Institute of Mathematics AS CR, v. v. i.
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Special issue dedicated to Professor Ivo Babuška, the founder of the journal Applications of Mathematics
No full textGeodesic metrics for RBF approximation of some physical quantities measured on sphere
No full textsummary:The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula. We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general
Denumerable Markov stopping games with risk-sensitive total reward criterion
Get PDFsummary:This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established
Class groups of large ranks in biquadratic fields
No full textsummary:For any integer , we provide a parametric family of biquadratic fields with class groups having -rank at least 2. Moreover, in some cases, the -rank is bigger than 4
Periodic solutions for a class of non-autonomous Hamiltonian systems with -Laplacian
Get PDFsummary:We investigate the existence of infinitely many periodic solutions for the -Laplacian Hamiltonian systems. By virtue of several auxiliary functions, we obtain a series of new super- growth and asymptotic- growth conditions. Using the minimax methods in critical point theory, some multiplicity theorems are established, which unify and generalize some known results in the literature. Meanwhile, we also present an example to illustrate our main results are new even in the case
Statistical inference according to Thomas Bayes
No full textsummary:Tradiční (frekventistické) statistické metody jsou založeny na pravděpodobnostních modelech použitelných pouze pro hromadné jevy, jejichž výskyt lze sledovat opakovaně v mnoha situacích. Pravděpodobnost je v tomto případě chápana jako relativní četnost výskytu sledovaného jevu. Naproti tomu bayesovský přístup definuje pravděpodobnost jako míru přesvědčení o pravdivosti daného tvrzení. Přestože je tato interpretace pravděpodobnosti historicky starší, byla dlouhou dobu kritizována pro svůj subjektivismus a byla mimo hlavní zájem vědecké komunity. Od 90. let 20. století však zažívají tyto metody jistou renesanci díky rozvoji výpočetní techniky a vhodného softwaru. V dnešní době jsou bayesovské metody považovány za významnou součást moderní statistiky s širokým praktickým uplatněním. Článek je zaměřen na objasnění základních myšlenek bayesovské statistické analýzy a všímá si i historie jejího vzniku.summary:Traditional (frequentist) statistical methods are based on probabilistic models applicable only to mass phenomena, the occurrence of which can be monitored repeatedly in many situations. In this case, the probability is understood as the relative frequency of the occurrence of the observed phenomenon. In contrast, the Bayesian approach defines probability as a measure of the belief in the truth of a given statement. The article focuses on clarifying the basic ideas of Bayesian statistic analysis and notes the history of its origin and development
PANGEA competition in 2022/2023
No full textsummary:Příspěvek informuje o průběhu finálového dne soutěže Pangea 2022/23
Delay dependent complex-valued bidirectional associative memory neural networks with stochastic and impulsive effects: An exponential stability approach
Get PDFsummary:This paper investigates the stability in an exponential sense of complex-valued Bidirectional Associative Memory (BAM) neural networks with time delays under the stochastic and impulsive effects. By utilizing the contracting mapping theorem, the existence and uniqueness of the equilibrium point for the proposed complex-valued neural networks are verified. Moreover, based on the Lyapunov - Krasovskii functional construction, matrix inequality techniques and stability theory, some novel time-delayed sufficient conditions are attained in linear matrix inequalities (LMIs) form, which ensure the exponential stability of the trivial solution for the addressed neural networks. Finally, to illustrate the superiority and effects of our theoretical results, two numerical examples with their simulations are provided via MATLAB LMI control toolbox
Some applications of Nevanlinna theory to entire functions that share a small function with two difference operators
Get PDFsummary:In this work, we are implementing some applications of Nevanlinna theory to entire functions that share a small function with two difference operators and we also generalize one of the results in the paper [3]
CSTUG at the TUG 2024 Conference
No full textsummary:Článek pojednává o účasti členů sdružení CSTUG na konferenci TUG 2024 v Praze.summary:This article reports on the participation of CSTUG members at TUG 2024 in Prague