Institute of Mathematics AS CR, v. v. i.
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On the range of some elementary operators
No full textsummary:Let denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space . For , the generalized derivation and the multiplication operator are defined on by and . In this paper, we give a characterization of bounded operators and such that the range of is closed. We present some sufficient conditions for to have closed range. Some related results are also given
Non-stochastic uncertainty quantification of a multi-model response
No full textsummary:The focus is put on the application of fuzzy sets and Dempster-Shafer theory in assessing the nature and extent of uncertainty in the response of models that model the same phenomenon and depend on fuzzy input data. Dempster-Shafer theory uses a weighted family of fixed sets called the focal elements to evaluate the relationship between an arbitrarily chosen set and the focal elements. It is proposed to create at least weighted focal elements on the basis of 1) the responses to fuzzy inputs to the models, and 2) the weights associated with the models. Four variants of this approach are illustrated by academic examples
Simplified mathematical models of fluid-structure-acoustic interaction problem motivated by human phonation process
No full textsummary:Human phonation process represents an interesting and complex problem of fluid-structure-acoustic interaction, where the deformation of the vocal folds (elastic body) are interplaying with the fluid flow (air stream) and the acoustics. Due to its high complexity, two simplified mathematical models are described - the fluid-structure interaction (FSI) problem describing the self-induced vibrations of the vocal folds, and the fluid-structure-acoustic interaction (FSAI) problem, which also involves aeroacoustic phenomena. The FSI model is based on the incompressible Navier-Stokes equations in the ALE formulation coupled with the linear elasticity model. Both the fluid and structural models are approximated using finite element methods, and the influence of different inlet boundary conditions is discussed in detail. For the FSAI model, an aeroacoustic hybrid approach is used, incorporating the Lighthill analogy or the perturbed convective wave equation. The acoustic results strongly depend on the proper choice of the computational acoustic domain (i.e. vocal tract model). Further, the spatial and frequency distributions of sound sources computed from the FSI solution are compared for both used approaches. The final frequency spectra of acoustic pressure at the mouth position are also analyzed for both approaches
Benoît B. Mandelbrot – 100 years since birth
No full textsummary:Benoît Mandelbrot, narozený ve Varšavě v roce 1924, je považován za otce fraktální geometrie. Mandelbrotův koncept fraktálů významně ovlivnil matematiku i řadu dalších oborů. Mandelbrotova množina se stala ikonickým symbolem fraktální geometrie. Tento článek představuje život a dílo tohoto významného matematika.summary:Benoît Mandelbrot, born in Warsaw in 1924, is considered the father of fractal geometry. Mandelbrot's concept of fractals has significantly influenced mathematics and numerous other fields. The Mandelbrot set has become an iconic symbol of fractal geometry. This article presents the life and work of this significant mathematician
Finding a Hamiltonian cycle using the Chebyshev polynomials
No full textsummary:We present an algorithm of finding the Hamiltonian cycle in a general undirected graph by minimization of an appropriately chosen functional. This functional depends on the characteristic polynomial of the graph Laplacian matrix and attains its minimum at the characteristic polynomial of the Laplacian matrix of the Hamiltonian cycle
Nonsmooth equation method for nonlinear nonconvex optimization
No full textsummary:The contribution deals with the description of two nonsmooth equation methods for inequality constrained mathematical programming problems. Three algorithms are presented and their efficiency is demonstrated by numerical experiments
On open maps and related functions over the Salbany compactification
Get PDFsummary:Given a topological space , let and denote, respectively, the Salbany compactification of and the compactification map called the Salbany map of . For every continuous function , there is a continuous function , called the Salbany lift of , satisfying . If a continuous function has a stably compact codomain , then there is a Salbany extension of , not necessarily unique, such that . In this paper, we give a condition on a space such that its Salbany map is open. In particular, we prove that in a class of Hausdorff spaces, the spaces with open Salbany maps are precisely those that are almost discrete. We also investigate openness of the Salbany lift and a Salbany extension of a continuous function. Related to open continuous functions are initial maps as well as nearly open maps. It turns out that the Salbany map of every space is both initial and nearly open. We repeat the procedure done for openness of Salbany maps, Salbany lifts and Salbany extensions to their initiality and nearly openness
Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid
No full textsummary:We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on . To prove these results, some new average quantities are introduced
Entire function sharing two polynomials with its th derivative
Get PDFsummary:We investigate the uniqueness problem of entire functions that share two polynomials with their th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible
On Lie semiheaps and ternary principal bundles
Get PDFsummary:We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifolds are related to Lie groups and establish the analogue of principal bundles in this ternary setting. In particular, we generalise the well-known ‘heapification’ functor to the ambience of Lie groups and principal bundles