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Optimal state feedback controller for balancing cube
- Adam Kowalczyk
- Robert Piotrowski
2022 Pełny tekst Journal of Automation, Mobile Robotics and Intelligent Systems - JAMRIS
In this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive mathematical model. It was based on the Lagrange method. Next, a mathematical model for control purposes was derived. The project of the physical model of the balancing cube was presented. A stabilization system based on a linear quadratic regulator (LQR) was developed. Moreover, a swing-up mechanism was used to bring the cube close to the upper equilibrium point. The algorithm switching condition was important to enable the correct functioning of the system. The developed control system was verified in the Matlab environment. Finally, verifying experiments and comparisons among models (mathematical and physical) were performed.
Optimally regularized local basis function approach to identification of time-varying systems
- Maciej Niedźwiecki
- Artur Gańcza
2022
Accurate identification of stochastic systems with fast-varying parameters is a challenging task which cannot be accomplished using model-free estimation methods, such as weighted least squares, which assume only that system coefficients can be regarded as locally constant. The current state of the art solutions are based on the assumption that system parameters can be locally approximated by a linear combination of appropriately chosen basis functions. The paper shows that when the internal correlation structure of estimated parameters is known, the tracking performance of the local basis function estimation algorithms can be further improved by means of regularization. The optimal form of the regularization matrix is derived analytically and it is shown that the best settings of the regularized algorithm can be determined in the computationally efficient way using cross-validation.
Optimization of biocorrosion resistance and mechanical properties of PM Ti–XAl–2Fe–3Cu alloys by response surface methodology
- Mojtaba Najafizadeh
- Mehran Ghasempour-Mouziraji
- Morteza Hosseinzadeh
- Sahar Yazdi
- Ahmadreza Sarrafan
- Mansoor Bozorg
- Pasquale Cavaliere
- Aleksandra Laska
- Marek Szkodo
2022 Pełny tekst JOURNAL OF MATERIALS SCIENCE
In the current study, the biocorrosion resistance and mechanical properties of the Ti–XAl–2Fe–3Cu (wt%) (X = 6, 4, 2 wt%) alloy produced by powder compact extrusion of blended elemental powders were optimized by using the response surface methodology in order to gain the best combination of processing parameters. To run the optimization process, central composite design with three equal levels of oxygen, hydrogen and aluminum was used and, by employing ANOVA, the analysis of variance was implemented. The results showed that the content of aluminum has a significant effect on the microstructure, mechanical properties, biocorrosion resistance and fracture behavior of the extruded rods. The highest aluminum content corresponds to the highest alloy strength and biocorrosion resistance. This was due to the reduction of the lamella thickness and of the material colonies as the aluminum content increases. Also, by running the experimental and optimization tests, the mechanical properties resulted 1245 MPa in yield strength and 1340 MPa in ultimate tensile strength with 0.1 lAcm-2 in corrosion current.
Optimization-Based High-Frequency Circuit Miniaturization through Implicit and Explicit Constraint Handling: Recent Advances
- Anna Pietrenko-Dąbrowska
- Sławomir Kozieł
- Marzieh Mahrokh
2022 Pełny tekst ENERGIES
Miniaturization trends in high-frequency electronics have led to accommodation challenges in the integration of the corresponding components. Size reduction thereof has become a practical necessity. At the same time, the increasing performance demands imposed on electronic systems remain in conflict with component miniaturization. On the practical side, the challenges related to handling design constraints are aggravated by the high cost of system evaluation, normally requiring full-wave electromagnetic (EM) analysis. Some of these issues can be alleviated by implicit constraint handling using the penalty function approach. Yet, its performance depends on the arrangement of the penalty factors, necessitating a costly trial-and-error procedure to identify their optimum setup. A workaround is offered by the recently proposed algorithms with automatic adaptation of the penalty factors using different adjustment schemes. However, these intricate strategies require a continuous problem-dependent adaptation of the penalty function throughout the entire optimization process. Alternative methodologies have been proposed by taking an explicit approach to handle the inequality constraints, along with correc-tion-based control over equality conditions, combination of which proves to be demonstrably competitive for some miniaturization tasks. Nevertheless, optimization-based miniaturization, whether using implicit or explicit constraint handling, remains a computationally expensive task. A reliable way of reducing the aforementioned costs is the incorporation of mul-ti-resolution EM fidelity models into the miniaturization procedure. Therein, the principal op-eration is based on a simultaneous monitoring of factors such as quality of the constraint satis-faction, as well as algorithm convergence status. This paper provides an overview of the abovementioned size-reduction algorithms, in which theoretical considerations are illustrated using a number of antenna and microwave circuit case studies.
Optimization-Based Robustness Enhancement of Compact Microwave Component Designs with Response Feature Regression Surrogates
- Anna Pietrenko-Dąbrowska
- Julia Kozieł
2022 Pełny tekst KNOWLEDGE-BASED SYSTEMS
The ability to evaluate the effects of fabrication tolerances and other types of uncertainties is a critical part of microwave design process. Improving the immunity of the device to parameter deviations is equally important, especially when the performance specifications are stringent and can barely be met even assuming a perfect manufacturing process. In the case of modern miniaturized microwave components of complex topologies, it is of paramount importance to carry out tolerance-aware design at the highest available accuracy level (i.e., with the use of full-wave electromagnetic (EM) simulations). Although reliable, EM-driven tolerance-aware design is extremely costly if conventional techniques are to be applied (e.g., Monte Carlo simulation). To overcome this setback, this paper proposes a simple and computationally efficient algorithm for robustness enhancement of compact microwave component designs. The objective is to increase the allowed deviations of geometry parameter values (described using the coefficients of an underlying probability distributions, e.g., the variance) so that the prescribed performance specifications are still fulfilled. The presented approach incorporates knowledge-based surrogate models, constructed using the characteristic points (response features) of EM-simulated system outputs, and utilized for low-cost prediction of the fabrication yield. The parameter vector of the microwave circuit of interest is adjusted within the trust-region (TR) framework to identify the maximum levels of deviations still ensuring 100-percent yield. The employment of TR also permits the adaptive control of design relocation and ensures convergence of the optimization process. Numerical verification of the presented methodology is carried out using three miniaturized microstrip circuits, including two equal-split couplers and a wideband filter. The major finding is that incorporating knowledge-based feature surrogates allows for achieving a significant improvement of the acceptable input tolerance levels (nearly two fold on the average) at a remarkably low cost of few dozen EM simulations.
Optimized Stress and Geometry Control of Spherical structures under Lateral Loadings
- Aram Mahmood
- Javad Katebi
- Najmadeen Saeed
- Ahmed Manguri
2022
In this paper, a numerical model of a double-layer spherical structure has been examined under lateral loadings. When the structure has been distorted due to loadings, the dislocated joints have been moved to their original positions utilizing the adjustment techniques based on the force method. Meanwhile, the members’ internal forces were kept in the desired domain. Optimization techniques were also implemented in order to minimalize the amount of actuation and the number of actuators to reduce the cost of the controlling process. The results of the work confirm that the adjustment and optimization techniques can be easily applied to spherical structures to control their shape and stress in members. The optimization and actuation were obtained from MATLAB and the results were verified by SAP2000.
Optymalizacja procesów biologicznych w oczyszczalni ścieków typu SBR
- Robert Piotrowski
2022
Obiektem zainteresowania jest biologiczna, sekwencyjna oczyszczalnia ścieków (Sequ-encing Batch Reactor – SBR). Jest to złożony system sterowania z powodu nieliniowej dyna-miki, niepewności, wielu skal czasu, wielowymiarowości i braku wystarczającej liczby pomia-rów. Warunkiem koniecznym zachodzenia większości procesów biologicznych jest dostar-czenie bakteriom oczyszczającym ścieki, odpowiedniej ilości tlenu, za pomocą instalacji na-powietrzającej. Napowietrzanie spełnia bardzo ważną rolę w oczyszczalni ścieków. Powietrze dostarczane do oczyszczalni ścieków z jednej strony służy jako pokarm dla bakterii oczyszcza-jących ścieki, z drugiej strony pomaga w procesach mieszania ścieków. Koszty napowietrzania są wysokie i stanowią główny składnik kosztów operacyjnych w oczyszczalni ścieków, dlate-go bardzo ważne jest ich zmniejszanie, z jednoczesną poprawą jakości oczyszczania ścieków. W zakresie sterowania, w praktyce eksploatacyjnej oczyszczalni ścieków w dalszym cią-gu stosuje się proste algorytmy sterowania stężeniem tlenu oparte na regułach i regulatorach typu PI ze stałymi wartościami nastaw. Ze względu na złożoność problemu sterowania i różne punkty pracy są one niewystarczające. Wynika to z faktu, iż zapotrzebowanie na tlen, a tym samym na ilość powietrza dostarczanego przez instalację napowietrzającą, jest zmienne w cza-sie. W monografii zaprojektowano dwa nowoczesne, zaawansowanwane algorytmy stero-wania stężeniem tlenu: adaptacyjnego z nadrzędnym regulatorem regułowym i adaptacyjnego z nadrzędnym regulatorem heurystycznym. Układy regulacji oparto o pomiary stężenia tlenu, azotu amonowego i azotanów. Następnie zaproponowano i rozwiązano trzy zadania optymali-zacji procesów biologicznych. Przeprowadzono analizę symulacyjną efektywności zapropo-nowanych struktur i algorytmów optymalizacji dla różnych warunków obciążeń oczyszczalni ścieków w Swarzewie. Zaproponowane rozwiązania przyniosły znaczącą poprawę efektywno-ści oczyszczania ścieków, z równoczesną redukcją kosztów operacyjnych pracy tego złożone-go systemu przemysłowego.
Optymalizacja procesów prefabrykacyjnych przyszłością branży budowlanej
- Rafał Ziółkowski
- Marzena Kurpińska
2022 Pełny tekst Materiały Budowlane
Intensywny rozwój technologiczny w zakładach prefabrykacji będzie miał wpływ na: krótszy czas wznoszenia obiektów; lepszą jakość końcową obiektów uzyskiwaną dzięki wprowadzeniu automatyzacji linii produkcyjnych w zakładach prefabrykacji; ochronę środowiska przez lepsze zarządzanie surowcami; wprowadzanie nowych rozwiązań technologicznych pozwalających na produkcję m.in. smuklejszych elementów, przez co możliwe będzie uzyskanie większej powierzchni użytkowej obiektów budowlanych; zmniejszenie liczby wypadków na budowach; możliwość zmniejszenia liczby pracowników na placu budowy przez przeniesienie części pracochłonnych i czasochłonnych procesów do zakładów prefabrykacji; zmniejszenie wpływu warunków atmosferycznych na prowadzone prace na budowie. Rozwój zakładów prefabrykacji oznacza przyjęcie nowych strategii zarządzania zarówno w samych zakładach, jak i na budowach. Pozwoli to na zaspokojenie potrzeb inicjatyw co do ochrony, utrzymywania i podnoszenia wartości ludzkich oraz zasobów naturalnych, które będą potrzebne w przyszłości – zarównoważenia interesów ekonomicznych, społecznych i ekologicznych.
Organic solvents aggregating and shaping structural folding of protein, a case study of the protease enzyme
- Monikaben Padariya
- Maciej Bagiński
- Minofar Babak
- Umesh Kalathiya
2022 Pełny tekst BIOPHYSICAL CHEMISTRY
Low solubility of reactants or products in aqueous solutions can result in the enzymatic catalytic reactions that can occur in non-aqueous solutions. In current study we investigated aqueous solutions containing different organic solvents / deep eutectic solvents (DESs) that can influence the protease enzyme's activity, structural, and thermal stabilities. Retroviral aspartic protease enzyme is responsible for the cleavage of the polypeptide pre- cursors into mature viral components, a very crucial step for virus life cycle. In molecular dynamic simulations (MDS), the complex of the protease enzyme with Darunavirwas found highly stable in urea aqueous solution compared to when with the ethylene glycol (EG) or glycerol solvents. Particularly, in different organic solvents the presence of Darunavir induced protein-protein interactions within the protease homodimer. For the systems with EG or glycerol solvents, the flap domains of the enzyme formed an “open” conformation which lead to a weak binding affinity with the drug. Conserved D25 and G27 residues among this family of the aspartic protease enzymes made a stable binding with Darunavir in the urea systems. Unfolding of the protease dimer was initiated due to self-aggregation for the EG or glycerol organic solvents, which formed an “open” conformation for the flap domains. On the contrary lack of such clustering in urea solvent, the protease showed conventional structural folding in the presence or absence of the drug molecule. These novel findings may help to better understand the protease enzymes, which could be controlled by deep eutectic solvents.
Organic Vapor Sensing Mechanisms by Large-Area Graphene Back-Gated Field-Effect Transistors under UV Irradiation
- Katarzyna Drozdowska
- Adil Rehman
- Pavlo Sai
- Bartłomiej Stonio
- Aleksandra Krajewska
- Maksym Dub
- Jacek Kacperski
- Grzegorz Cywiński
- Maciej Haras
- Sergey Rumyantsev
- Lars Österlund
- Janusz Smulko
- Andrzej Kwiatkowski
2022 Pełny tekst ACS Sensors
The gas sensing properties of graphene back-gated field-effect transistor (GFET) sensors toward acetonitrile, tetrahydrofuran, and chloroform vapors were investigated with the focus on unfolding possible gas detection mechanisms. The FET configuration of the sensor device enabled gate voltage tuning for enhanced measurements of changes in DC electrical characteristics. Electrical measurements were combined with a fluctuation-enhanced sensing methodology and intermittent UV irradiation. Distinctly different features in 1/f noise spectra for the organic gases measured under UV irradiation and in the dark were observed. The most intense response observed for tetrahydrofuran prompted the decomposition of the DC characteristic, revealing the photoconductive and photogating effect occurring in the graphene channel with the dominance of the latter. Our observations shed light on understanding surface processes at the interface between graphene and volatile organic compounds for graphene-based sensors in ambient conditions that yield enhanced sensitivity and selectivity.
Osiedle Naturia/Toruń
- Agnieszka Błażko
2022 Pełny tekst Architektura-Murator
Osiedle Jar, zlokalizowane na leśnych terenach powojskowych, to niezwykle atrakcyjny i dynamicznie rozwijający się obszar budownictwa mieszkaniowego w Toruniu. W jego północnej części, w miejscu ograniczonym ulicami Strobanda, Grasera i Watzenrodego powstaje zanurzony w zieleni zespół wielorodzinnych budynków mieszkalnych autorstwa KURYŁOWICZ & ASSOCIATES - egzemplifikacja modernistycznego modelu zespołu mieszkalnego złożonego z otoczonych zielenią wolnostojących domów, z odpowiednio nasłonecznionymi i przewietrzanymi mieszkaniami różnych typów. Główną ideą projektu odwołującą się chociażby do tonącego w zieleni Hansaviertel w Berlin Mitte było takie wpisanie budynków mieszkalnych w piękne leśne otoczenie aby możliwe było zachowanie i wyeksponowanie jak największej liczby drzew i naturalnego, urozmaiconego ukształtowania terenu.
OVERALL SET OF BANDSAW TEETH VERSUS METHODS OF MEASUREMENTS
- Dawid Stenka
- Kazimierz Orłowski
- Daniel Chuchała
2022 Pełny tekst Trieskove a Beztrieskove Obrabanie Dreva
This article deals with the impact of the manual methods of measurement on the overall set measurement results. It describes the results of the measurement of bandsaw teeth kerf with the use of a micrometer and a digital calliper. It is commonly known that the cutting process causes the wear of cutting tools. The wear of the cutting edge depends on the cutting conditions as well as on the mechanical properties of the processed material. One of the methods used to estimate the state of saw teeth uses kerf measurements. The overall set of teeth of the bandsaw Prime ST 0.8/1.2 by Wintersteiger, which was used in the oak wood re-saving process, was measured using a micrometer and a digital calliper. The results of different measurements were compared to estimate the accuracy and precision of those methods. It was shown that micrometer measurements were much more precise than calliper measurements. It was also noted that the kerf varied between two tooth ranges
Overcoming carboxylic acid inhibition by granular consortia in high-load liquefied food waste fermentation for efficient lactate accumulation
- Xianbao Xu
- Xia Gu
- Tingting Ye
- Yanbiao Liu
- Yanan Liu
- Gang Xue
- Xiang Li
- Jacek Mąkinia
2022 JOURNAL OF CLEANER PRODUCTION
Granular sludge, a self-aggregating spherical biofilm, possesses better stability compared to flocculent sludge under extreme conditions. This study compared the ability of anaerobic granular sludge (AnGS) and flocculent waste activated sludge (WAS) to convert food waste (FW) into highly-valuable optically active lactic acid (LA), a central and versatile intermediate platform molecule. Different loadings (30–60 g volatile suspended solids (VSS)/L) were applied and LA was accumulated to 52.7 g chemical oxygen demand (COD)/L on day 7 with optical activity (OA) of 77% using granular consortia under the highest FW loading, exhibiting a 48% increase in the yield over flocculent WAS on day 6. An initially delayed utilization of carbohydrates and subsequently enhanced glycolysis occurred with AnGS, which was in line with its high accumulation of LA. Furthermore, the AnGS consortia were dominated by LA bacteria (81%), including Bacillus, Lactobacillus, and Bifidobacterium, much higher than the WAS consortia (48%). The AnGS was more tolerant to LA inhibition, preventing cytoplasmic pH decrease (intracellular H+ in AnGS was 42% lower than in WAS) from the dissociation of carboxylic acid inside the cells. This might be due to its particular multi-layered aggregate extracellular polymeric substance structure and the enhancement of H+-transporting ATPase (increased by 120% in AnGS). This study provides a practical way to overcome carboxylic acid inhibition and increase the recovery of value-added platform molecules from organic wastes.
Overcoming gender bias in the digital economy. Empirical evidence for European countries
- Ewa Lechman
- Magdalena Popowska
2022 Gender, Technology and Development
This study aims to contribute to understanding the gender biases that emerge in the digital technology-related field. More specifically we concentrate on examining whether gender gaps are diminishing or are persistent in terms of women’s enrollment in technology-related programs at the tertiary level of education and for female STEM graduates. Next, this evidence is confronted with gender biases in the labor market regarding changing female and male employment in high-tech sectors; we detect whether gender gaps grow or diminish in this respect. Our data cover 29 European countries in the period 2011–2020 and are extracted from World Economic Forum reports, Eurostat, and UNESCO databases. Our methodological framework combines time trends analysis, cross-country inequalities, distributional changes, and non-parametric approximations examining relationships between variables. Our major conclusions support the view of negligibly diminishing gender inequalities in technology-related education and demonstrate increasing gender gaps regarding high-tech employment.
Overview of Approaches for Compensating Inherent Metamaterials Losses
- Bashar Esmail
- Sławomir Kozieł
- Stanisław Szczepański
- Huda Majid
2022 Pełny tekst IEEE Access
Metamaterials are synthetic composite structures with extraordinary electromagnetic properties not readily accessible in ordinary materials. These media attracted massive attention due to their exotic characteristics. However, several issues have been encountered, such as the narrow bandwidth and inherent losses that restrict the spectrum and the variety of their applications. The losses have become the principal limiting factor when employing metamaterials in real-world applications. Consequently, overcoming them is crucially important and of practical necessity. This paper discusses the practical applications of metamaterials in constructing functional devices and the effects of the losses on such devices. In more depth, it reviews the available approaches for reducing the metamaterial losses developed over the last two decades in the light of available literature. These approaches include the utilization of the principles of electromagnetically induced transparency (EIT), geometric tailoring of the metamaterial structures, and embedding gain materials. Further, computational optimization techniques, such as particle swarm optimization (PSO) and genetic algorithm (GA), are also discussed to design low-loss metamaterials. The EIT-like metamaterial and the including of gain materials are systematic and universal approaches exhibiting low loss approaching zero. In contrast, the other two are not systematic and universal approaches.
Overview of Knowledge Management in Occupational Safety, Health, and Ergonomics
- Syed Imran
- Edward Szczerbicki
- Cesar Sanin
2022
Occupational safety, health, and ergonomics (OSHE) are strategic pillars of contemporary organizations. In order to provide safer workplace, it is vital to manage the organizational knowledge, so that effective decision making along with absolute compliance to standards can be executed. The critical challenge for OSHE in modern industry is management of existing individual knowledge (experience), structure knowledge, and organizational knowledge in the vast domains of practical applications. This paper firstly investigates the requirements for effective knowledge management (KM) in OSHE, secondly it reviews the present knowledge models and finally proposes a new knowledge model in OSHE. The proposed model is based on a technique called set of experience knowledge structure (SOEKS); it is not only capable of knowledge creation, distribution, elaboration, and consolidation but also possesses features to review and reflect decisions taken in past.
Overview of Metamaterials-Integrated Antennas for Beam Manipulation Applications: The Two Decades of Progress
- Bashar Esmail
- Sławomir Kozieł
- Łukasz Gołuński
- Huda Majid
- Rusan Kumar Barik
2022 Pełny tekst IEEE Access
Metamaterials (MMs) are synthetic composite structures with superior properties not found in naturally occurring materials. MMs have gained massive attention over the last two decades because of their extraordinary properties, such as negative permittivity and permeability. These materials enable many applications in communication subsystems, especially in the field of antenna design, to enhance gain, bandwidth, and efficiency, reduce the size, and deflect the radiation pattern. The demand for beam-deflection antennas is significant in modern wireless communication research studies due to their importance in enhancing service quality, system security, avoiding interference, and economizing power. The MM structures are usually included in the vicinity of the radiating element or incorporated in the antenna substrate for controlling the radiation pattern. This review study provides an introduction to MMs, focusing on their electromagnetic properties, classification, and design approaches. Furthermore, a detailed study of using the MMs to manipulate the radiation is carried out, where different properties such as the positive/negative refractive index, epsilon-near-zero (ENZ), and mu near-zero (MNZ) are employed to achieve a beam-deflection antenna. Reconfigurable MMs are also loaded to the antenna to achieve multi-directional beam deflection with negligible effect on the antenna's physical size. Moreover, the gradient-index (GRIN) based on MMs is used to obtain high deflection angles with minor effects on other antenna properties.
Overview of planar antenna loading metamaterials for gain performance enhancement: the two decades of progress
- Bashar Esmail
- Sławomir Kozieł
- Stanisław Szczepański
2022 Pełny tekst IEEE Access
Metamaterials (MTMs) are artificially engineered materials with unique electromagnetic properties not occurring in natural materials. MTMs have gained considerable attention owing to their exotic electromagnetic characteristics such as negative permittivity and permeability, thereby a negative refraction index. These extraordinary properties enable many practical applications such as super-lenses, and cloaking technology, and are used to design different electromagnetic devices like filters, polarization converters, sensors, and absorbers. Advances in MTMs have made new application fields to emerge in communication subsystems, especially in the field of antennas. MTMs are usually arranged in front or above the radiating element, or incorporated in the same substrate to improve the performance of planar antennas, in terms of improving directivity, gain, bandwidth, and efficiency, reducing the size and mutual coupling, and deflecting the radiation characteristics. High gain antennas are demanded in modern wireless communication systems. Their importance is in improving the signal strength by reducing the interference and alleviating the free space path loss. This review paper provides a brief introduction to MTMs, with the focus on their operating principles. Furthermore, a detailed study of antenna gain enhancement based on the various properties of MTMs is carried out. MTMs with low values of constitutive parameters; zero-index material (ZIM), low-index material (LIM), epsilon-near-zero (ENZ), and mu-near-zero (MNZ) are discussed in detail in the context of their capability to enhance the gain of a broad class of planar antennas. The low impedance property and lensing property, which is achieved by three different characteristics: high refractive index (HRI), gradient refractive index (GRIN), and negative refractive index (NRI) materials, are loaded to planar antennas for gain enhancement. The scope of this review has been limited to antennas that were experimentally validated in the respective source papers.
Oznakowanie robót drogowych – studium przypadków
- Natalia Konkel
- Joanna Wachnicka
2022 Drogownictwo
W artykule przedstawiono zagadnienia związane ze sposobami oznaczania stref robót drogowych oraz stanem technicznym zastosowanych znaków pionowych i urządzeń bezpieczeństwa ruchu drogowego. Wpływ na bezpieczeństwo, oprócz nieodpowiedniego umiejscowienia oznakowania, ma również jego odblaskowość oraz czytelność. Omawiane niespełnienie wymagań przedmiotowych cech wynika z nienależytego dbania o zapewnienie właściwych parametrów i stanu technicznego używanych znaków pionowych i urządzeń bezpieczeństwa ruchu drogowego do oznakowania tymczasowych organizacji ruchu oraz w całym okresie ich stosowania. W głównej części artykułu opisano inwentaryzację istniejącego oznakowania na drogach w czasie prowadzenia prac budowlanych oraz przeprowadzono analizę zastosowanej organizacji ruchu, stanu technicznego znaków drogowych i wpływu tych elementów na bezpieczeństwo użytkowników ruchu drogowego.
Paired domination versus domination and packing number in graphs
- Magda Dettlaff
- Didem Gözüpek
- Joanna Raczek
2022 Pełny tekst JOURNAL OF COMBINATORIAL OPTIMIZATION
Given a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and is denoted by ρk (G). It is well known that γpr(G) ≤ 2γ (G). In this paper, we prove that it is NP-hard to determine whether γpr(G) = 2γ (G) even for bipartite graphs. We provide a simple characterization of trees with γpr(G) = 2γ (G), implying a polynomial-time recognition algorithm. We also prove that even for a bipartite graph, it is NP-hard to determine whether γpr(G) = γt(G). We finally prove that it is both NP-hard to determine whether γpr(G) = 2ρ4(G) and whether γpr(G) = 2ρ3(G).