Publikační činnost Katedry matematiky / Publications of Department of Mathematics (230)

Permanent URI for this collectionhttp://hdl.handle.net/10084/122998

Kolekce obsahuje bibliografické záznamy publikační činnosti (článků) akademických pracovníků Katedry matematiky (230) v časopisech registrovaných ve Web of Science od roku 2003 po současnost.
Do kolekce jsou zařazeny:
a) publikace, u nichž je v originálních dokumentech jako působiště autora (adresa) uvedena Vysoká škola báňská-Technická univerzita Ostrava (VŠB-TUO),
b) publikace, u nichž v originálních dokumentech není v adrese VŠB-TUO uvedena, ale autoři prokazatelně v době jejich zpracování a uveřejnění působili na VŠB-TUO.

Bibliografické záznamy byly původně vytvořeny v kolekci Publikační činnost akademických pracovníků VŠB-TUO, která sleduje publikování akademických pracovníků od roku 1990.

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Now showing 1 - 20 out of 36 results

Mortar method for 2D elastic bounded contact problems
(Sciendo, 2023) Světlík, Tadeáš; Varga, Radek; Pospíšil, Lukáš; Čermák, Martin
This paper presents a contribution to the field of numerical solutions for contact problems, which pose significant challenges in engineering and simulations. Specifically, we address the intricate task of connecting bodies that have been discretized using non-conforming and non-overlapping meshes. Our primary focus lies in investigating the efficacy of the mortar method with a segment-to-segment approach. In this context, we provide a concise overview of the underlying theoretical framework and present our implementation in the MATLAB programming environment. To ascertain the reliability and accuracy of our proposed methodology, we conduct a rigorous validation study by comparing the outcomes obtained from our implementation with those derived from the widely adopted commercial software, ANSYS. To enable a comprehensive evaluation, we select specific benchmark problems that involve the interaction of two elastic bodies. Through a meticulous analysis and comparison of results, we demonstrate the effectiveness and robustness of our approach. The findings of this study contribute substantively to the advancement of numerical techniques for solving contact problems. The validated methodology not only establishes a solid foundation for future research endeavors but also offers a reliable framework for conducting simulations in this domain. Furthermore, the insights gained from this study can potentially facilitate the development of more efficient and accurate computational algorithms for addressing contact problems encountered in various engineering applications.
The process of developing model research for the technology of obtaining energy resources
(MDPI, 2023) Szurgacz, Dawid; Borska, Beata; Pospíšil, Lukáš; Dlouhá, Dagmar; Pokorný, Jiří; Zhironkin, Sergey
The current problems associated with the maintenance of hard coal longwall mining depend on the application or use of extraction technologies. In order to make the best use of these technologies, a new approach based on simulation studies is necessary. This paper aims to develop a mathematical model for the powered roof support’s operation. The three groups of professionals involved in the testing of the roof support were involved in the work on changing the hydraulic system of the powered roof support stand. These professionals were powered roof support’s designers, researchers and users. The research subject was the development of a mathematical model as a starting point for conducting simulations. The model is based on d’Alembert’s principle and the equation of the balance of flow rates. Based on the developed model, it is possible to determine the pressure in the space under the piston of the hydraulic prop. The results obtained in the simulations are the basic assumptions for the development of a prototype that would solve the current problems in the hydraulic systems of powered roof supports. The adopted research methodology assumed the development of a mathematical model, simulation in the MATLAB environment and verification of the model on a test stand. The obtained results of simulation tests based on the developed mathematical model were confirmed in bench tests. Simulation and bench tests determined the correctness of the assumptions made for the development of the prototype model. Based on the analysis of the results, the nature of the work of the future prototype has been predetermined. The next stage will be the testing of the prototype, which is to be included in the hydraulic system of the prop of powered roof support in the future. The model mentioned before is the baseline model, and it will be modified depending on the application of the future design in real conditions. Simulation studies of powered roof support will allow the structure that is used currently to be optimised, so as to adapt it to increasingly difficult working conditions.
The simple network-based measuring system for improving the evaporation estimation
(De Gruyter, 2023) Dlouhá, Dagmar; Pospíšil, Lukáš; Dubovský, Viktor
This paper presents a novel method for measuring the data for evaporation estimation as the key in gredient for the final decision of the reclamation form in the area of the Most Basin. The area has been intensively mined for many decades, resulting in significant landscape devastation, loss of natural habitats, and negative environmental impact. Currently, it is assumed that by 2050, three large-scale reclamation projects will be implemented in the area and it is necessary to decide which form of rec lamation to choose. Whether to build lakes according to the currently valid rehabilitation and recla mation plan or to leave the area of the quarries in succession with the support of spontaneous inflow of water up to a naturally sustainable water level. Whether the first or second option is approved, or a combination of both, the prediction of evaporation from the free water surface will always be of great importance. To deal with this goal, the available meteorological data must be combined with a suitable calculation method. In our work, we suggest utilizing a measuring network of meteorologi cal devices that describe the character of the weather in a given area of interest in a long-term time series. Together with the state-of-the-art calibration of models for calculating evaporation, the meas urement network helps to provide more accurate evaporation data for a given area. Based on the anal ysis of research results, it will be possible to choose a specific right decision and thus contribute to the long-term sustainability of these reclamations.
Influence of the external environment on the moisture spectrum of Norway spruce (Picea abies (L.) KARST.)
(MDPI, 2023) Lexa, Martin; Fojtík, Roman; Dubovský, Viktor; Sedlecký, Miroslav; Zeidler, Aleš; Sikora, Adam
The fluctuation of relative humidity and temperature in the surrounding environments of wood products is an important parameter influencing their mechanical properties. The objective of this study was to investigate the complex relationship between the moisture content and mechanical properties of wood as a critical aspect in the design of durable and reliable structures. Over a period of 669 days, a simulated type of experiment was conducted, during which the moisture content and external temperature were continuously measured in a compact profile of Norway spruce (Picea abies (L.) KARST.). The data were processed using quadratic and cubic models to establish a predictive model. It was found that the quadratic models slightly outperformed the cubic models when considering time lags greater than six days. The final model demonstrated a significant improvement in explaining the variance of the dependent variable compared to the basic model. Based on these findings, it can be concluded that understanding the relationship between the moisture content and temperature of wood samples plays an important role in wood’s efficient use, particularly for timber constructions. This understanding is vital for accurately predicting the mechanical characteristics of wood, which, in turn, contributes to the development of more durable and reliable structures.
Probabilistic expression of the function of the change in prestressing force of timber elements depending on climatic conditions in situ
(Elsevier, 2023) Fojtík, Roman; Dubovský, Viktor; Kubíncová, Lenka; Stejskalová, Kateřina; Machovčáková, Eva; Lesňák, Michal
Today demand for sustainability forces us to use an ever-increasing share of renewable materials in construction and the associated increase in their mechanical resistance is related to this. The application of transverse prestress in timber structures will increase the overall stiffness and load-bearing capacity of the structural system. However, the prestressing force and subsequent rectification of the system depends on the relative environmental conditions for the specific location of the construction site. The climatic conditions have a significant impact on changes in the size of the prestressing force. Into the experimental sample, transverse prestressed was introduced by means of prestressing elements. The values of prestressing force and climatic conditions to which the sample was exposed were monitored and recorded. Based on experimentally obtained data, mathematical models were created and evaluated using methods such as principal component method and cross-validation method. The result of the analysis is the function for determining changes in the size of the prestressing force over time depending on the climatic conditions. Using this function, it is possible to determine the time when it is necessary to manually increase the amount of preload in the structure so that it correctly fulfils the purpose for which it was designed.
Low-cost probabilistic 3D denoising with applications for ultra-low-radiation computed tomography
(MDPI, 2022) Horenko, Illia; Pospíšil, Lukáš; Vecchi, Edoardo; Albrecht, Steffen; Gerber, Alexander; Rehbock, Beate; Stroh, Albrecht; Gerber, Susanne
We propose a pipeline for synthetic generation of personalized Computer Tomography (CT) images, with a radiation exposure evaluation and a lifetime attributable risk (LAR) assessment. We perform a patient-specific performance evaluation for a broad range of denoising algorithms (including the most popular deep learning denoising approaches, wavelets-based methods, methods based on Mumford-Shah denoising, etc.), focusing both on accessing the capability to reduce the patient-specific CT-induced LAR and on computational cost scalability. We introduce a parallel Probabilistic Mumford-Shah denoising model (PMS) and show that it markedly-outperforms the compared common denoising methods in denoising quality and cost scaling. In particular, we show that it allows an approximately 22-fold robust patient-specific LAR reduction for infants and a 10-fold LAR reduction for adults. Using a normal laptop, the proposed algorithm for PMS allows cheap and robust (with a multiscale structural similarity index >90%) denoising of very large 2D videos and 3D images (with over 107 voxels) that are subject to ultra-strong noise (Gaussian and non-Gaussian) for signal-to-noise ratios far below 1.0. The code is provided for open access.
Nonlocal gravity cosmology: An overview
(World Scientific Publishing Co Pte Ltd, 2022) Capozziello, Salvatore; Bajardi, Francesco
We discuss some main aspects of theories of gravity containing nonlocal terms in view of cosmological applications. In particular, we consider various extensions of general relativity based on geometrical invariants as f (R, square(-1) R), f (G, square(-1) G) and f (T, square(-1) T) gravity where R is the Ricci curvature scalar, G is the Gauss-Bonnet topological invariant, T the torsion scalar and the operator square(-1) gives rise to nonlocality. After selecting their functional form by using Noether symmetries, we find out exact solutions in a cosmological background. It is possible to reduce the dynamics of selected models and to find analytic solutions for the equations of motion. As a general feature of the approach, it is possible to address the accelerated expansion of the Hubble flow at various epochs, in particular the dark energy issues, by taking into account nonlocality corrections to the gravitational Lagrangian. On the other hand, it is possible to search for gravitational nonlocal effects also at astrophysical scales. In this perspective, we search for symmetries of f(R, square R-1) gravity also in a spherically symmetric background and constrain the free parameters, Specifically, by taking into account the S2 star orbiting around the Galactic Center SgrA*, it is possible to study how nonlocality affects stellar orbits around such a massive self-gravitating object.
Energy-momentum complex in higher order curvature-based local gravity
(MDPI, 2022) Capozziello, Salvatore; Capriolo, Maurizio; Lambiase, Gaetano
An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Moller, and Weinberg. In this review, we firstly explored the energy-momentum complex in an nth order gravitational Lagrangian L=L (g(mu nu),g(mu nu),i(1),g(mu nu),i(1)i(2),g(mu nu),i(1)i(2)i(3),. . .,g(mu nu),i(1)i(2)i(3) . . .i(n)) and then in a gravitational Lagrangian as Lg=((R) over bar +a(0)R(2)+ Sigma(p)(k=1)a(k)R square R-k)root-g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether's theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor tau(eta)(alpha) becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy-momentum complex in f(R) gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor tau(eta)(alpha) to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle omega emitted by a localized source carried by a gravitational wave in a direction (x) over cap for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann-Lemaitre-Robertson-Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy-momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving -k terms.
Cosmological constant and AdS spacetimes from Minkowski spheres
(World Scientific Publishing, 2022) Boskoff, Wladimir-Georges; Capozziello, Salvatore
A theory of gravity without masses can be constructed starting from Minkowski M-(p,M-q) spaces. The corresponding adapted (p, q) Minkowski potentials, gradients and Laplacians built on each signature lead to a field equation similar to the Newton-Laplace one. In this framework, the anti-de Sitter spacetime is a hypersurface described by a constant potential of Minkowski gravitational force in absence of matter. We show that the cosmological constant of the anti-de Sitter spacetimes is related to a geometric property of Minkowski spheres: the centro-affine conservation of volumes defined from the so-called Minkowski-Tzizteica affine spheres. It is possible to show the connection between the anti-de Sitter AdS(2, 3) space, the non-Euclidean geometry and the difference between Minkowski M-(2,M-3) sphere and the pseudosphere seen as a surface of the 3-Euclidean space. According to a suitable parameterization, the relation between de Sitter and anti-de Sitter spacetimes in any dimension is fixed. As a consequence, the light can travel in any anti-de Sitter spacetime defining the geodesic structure. These considerations can be recast in terms of Einstein field equations with cosmological constant and extended to f(R) gravity.
New calculation technique for assessment of smoke layer interface in large buildings in connection with the design of buildings in the Czech Republic
(MDPI, 2022) Podkul, Marek; Pokorný, Jiří; Brumarová, Lenka; Dlouhá, Dagmar; Heinzová, Zuzana; Kubrická, Kateřina; Szurgacz, Dawid; Fanta, Miroslav
The sustainability of the indoor environment of buildings is also related to the conditions that arise in the case of fires. Fires in buildings are characterized by the formation of combustion products, which can significantly endanger the life and health of people. One of the major sources of danger is smoke. If there is no smoke exhaust into the outside environment during the development of the fire, the building is gradually filled with smoke. The important characteristic of the smoke layer is the level of the smoke layer, which changes over time. Several methods have been derived for determining the descent of the smoke layer in an enclosed area of space, which mainly differ in terms of the application area and limits of use. The methods used in the Czech Republic for the assessment of smoke layer descent in the case of fires do not have a clear rationale and in many cases lead to completely misleading results. For this reason, in connection with the standards for the assessment of the buildings in the Czech Republic, a new calculation technique (CSN) has been derived, which has been compared with the selected simple calculation techniques in large buildings. The deviations between the results have been evaluated by the percentage bias method (PBIAS), while the largest deviation, compared to the ISO standard technique, did not exceed 20%. The CSN calculation technique shows a favourable compliance with the technique presented by the ISO standard, where the deviation did not exceed 1.6%. In response to the proposed standards in the Czech Republic, the CSN calculation technique enables the assessment of safe evacuation in relation to the smoke layer interface and can be a considered perspective.
Non-local curvature gravity cosmology via Noether symmetries
(Elsevier, 2022) Acunzo, Adriano; Bajardi, Francesco; Capozziello, Salvatore
We consider extensions of General Relativity based on the non-local function f (R, rectangle(-1) R), where R is the Ricci curvature scalar and the non-locality is due to the term rectangle(-1) R. We focus on cosmological minisuperspaces and select viable models by the Noether Symmetry Approach. Then we find viable exact solutions pointing out the role of non-locality in cosmology.
Gravitational energy–momentum pseudo-tensor in Palatini and metric f ( R ) gravity
(Elsevier, 2022) Abedi, Habib; Capozziello, Salvatore; Capriolo, Maurizio; Abbassi, Amir M.
We derive the gravitational energy-momentum pseudo-tensor tau(mu)(upsilon) in both Palatini and metric approaches to f (R) gravity. We then obtain the related cosmological gravitational energy density. Considering a flat Friedmann-Lemaitre-Robertson-Walker spacetime, the energy density complex of matter and gravitation vanishes in the metric approach, but results non-vanishing in the Palatini formalism. This feature could be relevant in order to physically discriminate between the two approaches.
Thermodynamics of small mercury clusters and the role of electronically excited states: a case study on Hg-13
(Royal Society of Chemistry, 2022) Vítek, Aleš; Kalus, René
Classical Monte Carlo simulations in the isothermal-isobaric ensemble have been performed for the Hg-13 cluster with the main emphasis paid to structural changes in this cluster induced by elevated temperature and pressure. Broad ranges of temperatures and pressures have been considered so that a comprehensive picture of the structural changes in Hg-13 could be obtained and represented in the form of a phase diagram constructed in the temperature-pressure plane. The effect of the complex electronic structure of the cluster on its electronic ground state potential energy surface and equilibrium thermodynamics has been studied within a semi-empirical electronic structure model based on the diatomics-in-molecules approach. The involvement of (three) lowest excited electronic states has been revealed while the higher excited states available within this model do not contribute.
eSPA plus : Scalable entropy-optimal machine learning classification for small data problems
(MIT Press, 2022) Vecchi, Edoardo; Pospíšil, Lukáš; Albrecht, Steffen; O'Kane, Terence J.; Horenko, Illia
Classification problems in the small data regime (with small data statistic T and relatively large feature space dimension D) impose challenges for the common machine learning (ML) and deep learning (DL) tools. The standard learning methods from these areas tend to show a lack of robustness when applied to data sets with significantly fewer data points than dimensions and quickly reach the overfitting bound, thus leading to poor performance beyond the training set. To tackle this issue, we propose eSPA+, a significant extension of the recently formulated entropy-optimal scalable probabilistic approximation algorithm (eSPA). Specifically, we propose to change the order of the optimization steps and replace the most computationally expensive subproblem of eSPA with its closed-form solution. We prove that with these two enhancements, eSPA+ moves from the polynomial to the linear class of complexity scaling algorithms. On several small data learning benchmarks, we show that the eSPA+ algorithm achieves a many-fold speed-up with respect to eSPA and even better performance results when compared to a wide array of ML and DL tools. In particular, we benchmark eSPA+ against the standard eSPA and the main classes of common learning algorithms in the small data regime: various forms of support vector machines, random forests, and long short-term memory algorithms. In all the considered applications, the common learning methods and eSPA are markedly outperformed by eSPA+, which achieves significantly higher prediction accuracy with an orders-of-magnitude lower computational cost.
The fundamental Lepage form in two independent variables: A generalization using order-reducibility
(MDPI, 2022) Urban, Zbyněk; Volná, Jana
A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) an equivalence relation "Lepage differential 2-form is closed if and only if the associated Lagrangian is trivial" and (ii) the principal component of Lepage form, extending the well-known Poincare-Cartan form, preserving order prescribed by a given Lagrangian. This approach completes several attempts of finding a Lepage equivalent of a second-order Lagrangian possessing condition (i), which is well-known for first-order Lagrangians in field theory due to Krupka and Betounes.
Specification of the climate character in the study area of projected hydric reclamation
(Polskie Towarzystwo Przeróbki Kopalin, 2021) Dlouhá, Dagmar; Dubovský, Viktor
Hydrical reclamation of the residual pit of Most-Leitiky is part of the comprehensive revitalisation of the land affected in the past by mining activity with an area of 1264 ha. Thus, in terms of remediation and reclamation, the most appropriate way to reclaim the residual pit, as one of the final stages of the long-term reclamation activities that have been going on in the area for more than half a century, occurs under the given conditions. The Lake Most, our study area, was planned and created as a hydric recultivation of the former surface Most-Laiky mine located near the town of Most, in the foothills of the Ore Mountains, approximately 80 kilometers northwest of the capital of the Czech Republic - Prague. The Lake Most represents extensive hydric reclamation, which is unique in the sense that it does not have a natural inflow and runoff, therefore an artificial feeder from the Oh& River had to be built. The main goal of the ongoing research is to construct a mathematical model predicting the water balance of Lake Most. Therefore, it is important to separate amount of water that is lost by the evaporation and amount of water that is lost into the subsoil. If we do not wish to use only temperature equations but more complex methods and equations to calculate evaporation instead, we need to have relative humidity, atmospheric pressure, wind speed, and daylight length values. In addition to the climatic data needed to calculate the evaporation, the amount of precipitation is needed to construct the balance equation of the area. An important objective in planning all hydric reclamation is to ensure their long-term sustainability, which is based on a detailed description of the study area's climate and local hydrological conditions. In our article we focus on assessing the evolution of climate in the area of this hydric reclamation. We have processed a long-term series of measurements in monthly averages from the Kopisty meteostation data provided by the Institute of Atmospheric Physics of the CAS.
Cosmological curvature acceleration
(Springer Nature, 2021) Capozziello, Salvatore; Lambiase, G.
Observed accelerated behavior of the Hubble flow, usually related to the existence of a mysterious unknown fluid dubbed dark energy, can be framed in natural extensions of General Relativity that work at infrared scales. This approach gives rise to a geometric view of the phenomenon that does not require any new particle to be addressed. In this review paper, without claiming for completeness, we will give the main ingredients of such an approach considering models like f(R) gravity, with R the Ricci curvature scalar, and, in general, higher-order theories of gravity including other curvature invariants. In this context, we will review also Teleparallel Equivalent General Relativity and its extensions like f(T) gravity, where T is the torsion scalar. We will show that the curvature picture and the torsion picture can be related each other giving an equivalent paradigm where the observed cosmological acceleration can be addressed by extending the gravitational sector.
Material model identification from set of experiments and validation by DIC
(Elsevier, 2021) Rojíček, Jaroslav; Čermák, Martin; Halama, Radim; Paška, Zbyněk; Vaško, Milan
A methodology for calibration and validation of material models using more simultaneous experiments is presented. The procedure contains the selection of suitable parameters for identification using a sensitivity analysis, parameters identification, analysis of usability of the material model, and validation of the material model. Three elastoplastic models are evaluated in this study: the bilinear isotropic hardening model with Von Mises yield condition, the bilinear isotropic hardening model with the Hill anisotropic yield condition, and the nonlinear isotropic hardening model with Hill anisotropic yield condition. Five proportional as well as nonproportional monotonic loading experiments conducted on aluminium alloy 2124-T851 are used for the presentation of the inverse approach application, whereas four of them are the source of identification. The validation of calibrated material models is done based on the strain field measurement realised by the Digital Image Correlation method. The nonlinear isotropic hardening rule together with Hill yield condition brings the best description of stress-strain behaviour of the material under investigation.
Optimal calibration of evaporation models against Penman-Monteith equation
(MDPI, 2021) Dlouhá, Dagmar; Dubovský, Viktor; Pospíšil, Lukáš
We present an approach for the calibration of simplified evaporation model parameters based on the optimization of parameters against the most complex model for evaporation estimation, i.e., the Penman-Monteith equation. This model computes the evaporation from several input quantities, such as air temperature, wind speed, heat storage, net radiation etc. However, sometimes all these values are not available, therefore we must use simplified models. Our interest in free water surface evaporation is given by the need for ongoing hydric reclamation of the former LeZaky-Most quarry, i.e., the ongoing restoration of the land that has been mined to a natural and economically usable state. For emerging pit lakes, the prediction of evaporation and the level of water plays a crucial role. We examine the methodology on several popular models and standard statistical measures. The presented approach can be applied in a general model calibration process subject to any theoretical or measured evaporation.
On the Carathéodory form in higher-order variational field theory
(MDPI, 2021) Urban, Zbyněk; Volná, Jana
The Caratheodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrinsic geometric operations applied to the well-known Poincare-Cartan form and principal component of Lepage forms, respectively. For second-order theory, our definition coincides with the previous result obtained by Crampin and Saunders in a different way. The Caratheodory equivalent of the Hilbert Lagrangian in general relativity is discussed.

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