Článek pojednává o matematických úlohách souvisejících se šachovnicí a šachovými figurami. Ze šachu však budeme potřebovat pouze pravidla pro pohyb figur po šachovnici. Postupně se zaměřujeme na jezdcovy procházky po obdélníkových šachovnicích a dále na tzv. nezávislost a dominanci figur a vztah mezi nimi na čtvercových šachovnicích. Ukážeme, že některé problémy lze řešit elegantněji, pokud je přeformulujeme v řeči teorie grafů.
Cet article est consacré à la géométrie véhiculée par les écrits d’architecture, en particulier les écrits italiens de la seconde moité du xvie siècle. Il explore le rôle central attribué aux instruments dans cette géométrie. De quelle façon s’insère-t-elle dans les multiples traditions mathématiques de la même époque ? Elle se nourrit de fait à la fois d’apports de la tradition savante, de celle des abacistes et de la géométrie pratique. On s’attachera à mettre en évidence, dans les propositions...
A Fourier approximation method is used for modeling and simulation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton's method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of completely nonlinear surface waves and contribute to provide...
The digitization of papers born in the print-only era is vital for the health of the mathematical record. Many large scale retrodigitization projects are underway and, at this point, probably more that half of the mathematical history has been finished. Many smaller journals and books remain to be done. This paper gives a framework within which these may also be completed. It uses the digitization of the Canadian Journal of Mathematics (53,000 pages), completed as a one-man project over a few months,...
In the contribution, we are concerned with the exact interpolation of the data at nodes given and also with the smoothness of the interpolating curve and its derivatives. This task is called the problem of smooth approximation of data. The interpolating curve or surface is defined as the solution of a variational problem with constraints. We discuss the proper choice of basis systems for this way of approximation and present the results of several 1D numerical examples that show the quality of smooth...
The problem of a solving a class of hypersingular integral equations over the boundary of a nonplanar disc is considered. The solution is obtained by an expansion in basis functions that are orthogonal over the unit disc. A Fourier series in the azimuthal angle, with the Fourier coefficients expanded in terms of Gegenbauer polynomials is employed. These integral equations appear in the study of the interaction of water waves with submerged thin plates.
We present some comments on the diversity of the paintings by Johannes Vermeer (1632-1675) depicted on postage stamps. We have found 20 of the 36 "recognized" Vermeer paintings depicted on postage stamps issued by 29 "countries"; by country we mean here a stamp-issuing region that issues or has issued its own postage stamps. We apply Fisher's α index of biodiversity [11] to compare the diversity of Vermeer paintings depicted on postage stamps with the diversity of two other data sets [26]. We illustrate...
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may...
Several years ago, we discussed the problem of approximation polynomials with Milan Práger. This paper is a natural continuation of the work we collaborated on. An important part of numerical analysis is the problem of finding an approximation of a given function. This problem can be solved in many ways. The aim of this paper is to show how interpolation can be combined with the Chebyshev approximation.