Institute of Mathematics AS CR, v. v. i.
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A model and application of binary random sequence with probabilities depending on history
Get PDFsummary:This paper presents a model of binary random sequence with probabilities depending on previous sequence values as well as on a set of covariates. Both these dependencies are expressed via the logistic regression model, such a choice enables an easy and reliable model parameters estimation. Further, a model with time-depending parameters is considered and method of solution proposed. The main objective is then the application dealing with both artificial and real data cases, illustrating the method of model evaluation and its use
On the characterization of harmonic functions with initial data in Morrey space
No full textsummary:Let be a metric measure space satisfying the doubling condition and an -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on . We will show that a solution to on satisfies an \hbox {-Carleson} condition if and only if can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space , where is a nonnegative function defined on a class of balls in . This result extends the analogous characterization founded by R. Jiang, J. Xiao, D. Yang (2016) from the classical Morrey space on Euclidean space to the generalized Morrey space on the metric measure space
-generalized skew derivations acting on Lie ideals in prime rings
No full textsummary:Let be any noncommutative prime ring of , a noncentral Lie ideal of and , two nonzero -generalized skew derivations of . Suppose that for all . Then at least one of the following conclusions holds: \item {(1)} for all and for some , where is the extended centroid of ; \item {(2)} , the algebra of matrices over a field
On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values
Get PDFsummary:We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values with By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case of (P) in which the nonlinear term contains the sum . Under suitable conditions, we prove that the solution of converges to the solution of the corresponding problem as (in a certain sense), here is defined by in which is replaced by The proof is done by using the compactness lemma of Aubin-Lions and the method of continuity with a priori estimates. We end the paper with remarks related to similar problems
Sudoku pohledem matematiky: Odmocnina z jedné a soustava rovnic
Get PDFsummary:Sudoku se nadále těší popularitě, a proto může sloužit jako motivační zdroj k podnícení zájmu studentů o matematiku. V tomto článku ukazujeme způsob, jak lze sudoku ztotožnit s úlohou hledání řešení jistého systému lineárních a nelineárních rovnic
Proměnné hvězdy a význam pořizování jejich dat amatérsky
Get PDFsummary:Článek vychází z ročníkové práce ve 3. ročníku na gymnáziu. Cílem ročníkové práce bylo porozumět problematice proměnných hvězd, zpracovat napozorovaná data a předat informace srozumitelnou formou ostatním studentům. Teoretická část řeší fyzikální podstatu proměnných hvězd, jejich rozdělení, historii pozorování a současný výzkum. Praktická část je založená na pořízení vlastních dat proměnné zákrytové dvojhvězdy AB And. Představen je také způsob zpracování těchto dat a jejich následný rozbor. Nakonec je posuzován význam pořizování těchto dat v době, kdy za nás velkou práci odvádějí kosmické sondy
Some results on the weak dominance relation between ordered weighted averaging operators and T-norms
Get PDFsummary:Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More attention is paid to the weak dominance relation between ordered weighted averaging operators and Łukasiewicz t-norm. Furthermore, the relationships between weak dominance and some functional inequalities of aggregation operators are discussed
Role of the Harnack extension principle in the Kurzweil-Stieltjes integral
Get PDFsummary:In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous integrators. Moreover, in general, the existence of integral over an elementary set does not always imply the existence of integral over every subset of The goal of this paper is to construct the Harnack extension principle for the Kurzweil-Stieltjes integral with values in Banach spaces and then to demonstrate its role in guaranteeing the integrability over arbitrary subsets of elementary sets. New concepts of equiintegrability and equiregulatedness involving elementary sets are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration
Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants and
No full textsummary:I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by . Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values of the graph invariants and among all trees and molecular trees of order , and characterize the trees and molecular trees that achieve the extremal values, respectively. Thus, the problem is completely solved