Institute of Mathematics AS CR, v. v. i.
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Generalized Kotov-Ushakov attack on tropical Stickel protocol based on modified tropical circulant matrices
Get PDFsummary:After the Kotov-Ushakov attack on the tropical implementation of Stickel protocol, various attempts have been made to create a secure variant of such implementation. Some of these attempts used a special class of commuting matrices resembling tropical circulants, and they have been proposed with claims of resilience against the Kotov-Ushakov attack, and even being potential post-quantum candidates. This paper, however, reveals that a form of the Kotov-Ushakov attack remains applicable and, moreover, there are heuristic implementations of that attack which have a polynomial time complexity and show an overwhelmingly good success rate
Exact l penalty function for nonsmooth multiobjective interval-valued problems
Get PDFsummary:Our objective in this article is to explore the idea of an unconstrained problem using the exact l penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP) with the exact l penalty function. The utility of this transformation lies in the fact that it converts constrained problems to unconstrained ones. To accurately predict the applicability of the results presented in the paper, meticulously crafted examples are provided
Numerical study of two-level additive Schwarz preconditioner for discontinuous Galerkin method solving elliptic problems
No full textsummary:The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral -bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number. Finally, we present the numerical experiments supporting the theoretical results and demonstrate the efficiency of this approach for the solution of nonlinear problems
Transcendentní čísla a konstrukce pravítkem a kružítkem
Get PDFsummary:Transcendentní čísla jsou vysoce teoretický a vcelku obtížně uchopitelný matematický koncept a po staletích od jejich objevu stále skýtají mnoho nezodpovězených otázek. Cílem tohoto článku je ukázat jejich spojitost s takovou banalitou, jako jsou konstrukce pravítkem a kružítkem
Přirozená čísla ve zlomcích
Get PDFsummary:V tomto textu rozvíjíme myšlenky z článku Nepárne čísla v zlomkoch od V. Čerňanové. Zamýšlíme se nad tím, co se děje, když lichá čísla nahradíme přirozenými čísly
An LMI-based convex fault tolerant control of nonlinear descriptor systems via unknown input observers
Get PDFsummary:This paper proposes a fault tolerant control scheme for nonlinear systems in descriptor form. The approach is based on the design of an unknown input observer in order to estimate the missing state variables as well as actuator faults, such design is carried out once a proper estimation error system is obtained via a recent factorization method; then, the estimated signals are employed in the control law in order to drive the states asymptotically to the origin despite actuator faults. The designing conditions are given in terms of linear matrix inequalities. Numerical as well as physical systems are used to illustrate the advantages of the proposal
Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations
No full textsummary:We present a unified approach to studying the superconvergence property of the spectral volume (SV) method for high-order time-dependent partial differential equations using the local discontinuous Galerkin formulation. We choose the diffusion and third-order wave equations as our models to illustrate approach and the main idea. The SV scheme is designed with control volumes constructed using the Gauss points or Radau points in subintervals of the underlying meshes, which leads to two SV schemes referred to as GSV and RSV schemes, respectively. With a careful choice of numerical fluxes, we demonstrate that the schemes are stable and exhibit optimal error estimates. Furthermore, we establish superconvergence of the GSV and RSV for the solution itself and the auxiliary variables. To be more precise, we prove that the errors of numerical fluxes at nodes and for the cell averages are superconvergent with orders of and for RSV and GSV, respectively. Superconvergence for the function value and derivative value approximations is also studied and the superconvergence points are identified at Gauss points and Radau points. Numerical experiments are presented to illustrate theoretical findings