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A Reduction of the Graph Reconstruction Conjecture

100%
Monikandan S., Balakumar J.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 3
529-537
EN
A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible
2
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On one algorithm for solving the problem of source function reconstruction

100%
Maksimov V.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 2
239-247
EN
In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations in problems data.
3
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An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids

88%
Sit A., Mitchell J. C., Phillips G. N., Wright S. J.
Molecular Based Mathematical Biology
|
2013
|
tom 1
75-89
EN
Zernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.
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