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ISSN - 2391-9361

Volume 6, issue 4

Edition circulation: 130 copies


1 vol. 6, iss. 4/1

Production engineering as a discipline and the possibilities to apply the organization of its achievements in practice

Abstract: The paper presented basic information concerning a new scientific discipline in Poland: production engineering, which was created in 2010 within the field of technical sciences. Brief characteristics of 10 scientific – research fields was presented, separated within this discipline. There has been defined a subject of production engineering studies and tasks in the area of innovation. Basing on information included in over 40 papers within project Crossborder exchange of experiences in production engineering with the use of mathematical methods, it was presented examples of practical application of solutions developed within the discipline. The paper presented various classifications of developed solutions and pointed out their application value. It was confirmed that the elaborated solutions may have a wide range of application in various organizations. Summing up, the paper stated a large scope of solutions in production engineering and indicated its great value for development of Polish and Czech economy.

Keywords: production engineering, scientific discipline, practical solution
p. 11 pobierz
2 vol. 6, iss. 4/2

Zygmunt KORBAN
Application of MERIT survey in the assessment process of the management quality of the occupational health safety – case study

Abstract: The experience of economically developed countries proves that the quality of actions undertaken in the realm involving the management of the occupational health and safety may substantially contribute the attainment of higher OHS standards. A significant role in the improvement of OHS management quality is played among others by audit surveys of the management system of OHS which is viewed as a form of controlling tool. One of the first solutions of that type was applied in the mining industry in Poland, and they were based on the MERIT survey (Management Evaluation Regarding Itemized Tendencies). The mathematical model applied within the scope of that survey makes it possible to determine assessment indexes (final index WZBP and partial indexes WOPi). The results obtained from the survey carried out on a group of respondents – employees of departments of mining coal – were then used for the prediction of the assessment of the quality of actions undertaken in the area of OHS management (the linear discriminant function was applied as the prediction method).

Keywords: management of occupational health and safety, MERIT
p. 19 pobierz
3 vol. 6, iss. 4/3

Stanisław KOWALIK
Research of correlation between temperature rock mass and energy of tremor

Abstract: In paper results of calculations of correlation between temperature of rock mass in coal mine "Jas-Mos", and energy of tremor are presented. Correlation referred temperatures before tremor and after tremor, temperatures before tremor and energy of tremor and temperatures after tremor and energy of tremor. Also multiple correlation was calculated between the test values. At the correlation between difference of temperatures and energy of tremor was also determined.

Keywords: rock mass, tremor, temperature, correlation
p. 27 pobierz
4 vol. 6, iss. 4/4

Radosław WOLNIAK
Application methods for analysis car accident in industry on the example of power

Abstract: The paper presents the concept of using the RCA method to failure analysis on the example of power plant. Nowadays, where the speed plays a big role in business, it’s not easy to get to the root causes of failure. RCA Method (Root Cause Analysis) is an analysis of root causes, it is an independent and comprehensive method of risk analysis used to study, identify and classify the root causes of incidents establishment in the work. The aim of the publication is to examine the benefits of using the analysis of RCA as a reactive method of identifying the causes, discovering problems and solving them in the company.

Keywords: RCA analysis, FMEA analysis, Ishikawa diagram, 5-Why method
p. 34 pobierz
5 vol. 6, iss. 4/5

Financial challenges in production engineering using key performance indicators – a case of different production process types

Abstract: The article investigates the management of production processes in case of differentiated manufacturing processes that occur in a small enterprise. Authors state that appropriate managerial decision-making should encompass non-financial indicators of important costing determinants that are crucial for cost management and their improvement. The aim of the article is to develop a possible set of key performance indicators helpful in achieving operational objectives in main performance areas. By incorporating non-financial (and non-monetary) data referring to production activities, authors indicated important determinants that should be included into effectiveness and economics evaluation carried out within production engineering.

Keywords: production engineering, cost management, KPI, cost allocation
p. 41 pobierz
6 vol. 6, iss. 4/6

Patrycja HĄBEK
The concept of using FMEA method for sustainable manufacturing

Abstract: Sustainable manufacturing is to ensure that cost-effective manufacturing processes do not endanger the environment, are implemented in a way that is safe for life and health of employees and the public. The question then arises of how to improve manufacturing processes to make them more sustainable? Such a question cannot be answered unequivocally. The author draws attention to the possibility of using for that purpose FMEA (Failure Mode and Effects Analysis) method, which aims to identify potential defects in the process/product and then eliminate them or minimize the risks associated with them. In the article it will be proposed modification of this method for using it in the process of sustainable manufacturing.

Keywords: sustainable manufacturing, failure mode and effects analysis, FMEA, manufacturing launch, purchasing
p. 49 pobierz
7 vol. 6, iss. 4/7

Statistical methods as a decision making tool for production engineering – an exemplary application

Abstract: Production engineering is the term given to the issues of planning, designing, implementing and managing production systems, logistics systems and securing their functioning (IIE, 1989). According to this definition, production engineering is focusing on the decisions aiming at maintaining the decision processes within the organization. Therefore, decision makers use different tools to ensure the accuracy and efficiency of this process. One group of methods than can be useful in production engineering are statistical methods organizing data collecting, presentation an processing. The article presents samples of statistical methods used in production engineering.

Keywords: statistical methods, decision, organization, production engineering
p. 56 pobierz
8 vol. 6, iss. 4/8

The overview of applied methods for occupational risk assessment

Abstract: The article presents the been reviewed most frequently used methods of risk assessment. They have been analyzed coefficients used in various methods of paying attention to the rules for their designation. Also important was the way we defined risk index and the rules of its interpretation in the various methods.

Keywords: occupational risk assessment, Risk Score method, WPR indicator method, extended five steps method, management of occupational risk
p. 63 pobierz
9 vol. 6, iss. 4/9

Justyna ORWAT
Possibility analysis of the use of smooth spline functions to determination the average course of mining area curvatures obtained from results of geodesic measurements

Abstract: In this paper was done an analysis of possibility of the use of smooth spline functions to obtaining of an average course of mining area curvatures. Their values were calculated on the basis of geodesic observations results, were conducted into the boundaries of some mining area. The analysis was done based on the counting of standard deviations between the empirical and mean values of curvatures (σC) and variability indicators of curvatures’ random dispersion (MC). They were compared with the pattern values occurring in the professional literature.

Keywords: random scattering (fluctuation) of the mining area curvatures, an approximation, a smooth spline
p. 69 pobierz
10 vol. 6, iss. 4/10

Matrix calculus and spreadsheet in planning and controlling of operating costs

Abstract: The article provides a discussion on a concept of using the matrix calculus for purposes of planning and controlling of operating costs. The opening paragraphs of the paper describe creating a plan of costs for an enterprise perceived as a series of interlinked components whose mutual relations are represented in corresponding matrices. Further sections of the article are focused on an analysis of the deviations emerging while planned costs are being compared with the reported actual costs. Different types of deviations comprising the total deviation have been identified. It is possible to determine these deviations based on the data contained in matrices used at the planning stage as well as with reference to appropriate real-life data acquired. For individual groups of deviations, the manner in which they can be determined has been explained. The final paragraphs of the article address potential applications of spreadsheets, both in creating the plan of costs and for purposes of its subsequent controlling.

Keywords: cost planning, cost controlling, IT tools
p. 76 pobierz
11 vol. 6, iss. 4/11

The support of projects risk management in production company using methods of production engineering

Abstract: Presented paper attempts to develop a methodology for supporting risk management in projects in production engineering. The methodology applies to manufacturing companies of the automotive industry, because it is one of the industries where the projects are comparable to each other. On this basis, it is possible to identify the risks that occurred in the past during the various stages of the projects, which can contribute to more effective risk management during the current and future projects. The developed methodology describes how to collect data on ongoing projects, as well as how to make their analysis to allow their subsequent use.

Keywords: projects risk management, methodology, production engineering
p. 83 pobierz
12 vol. 6, iss. 4/12

Analysis of factors affecting gas hazards in industrial plants

Abstract: The article presents characteristics of industrial gas installations and hazards associated with their operation. The methods of hazard identification used in industrial processes have been analyzed. An explosion hazard analysis was performed using the event tree method, taking into account the factors influencing employee error (human factor).

Keywords: hazard identification methods, gas installations, gas signaling system, human factor
p. 91 pobierz
13 vol. 6, iss. 4/13

Andrzej LOSKA
Analytical model of the exploitation policy assessment of technical network systems - case study

Abstract: The article take issues of the exploitation policy assessment of technical systems. After the discussion of the mathematical models possible for use in the assessment of the functioning of technical systems in enterprises, an analytical concept based on the resultant of the three features is presented: time, costs i quantity of maintenance tasks, referred to the four work categories. The proposed concept was verified for selected technical network systems. The last aspect of the article is the analysis and interpretation of the results obtained in the context of the exploitation policy assessment.

Keywords: exploitation policy, technical network systems, exploitation efficiency, maintenance management
p. 98 pobierz
14 vol. 6, iss. 4/14

Assessment of annoyance imact of road noise sources under the laboratory conditions

Abstract: The article presents an attempt to statistical assessment of the results of psychoacoustic studies of the experiment carried out on the annoyance of road noise sources. The study was subjected to noise annoyance assessment of emitted acoustic signals under laboratory conditions. The obtained results may be used in the acoustic quality modeling the acoustic quality of the urban environment at risk of noise.

Keywords: variance analysis, noise annoyance, road noise
p. 105 pobierz
15 vol. 6, iss. 4/15

Joanna MYTYCH, Mariusz J. LIGARSKI
Investigation into organizational structure influence on the functioning of an accredited testing laboratory

Abstract: The quality management systems compliant with the PN-EN ISO/IEC 17025:2005 standard are widely described in terms of the research methods. However, the construction and functioning of the management system are discussed on a much smaller scale. The Authors of this publication tried to assess selected results from the survey conducted among 1,213 accredited testing laboratories functioning in Poland. The Authors focused on analysing the survey results describing the influence of the organizational structure of the institution in which the laboratory was located on the functioning of an accredited management system in a testing laboratory.

Keywords: quality management system, ISO/IEC 17025:2005, accreditation, testing laboratory
p. 112 pobierz
16 vol. 6, iss. 4/16

Assessment of the level of maturity of the quality management system – applied models and sample test results

Abstract: In the article there are presented models and methods of assessment of the level of maturity of the quality management system in organizations included in the standards and promoted by the European Foundation for Quality Management. The fundamental principles of forming pro-quality approach to quality management are presented. The results of selfassessment of selected group of Polish pro-quality managed enterprises on the basis of the carried out research with the participation of the Finalists of Polish Quality Awards.

Keywords: quality management system, maturity assessment, self-assessment
p. 118 pobierz
17 vol. 6, iss. 4/17

Selected quantitative methods used in production engineering for the improvement of production processes

Abstract: In every manufacturing company are analysed and improvement of the life cycle of the process and the product. This is done at the stage of designing, manufacturing and control. The article presents the classification of selected quality management methods, such as QFD, FMEA, SPC, 8D, DOE.

Keywords: quantitative methods, process improvement, production, control
p. 125 pobierz
18 vol. 6, iss. 4/18

Use of work station performance indicator rating in the manufacturing processes improving

Abstract: The study presents the results of the research on improving the productivity of works executed of the up to 1400 mm conveyor belts fabrication workstation in Conbelts S.A. with its registered office in Bytom. Using the OEE indicator, the author conduct a performance evaluation of the work stations of the selected technology line. The results of the research have enabled us to design and implement solutions that eliminate irregularities and streamline the operation at the belt fabrication workstation. The post-implementation performance evaluation confirmed the effectiveness of the solutions taken.

Keywords: performance, OEE, conveyor belts
p. 130 pobierz
19 vol. 6, iss. 4/19

Piotr KALETA, Tomasz WAŁEK
Methodology of running cost analysis for high-efficiency gas micro-cogeneration application in objects of various demand of heat and power

Abstract: Conditions related to high-efficiency gas micro-cogeneration application in buildings with varying demand for heat and power were presented, focusing on joint application of microcogeneration and other sources of heat and power in buildings. Such joint application of Energy sources is characterized by specific critical parameters on which the most effective use of microcogeneration system in objects depends, as well as by the resulting maximal possible reduction of primary fuels and environmental pollutant emission. To ensure achievement of these, designing and application of a proper mathematical model, which has been described in the paper, is required. The model presented therein finds practical application in conducting a proper selection of micro-cogeneration units’ capacity for the needs of objects being analyzed, such as health resorts, swimming pools, hospitals, hotels, pensions or manufacturing plants.

Keywords: gas mircocogeneration, power and heat demand, load duration curves
p. 140 pobierz
20 vol. 6, iss. 4/20

Katarzyna MIDOR
Use of six sigma in the production process – case study

Abstract: Issues related to the quality of the final product and the individual components that comprise it are important in every branch of the industry. This is especially true for the automotive branch, where the consequences of quality errors are very severe and costly. The article presents the use of the Six Sigma method for the improvement of the process of height measurement of a controller board chip in a production stream for a premium-class client. The method used, which can be defined mathematically, allowed for minimising the causes for excessive rejection rates of the element in question, which was presented in the article.

Keywords: six sigma, production process, quality, process improvement
p. 147 pobierz
21 vol. 6, iss. 4/21

Application of quality engineering to improve the assembly process of the car cockpit elements

Abstract: The article presents an example of the use of quality engineering methods to improve the assembly process in the production company car accessories – varnished elements of the cockpit. The main part of the article is a description of the improvement project that was carried out in the selected company. This section describes problems with defect of the assembly process and its improvement. The end of the article is an assessment of the effectiveness of the improvement actions undertaken.

Keywords: quality improvement, 5why method, Pareto Chart
p. 153 pobierz
22 vol. 6, iss. 4/22

Statistical process control in the maintenance

Abstract: Improvement of processes connected with maintenance is important from the perspective of the company’s productivity. The proper functioning of the departments responsible for maintaining technical assets in working order affects the production efficiency, safety of the operating personnel, quality of the products and the effectiveness of realisation of the production plans. One of the most important tasks of the maintenance department is minimising the length of stoppages caused by breakdowns. The article presents a proposal of using SPC tools for the constant improvement of the maintenance process. Implementation of static process control allowed for identifying the major problems which lengthen the breakdown removal time, as well as continuously monitoring the breakdown removal process. The study is based on breakdown data gathered in a production company over the period of three years.

Keywords: maintenance, improvement, process, SPC, failure, downtime
p. 159 pobierz
23 vol. 6, iss. 4/23

Jacek SITKO, Krzysztof MICHALSKI
Analysis of the system processing waste products in energy and metallurgical industry

Abstract: The article presents an overview of selected issues related to the problem of processing and utilization of slags from the power industry and the Zn-Pb metallurgy. The varied chemical composition and structure creates for disposal technologies a number of difficulties that must be overcome to enable a wide use of slags in industry. Innovative approach to the disposal process increases the chances of solving many technological and organizational problems in the energy and metallurgical industry.

Keywords: process, recycling, slag, energy
p. 166 pobierz
24 vol. 6, iss. 4/24

Krzysztof MICHALSKI, Jacek SITKO
Analysis of degraded post-industrial areas for redevelopment. Case study

Abstract: Degraded post-industrial areas have considerable potential for redevelopment. However, the unstabilized legal situation, lack of information on the area, its infrastructure and key features make investors prefer undeveloped land. The following paper is an attempt to perform a preliminary analysis of a selected post-industrial site, in order to facilitate the choice of how to re-use it.

Keywords: post-industrial area, redevelopment
p. 172 pobierz
25 vol. 6, iss. 4/25

Dynamic model of a kaolin deposit

Abstract: This paper focuses on research within the project TE02000029 Competence Centre for Effective and Ecological Mining of Mineral Resources, granted by The Technology Agency of the Czech Republic, and, more specifically, on the research within its work package WP4 – Spatial modelling of mineral deposits. The focus of this work package is digital modelling of selected nonenergetic raw materials, which belong to the critical commodities, as defined by the European Union. For modelling these deposits, suitable mathematical procedures, based on study and reevaluation of archived data, are needed. One of the selected deposits is a kaolin deposit near the village Jimlíkov near the city Karlovy Vary. In this paper, we show a step-by-step procedure for creation, visualization and evaluation of a 3D model of the deposit. This methodology, along with our recently developed software allows a user to create a variant of this dynamic model for the same or similar types of deposits, enables rapid updating of these models when adding or changing the input data on the basis of new mining exploration or when changing modelling parameters such as using multiple variations interpolation parameters. Our methodology leads to a more advanced deposit evaluation, including adaptive estimates of the reserves based on the usability requirements we choose. In January 2017 our software was tried out in the company Sedlecký kaolin a. s. in Božičany and our dynamic model is fully applied in practice.

Keywords: spatial modelling of deposits, EU critical commodities, kaolin deposit, visualization, estimates of reserves
p. 179 pobierz
26 vol. 6, iss. 4/26

Implementation of a kaolin deposit model in Visual Studio 2015

Abstract: This paper focuses on research within the project TE02000029 Competence Centre for Effective and Ecological Mining of Mineral Resources, granted by The Technology Agency of the Czech Republic, and, more specifically, on the research within its work package WP4 – Spatial modelling of mineral deposits. The focus of this work package is digital modelling of selected nonenergetic raw materials, which belong to the critical commodities, as defined by the European Union. For modelling these deposits, suitable mathematical procedures, based on study and reevaluation of archived data, are needed. One of the selected deposits is a kaolin deposit near the village Jimlíkov near the city Karlovy Vary. The article describes the implementation of the methodology used for processing deposits of kaolin in Visual Studio 2015 by means of objects of Surfer and Voxler created by Golden Software. This software solution is installed at the company Sedlecky kaolin a.s. and thus is fully exploited in practice.

Keywords: kaolin deposit, Visual Studio 2015, spatial modeling, Surfer, Voxler
p. 191 pobierz
27 vol. 6, iss. 4/27

The determination of the mineral percentages in granite

Abstract: Recently a new method (CQMA) for the quantitative determination of minerals in solid samples has been suggested and verified on 6 standards of rocks samples. This method is based on the recalculation of the elemental bulk chemical analysis on the quantitative contents of the mineral phases identified in sample. This method is based on the optimization procedure and except elemental bulk chemical analysis requires the identification of minerals and finding their crystallochemical formulas. The mineral phases as well as chemical analysis are determined by usual analytical methods. In this contribution the results of quantitative calculated minerals by Chemical Quantitative Mineral Analysis (CQMA) are compared with the reference analysis of granite. Mineral analysis of granite was performed by optical and XRD methods, chemical analyses by classical and XRF methods and crystallochemical formulas of minerals were identified by Rietveld technique.

Keywords: quantitative mineral analysis, chemical analysis recalculation, a sample on analysis of granite
p. 200 pobierz
28 vol. 6, iss. 4/28

Prediction of subsidence depression development

Abstract: An extensive network of points was repeatedly surveyed by GPS method to monitor the surface manifestations of undermining in the Louky locality near Karvina from 2006 to 2011. The aim was not only to record the development of the creating subsidence depression, its range, size of subsidence and horizontal shifts, but the task was also to predict the future state in the area. Such information is essential for planning surface reclamation and other uses of the undermined areas. Prediction of further development on the basis of GPS data and theoretical knowledge of the subsidence depression development was provided by regression analysis.

Keywords: undermining; subsidence; prediction; regression analysis
p. 208 pobierz
29 vol. 6, iss. 4/29

Statistical evaluation of the efficiency of the two types of protection systems in carotid artery stenting

Abstract: The article deals with the evaluation of the efficiency of the two types of protection systems in carotid artery stenting (CAS). Carotid artery stenting is a treatment of carotid artery stenosis, which is a narrowing of the carotid artery caused by a plaque buildup in the artery wall. Pieces of plaque can break off and block the blood flow in the artery, which leads to a stroke. Carotid artery stenting is an endovascular surgery where a stent is deployed within the lumen of the affected carotid artery to dilate it and prevent a stroke. Two types of embolic protection devices are commonly used during CAS - distal protection devices (filters) and proximal protection devices. The aim of this study was to determine whether the two protection systems differ in the number and in the location of new ischemic lesions after surgery. Statistical analysis was carried out with the programs SPSS and Microsoft Excel. Mann-Whitney test, χ2 test and Arcsine test were used and the value of p = 0.05 was taken as a level of significance.

Keywords: carotid stenosis, embolic protection devices, statistical tests, Mann-Whitney test, χ2 test, Arcsine test
p. 215 pobierz
30 vol. 6, iss. 4/30

Mathematics yesterday and today on VSB-TU Ostrava

Abstract: The authors compare mathematics curricula at VŠB - Technical University of Ostrava in the year 1979 and at present. They compare the extents and the contents of the curriculum, numbers of lessons and above all the preparedness of students for applications in engineering practice. Reality is compared with the requirements of the European Society for Engineering Education (SEFI) in the material A Framework for Mathematics Curricula in Engineering Education.

Keywords: SEFI, mathematics curriculum, mathematics education
p. 222 pobierz
31 vol. 6, iss. 4/31

On homogeneous functions in second-order field theory

Abstract: The classical concept of a homogeneous function is introduced and extended within the theory of differential groups, known in the theory of differential invariants. Invariance under reparametrizations of solutions of partial differential equations is studied. On this basis the wellknown generalizations of the Euler theorem are obtained (the Zermelo conditions). The positive homogeneity concept is then applied to second-order variational equations in field theory.

Keywords: lagrangian, euler-lagrange equations, zermelo conditions, jet, differential group, field theory
p. 230 pobierz
32 vol. 6, iss. 4/32

Dagmar DLOUHÁ, František CERVENKA
Using hyperbola and one-sheeted hyperboloid in engineering practice

Abstract: We have begun to innovate our lectures within the course “Geometry on Computer”. These innovations are supported by the FRVS grants. We use programs GeoGebra and Open - SCAD for teaching plane and 3D geometry. The GeoGebra allows us to concentrate on mathematical and geometrical principles of solving problems. OpenSCAD is basic programmable 3D CAD modeler. The content of the course has been compiled with respect to requirements of students in their future studies and practical engineering use. In this paper we present application problems where following principals of classic geometry are used: articulated antiparallelogram, parametrization of functions and their use in 3D modeling and solving navigation problems.

Keywords: GeoGebra, OpenSCAD, 3D modelling, hyperbola, hyperboloid, antiparallelogram
p. 237 pobierz
33 vol. 6, iss. 4/33

Note on circulant matrices of degree 9

Abstract: Circulant matrices provide quite a wide range of applications in many different branches of mathematics, such as data and time-series analysis, signal processing or Fourier transformation. Huge number of results concerning circulant matrices could be found in algebraic number theory. This is because we could construct factor ring isomorphic to the p-th cyclotomic field Q(Ƈp) from the ring of circulant matrices degree p, where p is a prime. In this paper the connection between ring of circulant matrices of degree 9, C9, and the cyclotomic field Q(Ƈ9) is shown.

Keywords: circulant matrix, cyclotomic field
p. 243 pobierz
34 vol. 6, iss. 4/34

Youtube in teaching geometry

Abstract: More and more people are turning to the Internet for help in solving their problems. They seek guidance as texts and increasingly video. Even in technical practice people have come to watch the video on youtube that will help them solve their problem. To confirm this assumption, we conducted a survey among students on the basis of the result, we decided to put video tutorials on youtube and offer them to share not only our students but also the public.

Keywords: Youtube, video, video tutorials, studying materials
p. 252 pobierz
35 vol. 6, iss. 4/35

Math support centre at Technical University Ostrava

Abstract: The Math Support Centre was established at Technical University of Ostrava in 2016. Its goal is to help students to better understand mathematics in an unformal study atmosphere. The main task of the Support Centre is to overcome gaps between their knowledge from different types of secondary schools and level of mathematics needed for successful study at our Technical University. We also help students with their problems of any type arising within their studies of mathematical subjects.

Keywords: mathematics education, math support centre
p. 257 pobierz
36 vol. 6, iss. 4/36

Modern Taylor Series method in numerical integration: part I

Abstract: The paper deals with extremely exact, stable, and fast numerical solutions of systems of differential equations. It also involves solutions of problems that can be reduced to solving a system of differential equations. The approach is based on an original mathematical method, which uses the Taylor series method for solving differential equations in a non-traditional way. Even though this method is not much preferred in the literature, experimental calculations have verified that the accuracy and stability of the Taylor series method exceed the currently used algorithms for numerically solving differential equations. The Modern Taylor Series Method (MTSM) is based on a recurrent calculation of the Taylor series terms for each time interval. Thus, the complicated calculation of higher order derivatives (much criticised in the literature) need not be performed but rather the value of each Taylor series term is numerically calculated. An important part of the method is an automatic integration order setting, i.e. using as many Taylor series terms as the defined accuracy requires. The aim of our research is to propose the extremely exact, stable, and fast numerical solver for modelling technical initial value problems that offers wide applications in many engineering areas including modelling of electrical circuits, mechanics of rigid bodies, control loop feedback (controllers), etc.

Keywords: Taylor series method; ordinary differential equations; technical initial value problems
p. 263 pobierz
37 vol. 6, iss. 4/37

Preconditioning in the path-following algorithm for the stokes flow with stick-slip conditions

Abstract: The Stokes problem with the stick-slip boundary condition is solved by the mixed finite element method combined with the TFETI method. An interior point method for the minimization subject to box and equality constraints is used. The preconditioned projected conjugate gradient method solves the inner linear systems. The preconditioners are tested experimentally. The aim of our research is to develop efficient solvers for modelling of a flow over hydrophobic walls that exhibits applications in engineering areas including biomedical modelling or transport of fluid.

Keywords: Stokes problem; stick-slip condition; interior point method; TFETI method
p. 274 pobierz
38 vol. 6, iss. 4/38

Symmetrized semi-smooth newton method for solving 3D contact problems

Abstract: The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. 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. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).

Keywords: contact problem; Tresca friction; semi-smooth Newton method; conjugate gradient method; gradient projection; convergence rate
p. 286 pobierz
39 vol. 6, iss. 4/39

Extrema problems solved in GeoGebra

Abstract: The solving of applied problems is a reasonable way to gain better understanding of mathematical concepts, especially for future engineers. GeoGebra is a very useful tool for modeling these problems thanks to its interactivity.

Keywords: GeoGebra, extrema problems
p. 294 pobierz
40 vol. 6, iss. 4/40

History of the czechoslovak journal of actuarial sciences

Abstract: In this article we apprise with the history of the Czechoslovak Journal of Actuarial Sciences that was published in the era of the first republic before the World War II. We show its influence on the development of the insurance mathematics in Czechoslvakia and describe the circle of its authors. We show how the old proverb historia magistra vitae is useful for understanding the current development in actuarial sciences or, more generally, in social insurance.

Keywords: actuarial sciences, social insurance
p. 300 pobierz
41 vol. 6, iss. 4/41

Damped solutions of singular ivps with ø-Laplacian

Abstract: We study analytical properties of a singular nonlinear ordinary differential equation with a ø-Laplacian. We investigate solutions of the initial value problem (p(t)ø(u’(t)))’ + p(t)f(ø(u(t))) = 0, u(0) = u0 ≡ [L0,L], u’(0) = 0 on the half-line [0,∞). Here, f is a continuous function with three zeros, function p is positive on (0, ∞) and p(0) = 0. The integral ʃds ds./p(s) may be divergent which yields the time singularity at t = 0. Our equation generalizes equations which appear in hydrodynamics or in the nonlinear field theory.

Keywords: second order ODE, time singularity, existence and uniqueness, ø -Laplacian, damped solution
p. 306 pobierz
42 vol. 6, iss. 4/42

Uniform horizontal projectile motion

Abstract: In the paper we present the modification of the classical horizontal projectile motion in the homogeneous gravitational field called uniform horizontal projectile motion. The particle passing in the homogeneous gravitational field is treated as a mechanical system subjected to a nonholonomic nonlinear constraint which keeps the magnitude of the instantaneous velocity of the particle constant during the motion. We present the comparison of the kinematic parameters of both motions (classical and uniform horizontal projectile motions) under the same initial conditions. The presented problem can serve as a suitable topic for an elementary course of theoretical mechanics on the university level.

Keywords: nonholonomic mechanical systems, reduced and deformed equations of motion, Chetaev constraint force, horizontal projectile motion, kinematic parameters
p. 314 pobierz
43 vol. 6, iss. 4/43

Zbynek URBAN, Jana VOLNÁ
Variational equations on the Möbius strip

Abstract: In this paper, systems of second-order ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by the canonical embedding of the two-dimensional Möbius strip into the Euclidean space, are considered in the class of variational equations. For a given non-variational system, the conditions assuring variationality (Helmholtz conditions) for the induced system on the Möbius strip are formulated. The theory contributes to variational foundations of geometric mechanics.

Keywords: Lagrangian; Euler -Lagrange equations; Helmholtz conditions; fibered manifold; Möbius strip
p. 325 pobierz
44 vol. 6, iss. 4/44

Jaroslav VLCEK, Petr OTIPKA
Green tensor in material sciences

Abstract: Material properties of heterogeneous nanomaterials modelled by effective medium approximation (EMA) demand specific approaches when metallic inclusions in a host medium are exposed to external magnetic field. Resulting induced anisotropy of permittivity is manifested itself by a specific form of polarizability tensor. In presented work, this one is applied in the so called “strong-couple-dipole” (SCD) method, where the electromagnetic Green tensor is of key importance. The results are oriented to the magneto-plasmonic sensor element design for the use in biology or chemistry.

Keywords: anisotropy, effective medium, polarizability tensor, Green tensor
p. 334 pobierz


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