Publikační činnost Katedry matematiky a deskriptivní geometrie / Publications of Department of Mathematics and Descriptive Geometry (310)

Permanent URI for this collectionhttp://hdl.handle.net/10084/122997

Kolekce obsahuje bibliografické záznamy publikační činnosti (článků) akademických pracovníků Katedry matematiky a deskriptivní geometrie (310) v časopisech registrovaných ve Web of Science od roku 2018 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.

Záznamy vytvořené před rokem 2018 jsou uložené v této kolekci.

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Now showing 1 - 20 out of 22 results

Exploring diverse trajectory patterns in nonlinear dynamic systems
(Elsevier, 2024) Lampartová, Alžběta; Lampart, Marek
Describing the dynamical properties of explored systems, one finds the need to distinguish between various types of trajectories. The nature of trajectories is often split into regular and irregular, which will be shown in this paper as too crude. Hence, the main aim of this paper is to give a classification of trajectories reflecting persistence, regularity, chaos, intermittency, and transiency. To depict such phenomena, classical examples from discrete (the Rulkov map) and continuous (the Lorenz system) dynamical systems are applied. In these cases, the maximal Lyapunov exponent, the 0-1 test for chaos, the bifurcation diagram, and the Fourier analysis are applied, and these dynamics characteristics are confronted with trajectory types.
Shape optimization for the Stokes system with threshold leak boundary conditions
(Elsevier, 2024) Haslinger, Jaroslav; Mäkinen, Raino A.E.
This paper discusses the process of optimizing the shape of systems that are controlled by the Stokes flow with threshold leak boundary conditions. In the theoretical part it focuses on studying the stability of solutions to the state problem in relation to a specific set of domains. In order to facilitate computation, the slip term and impermeability condition are regulated. In the computational part, the optimized portion of the boundary is defined using Bezier polynomials, in order to create a finite dimensional optimization problem. The paper also includes numerical examples to demonstrate the computational efficiency of this approach.
On special exponential Diophantine equations
(Bulgarian Academy of Sciences, 2023) Riemel, Tomáš
In this paper, we will focus on the study of a special type of exponential Diophantine equations, including a proof. The main contribution of this article is the mentioned type of equations, which can only be solved by the methods of elementary mathematics.
On risk and market sentiments driving financial share price dynamics
(Springer Nature, 2023) Lampart, Marek; Lampartová, Alžběta; Orlando, Giuseppe
The goal is to investigate the dynamics of banks’ share prices and related financials that lead to potential disruptions to credit and the economy. We adopt a classic macroeconomic equilibrium model with households, banks, and non-financial companies and explain both market valuations and endogenous debt constraints in terms of risk. Heterogeneous market dynamics ranging from equilibrium to cycles and chaos are illustrated. Deposits and equity are proven to be management levers for chaos control/anticontrol, and the only feasible equilibrium is unstable. Finally, using real-world data, a test is conducted on the suggested model proving that our framework conforms well to reality.
The use of GeoGebra in technical mathematics
(MM Science, 2023) Schreiberová, Petra; Morávková, Zuzana
In many technical fields, it is necessary to have a basic set of mathematical skills. Engineers need to calculate and understand concepts. They have to know how to solve equations, analyse measurements, use tables and graphs for some processes. These are just some examples showing how mathematics learning is important. For better illustration and visualization of mathematical concepts and methods, it is appropriate to use a modern technology. This provides dynamic teaching opportunities in math classes. GeoGebra is a free math software that is very useful for this purpose. This article shows some practical examples of the GeoGebra usage both as in mathematics education and as a support in solving technical problems.
On extensive dynamics of a Cournot heterogeneous model with optimal response
(AIP Publishing, 2022) Lampart, Marek; Lampartová, Alžběta; Orlando, Giuseppe
The objective of this paper is the study of the dynamical properties analysis of an original specification of the classical Cournot heterogeneous model with optimal response; specifically, a new approach that considers ordinal utility instead of cardinal monetary amounts is proposed where the classical decision of quantity is disentangled from the decision on imitation. The analysis is performed by means of bifurcation diagrams, the 0-1 test for chaos, power spectral density, histograms, and trajectory analysis. For this purpose, a new perturbation parameter epsilon of the initial condition is introduced, and together with the intensity of choice parameter beta determining the share of responders vs imitators, the system is researched. Depending on epsilon and beta, extreme reach dynamics, and coexisting attractors, periodic and chaotic trajectories are investigated through massive simulations. Those dynamics represent alternation between stability, cycles and chaos in the market. As the dynamics are completely endogenous, it means that swings in economy are intrinsic to the system and that they may persist unless controlled.
Numerical modeling of the leak through semipermeable walls for 2D/3D Stokes flow: Experimental scalability of dual algorithms
(MDPI, 2021) Haslinger, Jaroslav; Kučera, Radek; Motyčková, Kristina; Šátek, Václav
The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity-pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.
Bie model of periodic diffraction problems in optics
(Akademie věd České republiky. Matematický ústav, 2021) Krček, Jiří
Optical diffraction on a periodical interface belongs to relatively lowly exploited applications of the boundary integral equations method. This contribution presents a less frequent approach to the diffraction problem based on vector tangential fields of electromagnetic intensities. The problem is formulated as the system of boundary integral equations for tangential fields, for which existence and uniqueness of weak solution is proved. The properties of introduced boundary operators with singular kernel are discussed with regard to performed numerical implementation. Presented theoretical model is of advantage when the electromagnetic field near the material interface is studied, that is illustrated by several application outputs.
Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D
(Elsevier, 2021) Haslinger, Jaroslav; Kučera, Radek; Sassi, Taoufik; Šátek, Václav
The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity-pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.
Evaluation of waste blends with sewage sludge as a potential material input for pyrolysis
(MDPI, 2021) Kuboňová, Lenka; Janáková, Iva; Malíková, Petra; Drabinová, Silvie; Dej, Milan; Smelík, Roman; Skalný, Pavel; Heviánková, Silvie
In line with the requirements of the circular economy, the European Union's waste management legislative changes also concern the treatment of sewage sludge. Although sewage sludge production cannot be prevented, its quantities may be reduced by the synergetic effect of energy recovery via choosing a proper technology. Sewage sludge is difficult to apply as fuel alone, because of its high moisture and ash content. However, its energy use will be increased by adding suitable waste materials (different types of plastics, waste tires and paper rejects). Most recently, the thermal utilization of sewage sludge via incineration or pyrolysis has grown in importance. This article describes the fuel parameters of particular waste materials and of their blends with sewage sludge in connection with laboratory-scale thermal decomposition in an inert atmosphere, for their potential use in a semi-pilot plant pyrolysis unit. For pyrolytic application, the results of thermogravimetric analysis are needed in order to know the maximal temperature of thermal decomposition in an inert atmosphere, maximal mass losses, and weight loss rates. The samples of different thermoplastics mixed with sewage sludge, and low-density polyethylene blends with sewage sludge, had the lowest residual masses (70-74%) and the highest weight loss rates (11-19%/min). On the other hand, the blend of polyester rejects from tire processing, paper rejects and sewage sludge had the second highest residual mass (60%) and the lowest weight loss rate (3%/min).
Monotonic tension-torsion experiments and FE modeling on notched specimens produced by SLM technology from SS316L
(MDPI, 2021) Kořínek, Michal; Halama, Radim; Fojtík, František; Pagáč, Marek; Krček, Jiří; Krzikalla, David; Kocich, Radim; Kunčická, Lenka
The aim of this work was to monitor the mechanical behavior of 316L stainless steel produced by 3D printing in the vertical direction. The material was tested in the "as printed" state. Digital Image Correlation measurements were used for 4 types of notched specimens. The behavior of these specimens under monotonic loading was investigated in two loading paths: tension and torsion. Based on the experimental data, two yield criteria were used in the finite element analyses. Von Mises criterion and Hill criterion were applied, together with the nonlinear isotropic hardening rule of Voce. Subsequently, the load-deformation responses of simulations and experiments were compared. Results of the Hill criterion show better correlation with experimental data. The numerical study shows that taking into account the difference in yield stress in the horizontal direction of printing plays a crucial role for modeling of notched geometries loaded in the vertical direction of printing. Ductility of 3D printed specimens in the "as printed" state is also compared with 3D printed machined specimens and specimens produced by conventional methods. "As printed" specimens have 2/3 lower ductility than specimens produced by a conventional production method. Machining of "as printed" specimens does not affect the yield stress, but a significant reduction of ductility was observed due to microcracks arising from the pores as a microscopic surface study showed.
Comparison of procedures for the evaluation of time dependent concrete diffusion coefficient model
(Elsevier, 2020) Konečný, Petr; Lehner, Petr; Ghosh, Pratanu; Morávková, Zuzana; Tran, Quang
The article focuses on approaches for the computation of the input parameters of the time-dependent service-life model for the resistance of High Performance Concrete mixtures (HPC) against chloride ion penetration. The resistance of chloride ion penetration due to corrosion is described by means of diffusion coefficient. The diffusion coefficient is derived from the non-destructive testing method of electrical resistivity based on electrochemistry and following AASTHTO TP-95 specification. The effect of concrete maturity on the diffusion coefficient is taken into account via aging factor. In addition, the application of the least square method is presented and compared with the logarithm-based method in order to approximate the aging factor and reference diffusion coefficient. The quality of approximation of both approaches including the effect of the reference diffusion coefficient selection is also evaluated. Further, the derivation for the computation of model input parameters of both methods is presented. Finally, evaluation of goodness of fit of both approaches is conducted, and recommendation has been proposed via Least Square method and coefficient of determination.
Chatbots for learning: A review of educational chatbots for the Facebook Messenger
(Elsevier, 2020) Smutný, Pavel; Schreiberová, Petra
With the exponential growth in the mobile device market over the last decade, chatbots are becoming an increasingly popular option to interact with users, and their popularity and adoption are rapidly spreading. These mobile devices change the way we communicate and allow ever-present learning in various environments. This study examined educational chatbots for Facebook Messenger to support learning. The independent web directory was screened to assess chatbots for this study resulting in the identification of 89 unique chatbots. Each chatbot was classified by language, subject matter and developer's platform. Finally, we evaluated 47 educational chatbots using the Facebook Messenger platform based on the analytic hierarchy process against the quality attributes of teaching, humanity, affect, and accessibility. We found that educational chatbots on the Facebook Messenger platform vary from the basic level of sending personalized messages to recommending learning content. Results show that chatbots which are part of the instant messaging application are still in its early stages to become artificial intelligence teaching assistants. The findings provide tips for teachers to integrate chatbots into classroom practice and advice what types of chatbots they can try out.
Prediction of CRI and CSR of cokes by two-step correction models for stamp-charged coals - Statistical analysis
(Elsevier, 2020) Klika, Zdeněk; Serenčíšová, Jana; Kolomazník, Ivan; Bartoňová, Lucie; Baran, Pavel
A new approach for the prediction of Coke Reactivity Index (CRI) and Coke Strength after Reaction with CO2 (CSR) was proposed. For this purpose, 41 coking coals (40 USCB and 1 Appalachian coals) and 36 coal blends were studied. Cokes were carbonized using a pilot-scale coke oven by a stamp charging. Coals and coal blends were characterized by 14 properties and cokes by CRI and CSR indexes. Experimentally determined CRI and CSR indexes of cokes (type II) did not fit well with their calculated values from regression equations based on different coal blend properties (R < ca. 0.370). The similar discrepancy was also observed if experimentally determined coke indexes were compared with weighted averages of C<(R)over tilde>I and C (S) over barR (R < ca. 0.390). With the view of low reliability, herein, the prediction of CRI and CSR values of 36 cokes (type II) was based on 2 newly proposed two-step models. In model 1, the first step consists of preliminary calculation (estimation) of CRI/CSR indexes using modified regression equations originally calculated for the prediction of cokes (type I) carbonized from unblended coking coals; in model 2 calculation of CRI/CSR values (type II) in the first step is carried out using calculated weighted averages of C<(R)over tilde>I and C (S) over barR from type I cokes. In both models, estimated CRI/CSR values were corrected using calculated correction coefficients from regression equations based on coal blend properties. If compared with a traditional one-step procedure, the results document that this novel (two-step) approach provides much better prediction of the coke characteristics.
Shape dependent EMA model of nanostructured anisotropic materials
(MDPI, 2019) Otipka, Petr; Vlček, Jaroslav
Heterogeneous nanostructures containing nanoparticles of various sizes and shapes have attracted significant attention in the development of nano-biosensors. Especially, plasmonic properties of such materials are advantageously exploited for the detection of biological and chemical substances. Since these media exhibit optical anisotropy, a valid homogenization procedure must be able to describe appropriately the relationship between the geometry of the inclusions and the nature of local field modes. We present a model approach for extension of the effective medium approximation (EMA) and its application to anisotropic nanostructures. The proposed model is based on a "strong-couple-dipole" (SCD) method including a volume-integral correction term in a Green tensor that enables to obtain more accurate representation of polarizability tensor. Derived depolarization factors for discs and bi-cone particles are compared with the early known shapes (spheroids, cylinders) and applied to nanostructures composed of the Fe or Au nanodots in polyacrylate.
On the inexact symmetrized globally convergent semi-smooth Newton method for 3D contact problems with Tresca friction: the R-linear convergence rate
(Taylor & Francis, 2020) Kučera, Radek; Motyčková, Kristina; Markopoulos, Alexandros; Haslinger, Jaroslav
The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three-dimensional space is analysed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper.
Design of plasmonic-waveguiding structures for sensor applications
(MDPI, 2019) Vlček, Jaroslav; Pištora, Jaromír; Lesňák, Michal
Surface plasmon resonance has become a widely accepted optical technique for studying biological and chemical interactions. Among others, detecting small changes in analyte concentration in complex solutions remains challenging, e.g., because of the need of distinguishing the interaction of interest from other effects. In our model study, the resolution ability of plasmonic sensing element was enhanced by two ways. Besides an implementation of metal-insulator-metal (MIM) plasmonic nanostructure, we suggest concatenation with waveguiding substructure to achieve mutual coupling of surface plasmon polariton (SPP) with an optical waveguiding mode. The dependence of coupling conditions on the multilayer parameters was analyzed to obtain optimal field intensity enhancement.
Power law Stokes equations with threshold slip boundary conditions: Numerical methods and implementation
(Wiley, 2019) Djoko, Jules K.; Koko, Jonas; Kučera, Radek
For the power law Stokes equations driven by nonlinear slip boundary conditions of friction type, we propose three iterative schemes based on augmented Lagrangian approach and interior point method to solve the finite element approximation associated to the continuous problem. We formulate the variational problem which in this case is a variational inequality and construct the weak solution of the continuous problem. Next, we formulate two alternating direction methods based on augmented Lagrangian formalism in order to separate the velocity from the symmetric part the velocity gradient and tangential part of the velocity. Thirdly, we present some salient points of a path-following variant of the interior point method associated to the finite element approximation of the problem. Some numerical experiments are performed to confirm the validity of the schemes and allow us to compare them.
Phase sensitive measurement of the wavelength dependence of the complex permittivity of a thin gold film using surface plasmon resonance
(Optical Society of America, 2019) Hlubina, Petr; Luňáčková, Milena; Ciprian, Dalibor
We report on a new method for measuring the wavelength dependence of the complex permittivity of a thin gold film of a surface plasmon resonance (SPR) structure comprising a gold-coated SF10 slide with an adhesion film of chromium attached to an SF10 glass prism. The method is based on spectral interferometry and utilizes a setup with a birefringent crystal and the SPR structure in the Kretschmann configuration, in which channeled spectra are recorded and from them, the phase functions of the SPR for air at different angles of incidence are retrieved. The SPR phenomenon is manifested as an abrupt phase change with respect to the reference phase difference for the interference resolved with the SF10 glass prism alone. The phase changes for different angles of incidence are processed in the vicinity of the resonance wavelengths to obtain the real and imaginary parts of the complex permittivity in a wavelength range from 530 to 850 nm or equivalently, the parameters of a modified Drude-Lorentz model. This research, to the best of the authors' knowledge, is the first demonstration of spectral interferometry-based measurement of the complex permittivity function of a thin metal film, which is important from the point of view of material characterization directly performed in the Kretschmann configuration.
Oral appliance effectiveness and patient satisfaction with obstructive sleep apnea treatment in adults
(International Scientific Information, 2019) Skalná, Markéta; Novák, Vilém; Bužga, Marek; Skalný, Pavel; Hybášková, Jaroslava; Stránský, Jiří; Štembírek, Jan
Background: Indication of oral appliances for the treatment of an obstructive sleep apnea (OSA) includes both patients with primary snoring and mild OSA, as well as patients with moderate to severe OSA who refuse other treatment or in whom such treatment failed. The aim of this study was to verify the effectiveness of current OSA treatment by objective measurements, and to assess by means of a questionnaire patients' satisfaction with oral appliances manufactured in our laboratory. Material/Methods: The study enrolled 58 adult patients (40 men, 18 women) with mean age of 50.5 years; most were overweight or had class I obesity; mean baseline apnea-hypopnea index (AHI) value prior to the beginning of treatment was 31.3, range 0.6-71. Results: Average AHI reduction in the entire group was 10.4; 31% of patients experienced AHI reduction by at least 50%. Significant AHI reduction was proven when using the appliance. Appliances affect the reduction of AHI and patients tolerate the appliances well. Conclusions: Oral appliances complement positive-pressure treatment and do not interfere with it in any way. Craniometric parameters seem to be applicable as predictors of success or failure of appliance treatment.

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