Wyniki wyszukiwania - BazTech

1

Statistical multivariate analysis of the dosing process results for predictive production and quality management – a case study from the food industry

Knop Krzysztof

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2023

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z. 176

277--292

EN

Purpose: The aim of this article is to perform a multivariate statistical analysis of package filling process results for predictive production and quality management. The article presents a case study from the food industry that demonstrates the feasibility of using an appropriate set of control charts for ongoing and predictive production and quality management. Design/methodology/approach: The objectives of the article were achieved through the use of Statistical Process Control (SPC) tools, in particular control charts. The control charts used include both traditional numerical chart such as Xbar and S and special charts such as MA, EWMA, CUSUM and GCC. Findings: SPC tools such as control charts have proven to be extremely useful in monitoring the filling process and predicting future performance. By carefully monitoring the process using traditional and special control charts, it is possible to quickly identify small, gradual or sudden changes that may occur in the production process before the process gets out of control. Research limitations/implications: The research will continue by identifying additional factors that affect the quality of the product, particularly as regards precision and accuracy of dosing, and by evaluating the process studied in terms of its ability to meet customer requirements. Other statistical techniques will also be used to identify patterns and relationships between the various parameters of the process under study. This approach will provide more comprehensive information about the quality and ability of the dosing process to meet customer requirements.. Practical implications: By implementing the right SPC toolkit and using dedicated software that significantly speeds up data analysis, companies can effectively control the quality of the production process. By monitoring the behaviour of the process over time and detecting small changes and trends, it is possible to respond to potential problems in advance. Originality/value: This article is intended for production process managers who want to learn how to use the right SPC toolkit to obtain information about the process behaviour and the moments when intervention actions should be taken.

2

Existence, uniqueness and parameter perturbation analysis results of a fractional integro-differential boundary problem

Zhang Nan, Zhang Lingling, Ngungu Mercy, Adeniji Adejimi, Addai Emmanuel

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 4

art. no. e145938

EN

In the formulation, the existence, uniqueness and stability of solutions and parameter perturbation analysis to Riemann-Liouville fractional differential equations with integro-differential boundary conditions are discussed by the properties of Green’s function and cone theory. First, some theorems have been established from standard fixed point theorems in a proper Banach space to guarantee the existence and uniqueness of positive solution. Moreover, we discuss the Hyers-Ulam stability and parameter perturbation analysis, which examines the stability of solutions in the presence of small changes in the equation main parameters, that is, the derivative order η, the integral order β of the boundary condition, the boundary parameter ξ , and the boundary value τ. As an application, we present a concrete example to demonstrate the accuracy and usefulness of the proposed work. By using numerical simulation, we obtain the figure of unique solution and change trend figure of the unique solution with small disturbances to occur in different kinds of parameters.

3

Damage and stability analysis of sandstone-type uranium ore body under physical and chemical action of leaching solution

Liu Yulong, Huang Lei, He Guicheng, Hu Nan, Zhou Shuhui, Yu Qing, Ding Dexin

Archives of Mining Sciences

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2023

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Vol. 68, no. 3

409--423

EN

In this paper, the typical sand-conglomerate uranium ore in north China was taken as the research object. The uniaxial compression and tensile tests of sand-conglomerate specimens under natural status and acidic solution status were used to research the compressive strength, tensile strength, Young’s modulus, cohesion and internal friction angle. Focusing on this type of uranium deposit, during the underground design of the in-situ leaching mining method, the three-dimensional finite element method was used to conduct a numerical simulation of the liquid collecting tunnel with different structural parameters of 10 m×2 m, 3 m×2 m, 2 m×2 m, and comprehensively analyse the vertical displacement, principal stress and plastic deformation zone changes of the tunnelbefore and after leaching. Based on the results, influenced by an acidic aqueous solution, the grain of the conglomerate became soft and secondary pores appeared, resulting in the superimposed effect of physical damage and chemical damage. Macroscopically, an obvious decrease was witnessed in mechanical property. Based on the stability and economy factor of three scenarios before and after leaching, the scenario was recommended as the experimental testing scenario, specifically, two longitudinal collecting tunnel were arranged along the strike of the orebody, with the size of 3 m×2 m and the width of the middle pillar of 4 m. The results of the numerical simulation are significant in guiding the design of underground in-situ leaching technology and determining the structural parameters of the deposit.

4

A study of landslide body control of black bovine cave copper ore mining and beneficiation project

Wu Hanhui

Archives of Civil Engineering

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2023

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Vol. 69, nr 2

291--309

EN

Landslide is a common geological disaster which causes huge losses to people’s properties and national economic development. How to prevent and control landslides has become an important issue. This article introduces the geological and geographical environment of the landslide body, analyzes the basic characteristics of the landslide, calculates the landslide stability based on the ultimate equilibrium theory-based transfer coefficient method, discusses the development trend of the landslide and comes up with corresponding control schemes by taking the landslide body of Black Bovine Cave Copper Ore Mining & Beneficiation Project as example. It is found that the control scheme - “anti-slide pile + retraining wall + baffle + anchor cable” can be used to effectively prevent and control the geological disaster according to calculation. The study results can provide a reference for landslide body control.

5

Stability of stored municipal waste for different sealing systems

Zabielska-Adamska Katarzyna, Markowska Justyna

Architecture Civil Engineering Environment

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2023

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Vol. 16, no. 4

125--133

EN

The paper presents analyses of the municipal waste stability, stored in a landfill with the specific parameters of the waste massif, such as height, width and slope inclination. The massif of waste is lined by a simple drainage/sealing layer, consisting of a sand layer, non-woven geotextile, HDPE double-textured geomembrane and two different sealing mineral layers. The structure stability analysis was performed using a numerical program, relating to the methods: Fellenius/Petterson, Bishop, Spencer, Janbu and Morgenstern-Price. The considerations were carried out according to approach 3 (DA3) for the ultimate limit state GEO of Eurocode 7. The values of the utilization factor and the factor of safety were compared. Municipal waste is generally stable if the slope of the waste is ≤25°. With a slope inclination of 30°, the structures of waste massifs are stable up to a height of 10 m. Using the Fellenius/Petterson method can lead to an underestimation of the factor of safety and an overstatement of the degree of utilization; other methods give comparable results. Changing the material of the mineral sealing layer leads to a change in the course of the circular slip line.

6

Sensitivity and stability analysis for groundwater numerical modeling: a field study of finite element application in the arid region

Jafarzadeh Ahmad, Pourreza-Bilondi Mohsen, Akbarpour Abolfazl, Khashei-Siuki Abbas, Azizi Mohsen

Acta Geophysica

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2023

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Vol. 71, no. 2

1045--1062

EN

This study intends to investigate the impacts of scheme type, time step, and error threshold on the stability of numerical simulation in the groundwater modeling. Hence, a two-dimensional finite element (FE) was implemented to simulate groundwater flow in a synthetic test case and a real-world study (Birjand aquifer). To verify the proposed model in both cases, the obtained results were compared with analytical solutions and observed values. The stability of numerical results was analyzed through different schemes and time-step sizes. Besides, the effect of the error threshold was examined by considering different threshold values. The results confirmed that the FE model has a good capacity to simulate groundwater fluctuations even for the real problem with more complexities. Examination of implicit outputs indicated that groundwater simulations based on this scheme have good accuracy, stability, and proper convergence in all time intervals. However, in the explicit and Crank–Nicolson schemes the time interval should be less than or equal to 0.001 and 0.1 day, respectively. Also, results reveal that for making stability in all schemes the value of the error threshold should not be more than 0.0001 m. Moreover, it derived that the boundary conditions of the aquifer influence the stability of numerical outputs. Finally, it was comprehended that as time interval and error threshold increases, the oscillation rate propagated.

7

Stability of GPS and GLONASS onboard clocks on a monthly basis

Ziętala Michał

Zeszyty Naukowe. Transport / Politechnika Śląska

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2022

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z. 114

193--209

EN

This paper presents the stability of the GPS and GLONASS system clocks’ stability. It describes the construction of these two systems and calculated four different Allan variances (AVAR), based on the MGEX (the Multi-GNSS Experiment) clock products. Four used variances allowed making a better analysis of each GNSS system clock. The results are shown at different averaging times from 5 s as successive multiples to 655,360 s in a monthly period. The stability of GPS and GLONASS clocks is included in the range of 10-12~10-14 s. The results showed that GLONASS clocks are stable (10-12~10-14 s) and are affected with white frequency noise (WFM). The GPS clock stability models have more fluctuations for τ > 40,960 s and the mean stability is concluded between 10-12~10-13 s. Mean frequency accuracy for GPS clocks is related with WFM and Random Walk Frequency (RWF). The differences in clock stability are caused by several factors – block type, type of clock and the time of a satellite in orbit. These factors have an influence on stability results.

8

A robust voltage H∞ controller in dg-connected inverter based on auto-calibration of adjustable fractional weights

Amieur Oualid, Zidani Fatiha

Przegląd Elektrotechniczny

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2022

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R. 98, nr 2

21--27

EN

In this paper a H∞ control technique addresses the voltage regulation in distributed generation (DG) system connected to power converter under harmonic disturbances. The DG control technique combines a discrete sliding mode control (DSMC) in the current control and a Robust Servomechanism Problem (RSP) in the voltage control. Besides, a fractional Order Proportional-Integral-Derivative (FOPID) controller synthesized with an automatic calibration of adjustable fractional weights is formulated in this work. For performance and high robustness requirements, the parameters of FOPID are optimized through solving a multiobjective optimization problematic based on the automatic calibration of the weighted-mixed sensitivity problem. Furthermore, for ensuring an adequate calibration of parameters, the Integral of Time Weighted Absolute Error (ITAE) criterion with Genetic Algorithm (GA) are used to achieve better voltage regulation. The simulation results show that it can achieve trade-off between nominal performance (NP) and robust stability (RS) margins for the constrained uncertain plants in the large range frequencies. Also, the results validate the effectiveness of the proposed control at which both low total harmonic distortion (THD) and low tracking error.

PL

W niniejszym artykule technika sterowania H∞ dotyczy regulacji napięcia w systemie generacji rozproszonej (DG) podłączonym do przekształtnika mocy w warunkach zakłóceń harmonicznych. Technika sterowania łączy dyskretne sterowanie w trybie ślizgowym (DSMC) w sterowaniu prądem i solidny problem z serwomechanizmem (RSP) w sterowaniu napięciem. Poza tym, w niniejszej pracy sformułowano regulator ułamkowo całkująco-różniczkujący (FOPID) zsyntetyzowany z automatyczną kalibracją regulowanych mas ułamkowych. Parametry FOPID są optymalizowane poprzez rozwiązanie problemu optymalizacji wielokryterialnej opartej na autokalibracji problemu wraźliwości mieszanej ważonej dla wymagań dotyczących odporności między nominalną wydajnością (NP), solidną stabilnością (RS) marżami i kompromisem między nimi w dużych zakres częstotliwości. Wyniki symulacji potwierdzają skuteczność proponowanego sterowania, przy którym zarówno wysoka odporność, jak i niskie całkowite zniekształcenia harmoniczne (THD).

9

Mathematical modeling and analysis of mycobacterium tuberculosis transmission in humans with hospitalization and reinfection

Mustapha Umar T., Idris Buhari, Musa Salihu S., Yusuf Abdullahi

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

55--66

EN

Tuberculosis (TB), a serious public health infection that mainly affects the lungs, is caused by bacteria (Mycobacterium tuberculosis, TB). This research is designed and analyzed using a compartmental modelling approach to study the transmission dynamics of TB with different stages of infection. Qualitative analysis of the proposed model reveals that the model exhibits two equilibrium points: the disease-free equilibrium point (DFE) and the endemic equilibrium (EE). The basic reproduction number (R0 ) is determined using the next generation matrix technique, and stability analysis is carried out to show whether the disease can persist or die out in population. Further analysis of the model shows that the EE is globally asymptotically stable (GAS) when R0 > 1. With the aid of the forward sensitivity index method, we determine the most sensitive parameters of the model to control the spread of TB infection effectively. Our analysis shows that treatment (medication) and campaign awareness coupled with other key control measures, could help maintain the spread of MTB infection in human geographical boundaries.

10

Mathematical analysis and numerical simulation of time-fractional host-parasitoid system with Caputo operator

Owolabi Kolade M., Pindza Edson

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

79--90

EN

In this paper, a time-fractional host-parasitoid dynamics which is regarded as a new variant of the novel Nicholson-Bailey model is considered in the sense of the Caputo operator. The model equation is examined for linear stability analysis to guide in ensuring the best choice of parameters when simulating the full dynamical system. Furthermore, this work provides a suitable numerical technique for the approximation of the Caputo fractional derivative with order ρ ∈ (0, 1]. To explore the dynamic richness of the model, numerical results are provided for different values of α.

11

Finite difference method for the fractional order pseudo telegraph integro-differential equation

Modanli Mahmut, Ozbag Fatih, Akgül Ali

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 1

41--54

EN

The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.

12

Dynamic performance and stability analysis of an active inerter-based suspension with time-delayed acceleration feedback control

Wang Yong, Jin Xian-Yu, Zhang Yun-Shun, Ding Hu, Chen Li-Qun

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140687

EN

An active inerter-based suspension with acceleration feedback control is proposed in this paper, the time delay generated in the controllers and actuators is considered, which constitutes the time-delayed active inerter-based (TDA-IB) suspension. The dynamic equation of the TDA-IB suspension is established and is a neutral type of delay differential equation (NDDE) in which the time delay exists in the highestorder derivative. The stability analysis is conducted by calculating the number of unstable characteristic roots based on the definite integral stability method, the stable and unstable regions are determined. The effect of time delay and feedback gain on the dynamic performance of the TDA-IB suspension under harmonic, random, and shock excitations is studied in detail and compared with the parallel-connected inerterbased (PC-IB) and traditional suspensions. The results show that the TDA-IB suspension is asymptotically stable for smaller feedback gain and time delay, through increasing the feedback gain, the stable regions shrink, and a smaller time delay could cause the system to become unstable. Furthermore, the time delay could regulate the resonance peak around the unsprung mass natural frequency and generate multiple high-frequency resonance peaks. If the time delay is chosen appropriately and falls into the stable range, the TDA-IB suspension could improve the dynamic performance for the suspension stroke and dynamic tire load while having a deterioration for the vehicle body acceleration compared with the PC-IB and traditional suspensions.

13

Stability analysis of hybrid Al2O3-TiO2 nano-cutting fluids

Arifuddin A., Redhwan A.A.M., Syafiq A.M., Zainal Ariffin S., Aminullah A.R.M., Azmi W.H.

Archives of Materials Science and Engineering

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2022

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Vol. 117, nr 1

5--12

EN

Purpose: This paper is to study the stability of the current combination of hybrid nano-cutting fluids due to the recent progress in the analysis of nano-cutting fluids, such as the assessment methods for the stability of nano-cutting fluids, have revealed that instability is a common problem associated with nano cutting fluids. Design/methodology/approach: Five samples of 0.001 vol% that are suitable to be tested at UV-Vis machine, Al2O3–TiO2 hybrid nano-cutting fluid was prepared using a one-step process with the help of a magnetic stirrer to stir for 30 minutes with different sonication time to determine the best or optimum sonication time for this hybrid nano-cutting fluid. Stability of nano-cutting fluids was analyses using UV–Vis spectrophotometer (0.001%, 0.0001%, 0.00001%), visual sedimentation (1%, 2%, 3%, 4%), TEM photograph capturing techniques (2%) and zeta potential analysis (0.001%, 0.00001%), that used different volume concentration that is suitable for each type of stability analysis. Findings: The stability analysis reveals that the best sonication time is 90 minutes, and the UV-vis spectrophotometer shows the stability of all samples is above 80% during a month compared to the initial value. Further, visual sedimentation shows good stability with minimum sedimentation and colour separation only. The zeta potential value also shows great stability with a value of 37.6 mV. It is found that the hybrid nano-cutting fluid is stable for more than a month when the nano is suspended in the base fluid of conventional coolant. Research limitations/implications: The result in this paper is based on the experimental study of Al2O3-TiO2/CNC coolant base hybrid nano-cutting fluid for a month. However, to further validate the results presented in this paper, it is recommended to prolong the stability assessment time for six months for longer shelf life. Practical implications: The finding of this experimental study can be useful for high-precision product machining using similar CNC coolants, especially for aircraft and airspace applications for machining parts. Originality/value: No thorough stability assessment using all four types of stability analysis is done on Al2O3-TiO2/CNC Coolant base hybrid nano cutting fluid.

14

Stability and robustness analysis of discrete-time fractional-piecewise-constant-order PID controller

Oziablo Piotr, Mozyrska Dorota, Wyrwas Malgorzata

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 5

art. no. e137937

EN

In the paper we propose a fractional-piecewise-constant-order PID controller and discuss the stability and robustness of a closed loop system. In stability analysis we use the transform method and include the Nyquist-like criteria. Simulations for designed controllers are performed for the second-order plant with a delay.

15

Research on stability and sensitivity of the rotating machines with overhung rotors to lateral vibrations

Szolc Tomasz, Konowrocki Robert

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 6

art. no. e137987

EN

The rotating machines with overhung rotors form a broad class of devices used in many types of industry. For this kind of rotor machine in the paper, there is investigated an inf luence of dynamic and static unbalance of a rotor, parallel and angular misalignments of shafts, and inner anisotropy of rigid couplings on system dynamic responses. The considerations are performed through a hybrid structural model of the machine rotor-shaft system, consisting of continuous beam finite elements and discrete oscillators. Numerical calculations are carried out for parameters characterizing a heavy blower applied in the mining industry. The main goal of the research is to assess the sensitivity of the imperfections mentioned above on excitation severity of rotor-shaft lateral vibrations and motion stability of the machine in question.

16

The stability of poro elastic wave equations in saturated porous media

Xiong Fansheng, Sun Weitao, Liu Jiawei

Acta Geophysica

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2021

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Vol. 69, no. 1

65--75

EN

Poro-elastic wave equations are one of the fundamental problems in seismic wave exploration and applied mathematics. In the past few decades, elastic wave theory and numerical method of porous media have developed rapidly. However, the math ematical stability of such wave equations have not been fully studied, which may lead to numerical divergence in the wave propagation simulation in complex porous media. In this paper, we focus on the stability of the wave equation derived from Tuncay’s model and volume averaging method. By analyzing the stability of the frst-order hyperbolic relaxation system, the mathematical stability of the wave equation is proved for the frst time. Compared with existing poro-elastic wave equations (such as Biot’s theory), the advantage of newly derived equations is that it is not necessary to assume uniform distribution of pores. Such wave equations can spontaneously incorporate complex microscale pore/fracture structures into large-scale media, which is critical for unconventional oil and gas exploration. The process of proof and numerical examples shows that the wave equations are mathematically stable. These results can be applied to numerical simulation of wave feld in reservoirs with pore/fracture networks, which is of great signifcance for unconventional oil and gas exploration.

17

Analiza stabilności lokomotywy EP09 – prędkość krytyczna pojazdu

Bryk Karol, Dudzik Marek, Inglot Jakub, Jakubas Wiesław

TTS Technika Transportu Szynowego

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2020

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R. 27, nr 7-8

67--72

PL

Ideą pracy badawczej była analiza wybranych właściwości mechanicznych lokomotywy EP09. Za główny cel artykułu obrano analizę stabilności lokomotywy EP09, poprzez określenie prędkości krytycznej pojazdu. W tym celu w powyższej publikacji opisano w jaki sposób został zamodelowany układ obliczeniowy, jakie parametry i założenia zostały przyjęte do przeprowadzenia symulacji oraz zaprezentowano końcowe wyniki na podstawie których określono prędkość krytyczną pojazdu. Aby wyniki symulacji były w jak największym stopniu tożsame z wynikami rzeczywistymi, do stworzenia modelów symulacyjnych lokomotywy oraz wózka wykorzystano materiały i wyniki badań uzyskane z Instytutu Pojazdów Szynowych Tabor w Poznaniu. Większość obliczeń została wykonana w programie SIMPAK. W wyniku przeprowadzonej symulacji i analizy uzyskanych wyników określona została prędkość krytyczna lokomotywy EP09, przy której pojazd traci stabilność ruchu.

EN

The idea of the research was analysis selected mechanical preferences of the locomotive EP09. As the main objective of article was chosen analysis of the stability of the locomotive EP09 by define the critical speed of the vehicle. With this and in view in this publication was described how the calculative model was built, what parameters and assumptions were taken to simulate and presented the final results on the basis of which identified the critical speed of the vehicle. In order to simulation results were as much as possible the same as the real results, to create simulation models locomotive and trolley, there have been used information and the research results obtained from the Institute of Rail Vehicles Tabor in Poznan. Most of the calculations has been made in the computer software SIMPLE. As a result of the simulation and analysis of the results was defined the critical speed of locomotive EP09, at which the vehicle loses stability movement.

18

Stability analysis of interconnected discrete-time fractional-order LTI state-space systems

Grzymkowski Łukasz, Trofimowicz Damian, Stefański Tomasz P.

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 4

649--658

EN

In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.

19

The NF-κB network as an example of a regulatory network with a positive and negative feedback loop

Grajek Julia, Bodnar Marek

Mathematica Applicanda

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2019

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Vol. 47, no. 2

165--176

EN

The family of transcription factors NF-κB plays a crucial role in immune response regulation, cell proliferation and cell survival; therefore, deregulated NF-κB activation results in severe health problems. However, its elaborate regulatory network is not yet fully understood. In this paper, we propose and analyze modifications of a mathematical model of the regulatory network that considers the positive feedback between NF-κB and cytokines and the negative feedback between NF-κB and its inhibitors. This mathematical framework captures the transient dynamics of NF-κB while remaining simple enough to obtain a stability condition of the equilibria. We anticipate that a deeper understanding of the NF-κB framework will increase the effectiveness of therapeutic strategies based on NF-κB inhibition. Moreover, the modified model is generic enough to prove useful in modelling different biological processes.

PL

Rodzina czynników transkrypcyjnych NF-κB pełni ważną rolę w regulacji odpowiedzi immunologicznej oraz profliferacji i przeżyciu komórek, w związku z czym niepoprawna aktywacja NF-κB prowadzi do poważnych problemów zdrowotnych. Jednak skomplikowany sposób aktywacji i regulacji NF-κB nie jest jeszcze w pełni zbadany. W tej pracy proponujemy i analizujemy dwie wersje modelu matematycznego uwzględniającego dodatnie sprzężenie zwrotne między NF-κB i cytokinami oraz ujemne sprzężenie zwrotne między NF-κB i jego inhibitorami. Ten model matematyczny obrazuje przejściową aktywację NF-κB, i jest jednocześnie na tyle prosty, aby pozwolić na otrzymanie analitycznych warunków na stabilność stanów stacjonarnych. Oczekujemy, że lepsze zrozumienie systemu regulacji NF-κB zwiększy efektywność terapii opartych na inhibicji tego czynnika transkrypcyjnego. Ponadto, zmodyfikowany model jest na tyle ogólny, że jego analiza może się okazać przydatna w modelowaniu innych procesów biologicznych.

20

Analysis of delay differential equations modelling tumor growth with angiogenesis

Szlenk Maja, Bodnar Marek

Mathematica Applicanda

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2019

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Vol. 47, no. 2

207--217

EN

Angiogenesis is a crucial process for the survival of cancer cells. Due to the rapid growth of the tumor, blood vessels delivering oxygen become insufficient, which leads to hypoxic regions inside the tumor and therefore death of the cells. Cancer cells deal with this problem by stimulating the growth of new vessels, thus providing the necessary amount of oxygen. The understanding of this process allowed to develop antiangiogenic therapy, which attack tumor vasculature instead of the cells themselves. It is believed that an effective treatment combines antiangiogenic factors with radio- and chemotherapy. Our aim is to construct a mathematical model describing this process, which would further allow to select an optimal dosage. In this paper we propose a delay differential model of tumor growth and perform its preliminary analysis. We then introduce a method, which enables further study of this model. The results are illustrated by numerical simulations.

PL

Angiogeneza jest procesem szczególnie istotnym w przypadku komórek nowotworowych. Na skutek gwałtownego wzrostu objętości guza, naczynia krwionośne zaopatrujące nowotwór stają się niewystarczające. Powoduje to tworzenie się niedotlenionych obszarów wewnątrz guza, a w konsekwencji obumarcie komórek. Komórki rakowe przeciwdziałają temu problemowi, stymulując rozrost nowych naczyń krwionośnych i zapewniając tym samym dopływ tlenu. Poznanie tego procesu pozwoliło na opracowanie terapii antyangiogenicznej, atakującej naczynia zaopatrujące nowotwór zamiast samych komórek. W tym artykule proponujemy model różniczkowy z opóźnieniem opisujący wzrost guza, uwzględniający proces angiogenezy. Przeprowadzamy jego wstępną analizę oraz formułujemy kilka wniosków dot. stabilności rozwiązań. Numerycznie symulacje ilustrują uzyskane wyniki.