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Tytuł:
Description of matrix converter in frequency domain
Autorzy:
Borkowski, D.
Sobczyk, T. J.
Powiązania:
https://bibliotekanauki.pl/articles/140584.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
harmonic balance method
atrix converter
requency domain
Opis:
The paper presents abilities and advantages following from the use of the harmonicbalance method for analysis of steady state of a multiphase system with switching devices on example of a matrix converter. Switching elements are modelled as resistances with step-wise variable parameters, what allows to describe the converter by a linear infinite set of equations. The analysis in frequency domain is presented on example of the one-periodic control strategy. External systems were also added using the Thevenin method approach. The numerical calculation results of a linear equations set were verified by the variable structure method in a time domain and the numerical convergence was confirmed. Furthermore, the exemplary complex system was analysed using the cascade method and current waveforms were obtained.
Źródło:
Archives of Electrical Engineering; 2013, 62, 3; 387-400
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Simplified analytical method for the robustness assessment of precast reinforced concrete structural systems
Autorzy:
Tur, Viktar
Tur, Andrei
Lizahub, Aliaksandr
Powiązania:
https://bibliotekanauki.pl/articles/1955933.pdf
Data publikacji:
2021
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
robustness
dynamic resistance
ties
energy balance method
membrane effect
Opis:
The article presents the simplified implementation of alternative load path method based on the energy balance approach. This method should be used to check the global resistance of a damaged structural system after the occurrence of an accidental event. Basic assumptions of simplified analytical models for modelling resistance of horizontal ties in a damaged structural system, taking into account the membrane (chain) effects, were presented. An approach to modelling the dynamic resistance of a damaged structural system based on the energy balance method is described. Calculated dependencies for checking the robustness of a prefabricated multi-storey building with hollow-core slabs after the loss of the central column are proposed and considered using an example. On the considered example, a comparison of the required tie sections area with the dynamic resistance designed using the energy balance method (EBM) and according to the current standards, and a statistical assessment of the reliability of the load-bearing capacity models are carried out. In the end, a brief algorithm for the simplified calculation of the dynamic resistance of a damaged structural system is proposed.
Źródło:
Budownictwo i Architektura; 2021, 20, 4; 93-114
1899-0665
Pojawia się w:
Budownictwo i Architektura
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stator current spectrum analysis of a double cage induction motor with rotor asymmetry
Autorzy:
Tulicki, Jarosław
Sobczyk, Tadeusz Jan
Sułowicz, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/24202742.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
cage asymmetry
double cage induction motor
harmonic balance method
steady-state analysis
stator current Fourier spectra
Opis:
This study presents a method to directly calculate the stator current Fourier spectra in double-cage induction motors to diagnose faults in rotor cages. A circuit model is developed for this purpose, allowing the modelling of any asymmetry in the outer and inner rotor cages. The model extends the conventional model of a cage motor by considering the higher space harmonics generated by the stator windings. The asymmetry of the cages is modelled by growing the resistance of any of the rotor bars. This results in various model equations, to be solved by looking for diagnostic signals. Motor current signature analysis is typically used to diagnose cage motors based on the Fourier spectra of the stator currents during steady-state operation. This study determines these spectra for double cage motors using the harmonic balance method, omitting the transient calculations. The calculation results confirmed the sensitivity of the stator current Fourier spectra as a diagnostic signal to distinguish faults in the outer and inner cages.
Źródło:
Archives of Electrical Engineering; 2023, 72, 2; 357--371
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Influence of commutation conditions on steady states in matrix converter
Autorzy:
Borkowski, D.
Sobczyk, T. J.
Powiązania:
https://bibliotekanauki.pl/articles/141341.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
przekształtnik macierzowy
regulacja przepływu mocy
metoda bilansu harmonicznych
matrix converter
power flow control
harmonic balance method
Opis:
The paper investigates a significant influence of transients on steady states in a matrix converter with the one-periodic control strategy. Proposed controller can be used as an interconnection device within a power system for a power flow control. However, the presence of inductances in external systems has the significant influence on steady state of a matrix converter operation. The special current injection method has been developed to ensure a proper operation of a matrix converter. Presented analysis of steady states is carried out in a frequency domain using the harmonic balance method. Obtained numerical results, which are confirmed by a time domain analysis, prove the effectiveness of the proposed method.
Źródło:
Archives of Electrical Engineering; 2011, 60, 1; 77-83
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The thermal state modelling of cylinder liner of marine two-stroke combustion engine
Autorzy:
Kowalski, J.
Tarełko, W.
Powiązania:
https://bibliotekanauki.pl/articles/259669.pdf
Data publikacji:
2006
Wydawca:
Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa
Tematy:
silniki okrętowe
elementanre metody równowagi
stan cieplny
tuleja cylindrowa
ship engine
elementary balance method
thermal state
cylinder liner
Opis:
This paper presents a two-dimensional model of heat flow through structural elements of cylinder of two-stroke cross-head engine of longitudinal scavenging, obtained with the use of the elementary balance method. Special attention was paid to the modelling of temperature distribution within engine cylinder liner of "wet" construction. For modelling the unsteady heat flow multi-dimensional equations with Dirichlet - Fourier boundary conditions, were used. For the Fourier boundary conditions in the engine cylinder space local values of convective and radiant heat-transfer coefficients were applied. For calculations the KM3R method of solving differential equations, based on the elementary balance method, was used. Modelling results have been presented in the form of the temperature field of engine cylinder structural elements in function of the changeable angle of crankshaft position.
Źródło:
Polish Maritime Research; 2006, 2; 15-20
1233-2585
Pojawia się w:
Polish Maritime Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A mixed shooting - harmonic balance method for unilaterally constrained mechanical systems
Mieszana metoda strzałów i równowagi harmonicznych w zastosowaniu do systemów mechanicznych o jednostronnych więzach
Autorzy:
Schreyer, F.
Leine, R. I.
Powiązania:
https://bibliotekanauki.pl/articles/139775.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Shooting method
Harmonic Balance Method
local nonlinearities
periodic solutions
nonsmooth dynamics
metoda strzałów
metoda równowagi harmonicznych
lokalne nieliniowości
rozwiązanie okresowe
niegładka dynamika
Opis:
In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.
W artykule przedstawiono metodę będącą połączeniem metody strzałów i metody równowagi harmonicznych zastosowaną do dużych systemów mechanicznych, w których występują lokalne nieliniowości. Standardowa metoda równowagi harmonicznych (HBM), w której aproksymuje się rozwiązanie okresowe w dziedzinie częstotliwości, jest bardzo popularna, gdyż dobrze nadaje się do dużych systemów o wielu stopniach swobody. Niemniej, jej wadą jest to, że lokalne nieliniowości nie mogą być bezpośrednio ocenione w dziedzinie częstotliwości. W standardowej metodzie HBM wykonuje się odwrotną transformację Fouriera, potem oblicza nieliniową siłę w dziedzinie czasu, a następnie wyznacza współczynniki Fouriera siły nieliniowej. Silne nieliniowości są źle reprezentowane przez obcięty szereg Fouriera, co jest wadą tej metody. W przeciwieństwie do niej, metoda strzałów działa w dziedzinie czasu i opiera się na symulacji numerycznej przebiegów czasowych. Metoda działa skutecznie gdy prawa sił są oparte na wartościach zadanych, tak jak dla tarcia suchego i innych silnie nieliniowych, pod warunkiem, że dysponuje się odpowiednim integratorem numerycznym. Metoda strzałów nie daje się jednak stosować gdy system ma wiele stanów. Proponowana metoda mieszana, strzałów i równowagi harmonicznych, łączy zalety obydwu podejść.
Źródło:
Archive of Mechanical Engineering; 2016, LXIII, 2; 297-314
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modeling damaged precast structural system when its robustness check
Autorzy:
Tur, Viktar
Tur, Andrei
Lizahub, Aliaksandr
Powiązania:
https://bibliotekanauki.pl/articles/1819317.pdf
Data publikacji:
2021
Wydawca:
Centrum Rzeczoznawstwa Budowlanego Sp. z o.o.
Tematy:
robustness
resistance mechanism
progressive collapse
dynamic resistance
energy balance method
EBM
krzepkość
mechanizm oporowy
postępujące zawalenie
opór dynamiczny
metoda bilansu energetycznego
Opis:
Within the framework of traditional approaches to checking for resistance of reinforced concrete buildings and structures to the progressive collapse development, membrane (chain) forces in a damaged structural system are calculated separately, without considering its non-linear bending behavior during the formation of the plastic hinges and without checking the possibility of achieving large deflections. The authors propose an approach to modelling a nonlinear quasi-static reaction of a damaged structural system in an accidental design situation. This approach considers non-linear bending and the resistance of reserved horizontal ties, considering their ultimate ductility. The authors verified the proposed approach based on the results of experimental studies by others researchers. An example of the application of the proposed approach in assessing the robustness of a structural system made of precast concrete with a sudden removal of the central column is considered. In accordance with the provisions of the energy approach, an analysis is made of the contribution of individual resistance mechanisms to the total quasi-static and dynamic resistance of the damaged structural system. We show that the proposed calculation model adequately describes the behavior of a damaged structural system in an accidental design situation, and therefore to carry out parametric studies and check the robustness of building structures.
Źródło:
Inżynieria Bezpieczeństwa Obiektów Antropogenicznych; 2021, 3; 63--81
2450-1859
2450-8721
Pojawia się w:
Inżynieria Bezpieczeństwa Obiektów Antropogenicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical investigation of geometrically nonlinear clamped uniform rods and rods with sections varying exponentially free vibration
Autorzy:
Abdeddine, E.
Majid, A.
Bouzida, N.
Bouzida, Z.
Zarbane, Kh.
Powiązania:
https://bibliotekanauki.pl/articles/2201031.pdf
Data publikacji:
2022
Wydawca:
Stowarzyszenie Komputerowej Nauki o Materiałach i Inżynierii Powierzchni w Gliwicach
Tematy:
non-linear longitudinal vibration
Lagrange equations
harmonic balance method
linearized approach
drgania nieliniowe
drgania podłużne
równania Lagrange'a
metoda bilansu harmonicznych
podejście linearne
Opis:
Purpose: The present paper is intended to investigate the problem of linear and non-linear longitudinal free vibration of uniform rods and rods whose cross-sections vary exponentially at large vibration amplitudes. Design/methodology/approach: The method adopted consists in discretizing the energy term on linear kij and non-linear rigidity tensor bijkl, as well as the mass tensor mij. Therefore, the formulation of this structure is based on Lagrange equations and the harmonic balance method so as to obtain the nonlinear algebraic equations. These latter are solved numerically and analytically through the explicit and linearized method. Findings: The response of Clamped-Clamped uniform and non-uniform rods on our structure are highlighted in the amplitude frequency and associated first three mode shapes. Moreover, this research leads to study the influence of the exponential slope on the maximum displacement, thus emphasizing the non-uniform bars usefulness. The obtained results are then compared with the available literature with a view to validating this theory. Research limitations/implications: As a perspective, the method used in this paper would be pushed to study the FDM material, taking into account other parameters related to additive manufacturing, and later to be validated experimentally. Practical implications: Longitudinal vibrations are important in mechanical structures; therefore, the determination of their dynamic behaviour needs to be understood. In the present study, the effect of the displacement amplitude on the exponential slope of the structure was analysed, which led to the determination of the reduction range of the vibration amplitude under resonance. However, this should be taken into account in the design process. Besides, the usefulness of the non-linearity geometric effects was demonstrated to examine these structures by considering all the parameters involved. Originality/value: A linearized procedure is used to solve a nonlinear algebra equation. The use of this method leads to reduce calculation time contrary to iterative methods.
Źródło:
Journal of Achievements in Materials and Manufacturing Engineering; 2022, 112, 2; 49--63
1734-8412
Pojawia się w:
Journal of Achievements in Materials and Manufacturing Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Experimental and theoretical study of the reinforced concrete flat slabs with the central support loss
Autorzy:
Tur, Viktar
Tur, Andrei
Lizahub, Aliaksandr
Powiązania:
https://bibliotekanauki.pl/articles/2172407.pdf
Data publikacji:
2022
Wydawca:
Centrum Rzeczoznawstwa Budowlanego Sp. z o.o.
Tematy:
flat slab
robustness
resistance mechanism
membrane action
dynamic resistance
energy balance method
płaska płyta
krzepkość
mechanizm oporowy
działanie membranowe
opór dynamiczny
metoda bilansu energetycznego
Opis:
The paper experimentally and theoretically considers the issues of assessing the robustness and resistance to progressive collapse of a flat slab with a sudden removal of the central support. The results of testing two scale models of a fragment of a flat ceiling in the case of removal of the central support under static (specimen FS-1) and dynamic (specimen FS-2) loading are presented and analyzed. A theoretical approach to the quantitative assessment of robustness was tested, which is based on the provisions of the energy balance of a damaged structural system in an accidental design situation.
Źródło:
Inżynieria Bezpieczeństwa Obiektów Antropogenicznych; 2022, 4; 12--41
2450-1859
2450-8721
Pojawia się w:
Inżynieria Bezpieczeństwa Obiektów Antropogenicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Research methods in the study of heat transfer coefficient during flow in minichannels
Autorzy:
Tychanicz-Kwiecień, Maria
Grosicki, Sebastian
Powiązania:
https://bibliotekanauki.pl/articles/1819147.pdf
Data publikacji:
2021
Wydawca:
Politechnika Koszalińska. Wydawnictwo Uczelniane
Tematy:
heat transfer coefficient
minichannels
heat and mass transfer analogy
limiting current technique
thermal balance method
współczynnik przenikania ciepła
minikanały
analogia wymiany ciepła i masy
prąd graniczny
bilans cieplny
Opis:
The paper presents the specification of research methods commonly encountered in the studies of heat transfer processes in minichannels. In particular the following methods have been emphasized: electrochemical limiting current method as well as the thermal balance method. In thermal balance method the mean heat transfer coefficient is determined by the set of experimental thermal measurements of the investigated heat exchanger. In turn, limiting current method is based on heat and mass transfer analogy. The discussed research methods have been implemented on two specially designed and constructed test facilities with compact minichannel heat exchangers, which have been presented and described in details. In order to validate the designed setup, the preliminary experimental measurements of two minichannel heat exchangers with hydraulic diameter of 2 mm and rectangular cross sections during single-phase liquid flows have been carried out. In further perspective it is planned to extend the experimental studies of minichannel heat exchangers and to compare the results obtained by both methods described.
Źródło:
Journal of Mechanical and Energy Engineering; 2021, 5, 1; 59--68
2544-0780
2544-1671
Pojawia się w:
Journal of Mechanical and Energy Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Assessment the Risk of Falls Versus Postural Stability of the Elderly, Using a Stabilographic Platform
Autorzy:
Mańko, Grzegorz
Kocot, Izabela
Pieniążek, Magdalena
Sosulska, Angelika
Piwowar, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/1836622.pdf
Data publikacji:
2016
Wydawca:
Wyższa Szkoła Bezpieczeństwa Publicznego i Indywidualnego Apeiron w Krakowie
Tematy:
falls
balance
stabilographic method
Opis:
Aim: The purpose of this study was to show the characteristics of postural stability in the aging process of elderly people, using the stabilography method and risk assessment of falling occurring in this age group. Materials and methods: The overall study included 36 people engaged in the therapeutic process in Musculoskeletal Rehabilitation Centre in Krzeszowice ORNR. Their average age was 69,42 (± 7,12) years. The test consisted of unconstrained standing on the stabilograph platform for 30 seconds in different experimental conditions: (1) Unconstrained standing with open eyes, (2) Unconstrained standing with closed eyes, (3) Unconstrained standing with open eyes after 6 revolutions on the Barany’s chair. Results: This research showed that the posture of elderly people is characterized by higher values of displacement/COP lean in the sagittal plane rather than frontal plane. Furthermore, it demonstrated that limitations in impulses from sensory inputs (vestibular and visual system) result in an increase of oscillations of the stabilogram graphic curve. However, no strong link between the values of individual measurements (stabilogram) and the occurrence of fall was established. Conclusions: This study showed the usefulness of the stabilography method in describing the stability of the human body. Yet, in order to determine the objectivity of this method, further tests need to be done on larger sample groups and norms regarding people of different ages have to be elaborated. The results obtained in this research might however contribute towards the development of modern accident prevention programs.
Źródło:
Security Dimensions; 2016, 20(20); 111-130
2353-7000
Pojawia się w:
Security Dimensions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The basic closures of fluid mechanics in form characteristic for the Finite Volume Method
Autorzy:
Sobieski, W.
Powiązania:
https://bibliotekanauki.pl/articles/298283.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Warmińsko-Mazurski w Olsztynie
Tematy:
finite volume method
balance equations
closures
Opis:
This short article presents all basic “closures” that are needed to supplementation the general set of balance equations in form characteristic for the Finite Volume Method. In subsequent chapters the equation of state, viscous molecular stress tensor, turbulent stress tensor, molecular heat flux, turbulent heat flux and momentum and energy sources were described. This article is a second part of a cycle dedicated for the mathematical basis of Finite Volume Method. The motivation for writing the article follows from the observation that the Finite Volume Method is usually described in greater detail in monographic books, or very briefly in the basic books dedicated to fluid mechanics. This article is an attempt to center justifications of these approaches, so that in the simplest way show the readers the basic knowledge of the so-called Computational Fluid Mechanics. For this reason this article can be treated as a literature review.
Źródło:
Technical Sciences / University of Warmia and Mazury in Olsztyn; 2013, 16(2); 93-107
1505-4675
2083-4527
Pojawia się w:
Technical Sciences / University of Warmia and Mazury in Olsztyn
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Method For Estimating The Impact Of Migrants Remittances On The Financial And Economic Development Of A Country
Autorzy:
Chernobay, Liana
Malibroda, Sviatoslav
Powiązania:
https://bibliotekanauki.pl/articles/1402404.pdf
Data publikacji:
2020
Wydawca:
Wyższa Szkoła Ekonomiczno-Humanistyczna w Bielsku-Białej
Tematy:
migration
remittances
estimation
method
GDP
balance of payments
Opis:
The study presents a method for estimating the financial and economic impact of personal remittances on economic development migrants’ origin country. The relevance of the study refers to the high dependence of such countries on migrants' remittances. The developed method includes estimating the share of GDP, internal consumption, savings, imports and net cash flow in the balance of payments caused by remittances impact. Obtained estimation provides evidence of significant positive impact of remittances on receiving countries as their GDP, depending on the country, may decrease even for 5% when remittances drop for 10%.
Źródło:
MIND Journal; 2020, 10; 1-21
2451-4454
Pojawia się w:
MIND Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of semi-automated calibration system for pressure balances
Autorzy:
Türk, Ahmet
Hamarat, Abdullah
Durgut, Yasin
Powiązania:
https://bibliotekanauki.pl/articles/2173904.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
semi-automated calibration
pressure balance
digital manometer assisted method
Opis:
In this study, a digital manometer was used as a transfer standard to perform calibration of a pneumatic pressure balance. The same pressure balance was calibrated with the cross-floating method based on falling rate determination (FRD). Average of differences among the effective area results show an agreement of less than 10 ppm between the digital manometer-assisted calibration (DMAC) method and the FRD method. The method in which a digital pressure gauge is used as a transfer standard not only facilitates calibration but also enables the automation of pressure balance calibration. Full automation of pressure balance calibration requires an automatic mass loading system for both the reference instrument and the device under test. Since there is a lot of different kinds of pressure balances, it is nearly impossible for a pressure metrology laboratory to have an automatic mass-handler system for every type of pressure balance. Therefore, a more efficient way in which automated mass-handler systems are not required .., a semi-automatic calibration system, is designed. For that purpose, two different calibration procedures, increasing-decreasing cycles, and pressurize-vent (P-V) procedures are performed and compared. The equivalence of procedure results makes the semi-automated calibration design of pressure balances possible. The most distinguishing advantages of a semi-automated calibration system are the applicability to any type of pressure balance and low cost compared to full automation.
Źródło:
Metrology and Measurement Systems; 2022, 29, 4; 623--638
0860-8229
Pojawia się w:
Metrology and Measurement Systems
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Basic Equations of Fluid Mechanics in form Characteristic of the Finite Volume Method
Podstawowe równania mechaniki płynów w formie charakterystycznej dla metody objętości skończonych
Autorzy:
Sobieski, W.
Powiązania:
https://bibliotekanauki.pl/articles/298275.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Warmińsko-Mazurski w Olsztynie
Tematy:
CFD
metoda objętości skończonych
równania bilansowe
finite volume method
balance equations
Opis:
The article presents the derivation of the basic balance equations in form characteristic of the Finite Volume Method. In the following sections the origin of the balance equation of momentum, mass and energy is presented. Next, the conservation equations in vector form are described. The Finite Volume Method is used in Computational Fluid Mechanics for numerical modeling of fluid flows in wide range. The motivation for writing the article was the difficulty in finding short and concise articles on this subject in the literature. The current article is a first part of a cycle dedicated to the mathematical basis of the Finite Volume Method.
W artykule przedstawiono wyprowadzenie podstawowych równań bilansowych w formie charakterystycznej dla metody objętości skończonych. Przedstawiono pochodzenie równania bilansu pędu, masy i energii, następnie równania zachowania w formie wektorowej. Metoda objętości skończonych jest stosowana w tzw. numerycznej mechanice płynów do numerycznego modelowania przepływów płynów w możliwie szerokim zakresie. Motywacją do napisania artykułu była trudność w znalezieniu podobnego rodzaju krótkich i zwięzłych opracowań na ten temat w literaturze. Artykuł jest pierwszą częścią cyklu poświęconego matematycznym podstawom metody objętości skończonych.
Źródło:
Technical Sciences / University of Warmia and Mazury in Olsztyn; 2011, 14(2); 299-313
1505-4675
2083-4527
Pojawia się w:
Technical Sciences / University of Warmia and Mazury in Olsztyn
Dostawca treści:
Biblioteka Nauki
Artykuł
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