Institute of Mathematics AS CR, v. v. i.
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Non-central limit theorem for the oscillation of the Rosenblatt process
No full textsummary:Let be the Rosenblatt process with Hurst index . We analyze the limit behavior of the oscillation of the Rosenblatt process given by with and . Based on the Wiener chaos expansion, we prove that the quantity converges as , almost surely and in for any , to for any polynomial function with . We also obtain a second order result, i.e., after a proper renormalization, the quantity converges as , almost surely and in for any , to a Rosenblatt-distributed random variable
Věda vs. konspirace: Proč se vlastně zdržovat vědou?
No full textsummary:Jak poznat rozdíl mezi vědeckou teorií a konspiračním tvrzením? V článku ukazujeme, že vědecké teorie musí být v souladu s ověřenými poznatky, jejich výsledky musí být možné nezávisle zopakovat a procházejí přísným recenzním řízením. Na příkladech teorií duté Země, studené fúze nebo údajného supravodiče LK-99 ukazujeme, proč je reprodukovatelnost klíčem k potvrzení objevů. Zároveň upozorňujeme na rozdíl mezi skutečnými odbornými časopisy a publikacemi, které otiskují „zázračné“ výsledky bez kritické kontroly
What Is Happening in the World of ConTeXt
No full textsummary:Matematická a informatická komunita má povědomí především o formátech plain TeX a LaTeX. Existuje však spousta dalších a zajímavých alternativních TeXových formátů. Jedním z nich je například ConTeXt, jehož vývoji v posledních letech se budeme věnovat podrobněji v tomto článku. Konkrétně se podíváme na webové rozhraní pro tvorbu ConTeXt ových dokumentů, jazyk XML pro sazbu matematiky, pokročilé práce se sloupci a modul pro zaokrouhlování s návazností na modul pro tvorbu statistických schémat. Dále se budeme zabývat přemostěním mezi AsciiDocem a ConTeXtem, způsoby pro signalizování průběhu překladu dokumentu a v neposlední řadě zmíníme technologie zpřístupňující dokumenty pro čtenáře se speciálními potřebami.summary:The mathematical and computer-science community is familiar with plain TeX and LaTeX, but there are other interesting TeX formats as well. One of them is ConTeXt, whose development we discuss in this article. We will explore an online environment for creating ConTeXt documents, an XML language for mathematical typesetting, and advanced column handling. We also introduce a module for statistical charts, a software bridge between AsciiDoc and ConTeXt, and, finally, several ways to signal the progress of a document's compilation
State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
No full textsummary:We investigate the Dirichlet boundary control of the Laplace equation, considering the control in , which is the natural space for Dirichlet data when the state belongs to . The cost of the control is measured in the norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size and the regularization parameter , balancing the energy cost for the control and the accuracy of the approximation of the desired state. This relationship is also crucial in designing efficient solvers. We also discuss additional box constraints imposed on the control and the state. Our theoretical findings are complemented by numerical examples, including one example with box constraints
Weighted Hardy-Sobolev type integrability for generalized Riesz potentials in weighted Morrey-Orlicz spaces
No full textsummary:We are concerned with weighted Hardy-Sobolev type integrabilities for generalized Riesz potentials of functions in weighted Morrey-Orlicz spaces, where and Those potentials are used to give a representation of -functions on the punctured space . As an application, we obtain Hardy-Sobolev type integrabilities for general double phase functionals given by \varphi (x,t) =\varphi _1(t) + \varphi _2(b(x)t). $
Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay
Full text linksummary:We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially
Fixed-time adaptive command-filter-based event-triggered control of constrained switched nonlinear systems with unmodeled dynamics
Full text linksummary:In this paper, we investigate the problem of global output-feedback regulation for a class of switched nonlinear systems with unknown linear growth condition and uncertain output function. Based on the backstepping method, an adaptive output-feedback controller is designed to guarantee that the state of the switched nonlinear system can be globally regulated to the origin while maintaining global boundedness of the resulting closed-loop switched system under arbitrary switchings. A numerical example is given to demonstrate the effectiveness of the proposed control scheme
Efficiency analysis of the rule-based defuzzification approach to fuzzy inference system for regression problems
Full text linksummary:A fuzzy inference system (FIS) is an effective prediction method based on fuzzy logic. The performance of this model may vary depending on the defuzzification process. In the Mamdani-type FIS model, the defuzzification process is applied to the fuzzy output of the system only once at the last stage. In the FIS with rule-based defuzzification (FIS-RBD) model, the defuzzification process is applied to the fuzzy consequent part of each rule and the overall result of the system is calculated as the weighted average of the separately defuzzified results of the rules. Note that, the original shapes of the combined rule results are lost in the aggregated fuzzy result of the classical Mamdani-type system and the effect of each rule on the system result decreases when aggregated. However, rule results can affect the overall result more significantly in the FIS-RBD approach. In this study, a comparative analysis was made on the effectiveness of the classical Mamdani-type FIS and FIS-RBD models for regression problems. Five datasets from different domains and various defuzzification methods were used in comparisons. In the results obtained, it was observed that the The FIS-RBD model gave better results than the classical Mamdani-type FIS model. To carry out calculation experiments, a new Python package called Fuzlab was developed by modifying the existing Python library called FuzzyLab. In addition to creating the FIS-RBD model, the developed package also allows the use of the Weighted Average Based on Levels (WABL) defuzzification method in fuzzy logic-based calculations
Projectively coresolved Gorenstein flat modules over trivial ring extensions
No full textsummary:Let be a trivial extension of a ring by an --bimodule . Sufficient and necessary conditions are established for projectively coresolved Gorenstein flat (PGF, for short) modules over . More pecisely, it is proved that is a PGF left \hbox {-module} if and only if is a PGF left -module and the sequence is exact under some assumptions on . As applications, it is characterized PGF modules over Morita rings with zero bimodule homomorphisms