses approximations of objects by classical piecewise constant splines. The internal structure of a three-dimensional body (density or absorption coefficient) is assumed to be given by a function of three variables of the form h(x, y, z ) = f (x)g( y, z), where g is an arbitrary function, provided that f is a monotone function on a closed segment. The method of optimal choice of the planes for placing the tomograms is implemented using MathCad computer software.Документ Construction of discontinuous interlineation polynomial splines for functions of two variables(НТУ "ХПІ", 2019) Pershyna, Iuliia Igorivna; Tokmakova, Iryna Anatoliyivna; Dumych, Yegor AndreevichThe article suggests a general method for constructing discontinuous interlineation polynomial splines, which, as a partial case, include discontinuous and continuously differentiable splines. The theorems on interlineation and approximation properties of such discontinuous structures are formulated and proved. On the basis of the constructed discontinuous splines, a method for restoration of functions of two variables with first kind discontinuities is created. The theorems on the error of the approximation of discontinuous functions by the constructed discontinuous interlineation splines are proved. Examples are given.Документ Representation of real numbers by Fibonacci sequence(НТУ "ХПІ", 2019) Tokmakova, Iryna AnatoliyivnaThe paper deals with imaging of real numbers by the Fibonacci sequence. An algorithm for changing from decimal representation of a number to its F−image is developed. The application of the algorithm is demonstrated by considering several specific examples. The correlation between binary numbers and numbers given as their F−images is analyzed.