Institute of Mathematics AS CR, v. v. i.
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On the duality of Dunford-Pettis operators on Banach lattices
No full textsummary:We establish sufficient conditions for the duality of regular Dunford-Pettis operators on Banach lattices and necessary conditions for the duality condition ``if the adjoint of a (positive) operator is Dunford-Pettis, then the operator itself is''. In particular, we show that if each operator from a Banach lattice with an order continuous norm to another Banach lattice is Dunford-Pettis whenever its adjoint is Dunford-Pettis, then has the Schur property or is a KB-space. As consequences, we deduce a characterization of the Schur property (and KB-spaces)
Exponential stability for Timoshenko model with thermal effect
No full textsummary:We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory
New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications
No full textsummary:Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators
A note on eigenvalue of tensors and its application
No full textsummary:The tensor eigenvalue problem has been widely studied in recent years. In this paper, several new properties of eigenvalues and determinants of tensors are explored. We also proposed a formula to compute the determinant of a tensor as a mimic of the matrix determinant. The Perron-Frobenius theorem, one of the most important results in non-negative matrix theory, is proposed for the class of non-negative tensors in the Einstein product framework. Further, the power method, a widely used matrix iterative method for finding the largest eigenvalue, is framed for tensors using the Einstein product. The proposed higher-order power method is applied to calculate the largest eigenvalue of the Laplacian tensors associated with hyper-stars and hyper-trees. The numerical results show that the higher-order power method with the Einstein product is stable
Two-grid penalty Arrow-Hurwicz iterative finite element methods for the stationary magnetohydrodynamics flow
No full textsummary:We propose and analyze three kinds of two-grid penalty Arrow-Hurwicz (A-H) iterative finite element methods for the stationary incompressible magnetohydrodynamic (MHD) equations, which adopt the existing A-H iterative method to obtain the coarse mesh solution, and then correct the solution by three different one-step schemes (Oseen type, Stokes type and Newton type) with the usual penalty method on the fine mesh. These methods combine the A-H iterative method, the penalty method and the two-grid strategy, maintaining the advantage of three methods and overcoming some of their limitations. Rigorous analysis of the optimal error estimate and stability for three methods are provided. Ample numerical experiments are reported to validate the theoretical results and the efficiency of the numerical schemes
A robust coefficient of determination based on implicit weighting
No full textsummary:In the linear regression model, the standard coefficient of determination and its weighted counterpart are commonly used to assess the quality of the linear fit. However, both metrics are susceptible to the influence of outliers and heteroskedasticity within the dataset. This paper introduces a robust version of , based on the least weighted squares (LWS) estimator, and examines its statistical properties in detail. We investigate the impact of data quantization on and its robust variants, and propose a hypothesis test for assessing the equality of expected values between two versions. Numerical experiments on 29 publicly available datasets reveal that confidence intervals for the LWS-based coefficient of determination are generally narrower than those for existing measures, especially in homoskedastic settings. In contrast, under heteroskedasticity, narrower intervals do not necessarily imply greater robustness, highlighting the nuanced behavior of these estimators. The comparison with the well-known least trimmed squares (LTS) estimator underscores the promise of the LWS approach, which exhibits favorable efficiency properties and more reliable interval estimation in many practical scenarios
Finite groups with many normalizers
No full textsummary:A group is said to have dense normalizers if every nonempty open interval in its subgroup lattice contains the normalizer of a certain subgroup of . We find all finite groups satisfying this property. We also classify the finite groups, in which subgroups are not normalizers for
Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection model
No full textsummary:HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. Understanding how these two viruses interact in coinfected individuals is essential, especially in populations under antiretroviral treatment. In this study, we develop and analyze a novel mathematical model capturing the coinfection dynamics of HIV and SARS-CoV-2 under the influence of highly active antiretroviral therapy (HAART). In contrast to previous models, our formulation includes the effect of HAART on both infections and derives the basic reproduction numbers for each virus. We prove that transcritical bifurcations occur when the basic reproduction numbers cross the threshold value of 1, and we establish the conditions for stability of the disease-free equilibria. Numerical simulations show that HAART, although designed to control HIV, also reduces SARS-CoV-2 proliferation in coinfected hosts, which, as far as we know, has not been fully addressed in previous models in the literature. These findings reveal a potentially beneficial indirect effect of antiretroviral therapy on SARS-CoV-2 dynamics, offering new theoretical insights into the control of viral coinfections
A generalised Ricci-Hessian equation on Riemannian manifolds
Full text linksummary:In this paper, we prove new rigidity results related to some generalised Ricci-Hessian equation on Riemannian manifolds
Natural numbers in fractions for the second time
No full textsummary:Ukážeme, jak neotřelými způsoby generovat zlomky s hodnotou , kde je přirozené číslo, přičemž v čitateli bude součet prvních přirozených čísel a ve jmenovateli bude součet členů jisté aritmetické posloupnosti. Identitu dokážeme algebraicky i geometricky