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Search results for: 3D-SVPWM
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Analysis of the Surface Stereometry of Alloyed Austenitic Steel after Fibre Laser Cutting using Confocal Microscopy
PublicationThe paper extends the concept of cut edge quality and examines the fibre laser cutting process. A Prima Power Platino Fiber Evo device with a reference speed (RS) of 3500 mm/min was used for laser cutting. In order to analyse the influence of the laser cutting speed on the cut edge quality of X5CrNi18-10 stainless steel sheets, macroscopic studies were conducted on a stereoscopic microscope and surface stereometry on a confocal...
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Investigation of the Effect of the Rocket's Suborbital Flight on Biofilm, Enzymes and Biosynthesis on Autonomous, Modular and Scalable Platforms For Conducting Experiments of an Astrobiotechnological Nature
PublicationWith new incentives for human space exploration, biotechnological experiments in orbit became imperative. Answering this need, we build an autonomous, modular, and scalable platform that enables those experiments on rockets. We called it AMBER. The aim of the payload of the R6 suborbital rocket is to perform an experiment to study the influence of rocket flights on biofilm, molecular biology enzymes and biosynthesis using our platform....
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Novel method of estimation of inertial and dissipative parameters of a railway pantograph model
PublicationAn increase in electric railway vehicles service velocity requires that correct interaction between the pantograph and the catenary is ensured. This implies the need for developing mathematical models of pantographs and catenaries and determining their parameters. The article presents a method to determine parameters of mechanical joints of a railway pantograph based on analysis of pantograph subassemblies in swinging motion. The...
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Morphology changes in Fe-Cr porous alloys upon high-temperature oxidation quantified by X-ray tomographic microscopy
PublicationThe effect of high-temperature oxidation at 850 C (10 h, 30 h, 100 h) and 900 C (10 h) on porous (30 % porosity) ferritic stainless steel (Fe22Cr) has been investigated using synchrotron tomographic microscopy, which allowed for visualisation, separation and quantitative analysis of the metallic core, closed pores, open pores and oxide scale phase. The same regions within the samples were investigated before and after oxidation...
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Modelling tunnelling-induced deformation in stiff soils with a hyperelastic–plastic anisotropic model
PublicationIn this paper, the tunnelling-induced deformation in anisotropic stiff soils is analysed using FE modelling. The influence of material description is investigated rather than an advanced simulation of the tunnelling method. A new hyperelastic– plastic model is proposed to describe the anisotropic mechanical behaviour of stiff highly overconsolidated soil. This model can reproduce the superposition of variable stress-induced anisotropy...
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Architektura przyszłości – przekraczanie granic poprzez interfejsy
PublicationArchitektura przyszłości rozpatrywana jest w kontekście rozwoju technologii cyfrowych, które umożliwiają nadawanie obiektom architektonicznym cech interfejsów. Przekraczanie granic dotyczy więc nadawania architekturze nowych funkcji - funkcjonalności zapożyczonych ze świata wirtualnego, emisji informacji oraz interakcji. W tym ujęciu „interfejs architektoniczny” stanowi płaszczyznę komunikacji pomiędzy obiektem architektonicznym...
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Statyka i dynamika powłok wielopłatowych. Nieliniowa teoria i metoda elementów skończonych.
PublicationW części teoretycznej monografii sformułowano ścisłe 2D powierzchniowe zasady dynamiki powłok jako wynik całkowania po grubości odpowiednich 3D zasad dynamiki ośrodka ciągłego. Odpowiadająca im 2D kinematyka powłoki jest konstruowana również ściśle na poziomie dwuwymiarowym. Przybliżenia są wprowadzane jedynie do równań konstytutywnych, które są z definicji zależnościami przybliżonymi, opartymi o badania eksperymentalne. Konsekwencją...
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Persistences: analysis of the image of Gdańsk and its cultural identity through survey processes and digital architectural representation
PublicationThe aim of the research was to analyse the historical legacy/heritage of the city of Gdańsk in order to characterise the narrative tools which can be used to promote the cultural identity of the urban landscape. The main focus was on the city's defence system - a cultural route that is spatially limited to a relatively small area, but temporally spanning almost a millennium. The fortifications demarcate a spatial boundary, limiting...
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Influence of soil anisotropic stiffness on the deformation induced by an open pit excavation.
PublicationIn this paper, the problem of deformation induced by an open pit excavation in anisotropic stiff soils is analysed by FE modelling. The presented research is focused on the influence of material model with anisotropic stiffness on the accuracy of deformation predictions as compared with the field measurements. A new hyperelastic-plastic model is applied to simulate anisotropic mechanical behaviour of stiff soils. It is capable...
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Shape Memory Alloy-Based Fluidically Reconfigurable Metasurfaced Beam Steering Antenna
PublicationA low-cost actuator-based fluidically programmable metasurface (FPMS) antenna is proposed to solve the slow tuning speed problem of the manually fluidic based reconfigurable antennas. The FPMS-based antenna is probe-fed and comprises a 4 × 4 square ring metasurface as a superstrate. Moreover, two shape memory alloy (SMA)-based electrically-controlled actuators are employed in the design for controlling the position of the 3D-printed...
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The shallow sea experiment with usage of linear hydrophone array
PublicationPurpose of this article is to present designed and made linear hydrophone array and the results obtained during in situ trails on Gulf of Gdańsk. The measuring system allowed to localize hydrophones in the selected points and perform measurements in both the horizontal antenna positioning and vertical. Made in this way recordings allow creating accurate 3D imaging of sound intensity/propagation. During research three floating objects...
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Kontrola parametrów obwodu wymuszającego w quasi-statycznych magnetycznych badaniach nieniszczących stali, cz. I: Model analityczny i 2D
PublicationW artykule zaprezentowane zostało dwuwymiarowe modelowanie Metodą Elementów Skończonych (MES) układu do badań nieniszczących (ang. non-destructive testing, w skrócie NDT), składającego się z elektromagnesu jarzmowego i płyty ferromagnetycznej magnesowanej w sposób quasi-statyczny. Wykazane zostały ograniczenia stosowalności opartych na równaniach Maxwella obliczeń analitycznych 1D, które przynoszą zadowalające wyniki jedynie w...
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Wavelet transform-based approach to defect identification in railway carbon contact strips.
PublicationPantographs of electric rail vehicles are fitted with carbon contact strips, which slide along the contact wire of catenary to provide constant electrical contact. Contact strips are exposed to wear and damages. Using damaged contact strips significantly increases the risk of catenary rupture. Therefore, their technical condition has to be inspected frequently. In previous work a 3D laser scanning system was proposed for recording...
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Analiza dokładności formuł do wyznaczania powierzchni ciała człowieka
PublicationPowierzchnia ciała człowieka (body surface area, BSA) jest wskaźnikiem o szerokim spektrum zastosowań w lecznictwie medycznym (m.in. w chemioterapii, transplantologii oraz toksykologii). Każdy z istniejących wzorów do wyznaczania wartości BSA charakteryzuje się pewnym (lepszym bądź gorszym) współczynnikiem zgodności pomiędzy wartością obliczoną, a wartością dokładną – uzyskaną na podstawie pomiaru skanerem 3D. Współczynnik ten...
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Objectivization of Audio-Visual Correlation analysis
PublicationSimultaneous perception of audio and visual stimuli often causes the concealment or misrepresentation of information actually contained in these stimuli. Such effects are called the ''image proximity effect'' or the ''ventriloquism effect'' in literature. Until recently, most research carried out to understand their nature was based on subjective assessments. The Authors of this paper propose a methodology based on both subjective...
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Research of leakage magnetic field in deenergized transformer
PublicationThe article deals with the issue of the numerical analysis of the magnetic field occurring around the transformer after it has been powered down. The main goal of this analysis was to examine if it is possible to identify the residual fluxes in the transformer legs based on this fields’ measurements. It was also intended to determine the type and the location of magnetic sensors. Numerical analysis of the magnetic field was performed....
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Non-Destructive Testing of the Longest Span Soil-Steel Bridge in Europe—Field Measurements and FEM Calculations
PublicationThe article describes interdisciplinary and comprehensive non-destructive diagnostic tests of final bridge inspection and acceptance proposed for a soil-steel bridge made of corrugated sheets, being the European span length record holder (25.74 m). As an effect of an original concept a detailed and precise information about the structure short-term response was collected. Periodic diagnostics of bridge deformations was done one...
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Shallow Water Equations as a Mathematical Model of Whitewater Course Hydrodynamics
PublicationPredicting the positions of local hydraulic phenomena, as well as accurately esti-mating the depth and velocity of the water flow are necessary to correctly config-ure a whitewater canoeing course. Currently, a laboratory and full 3D CFD model-ing are typically used in the design process to meet these needs. The article points to another possibility which can be useful at the preliminary stage of the design. The authors show that...
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Evolution of Ag nanostructures created from thin films: UV–vis absorption and its theoretical predictions
PublicationAg-based plasmonic nanostructures were manufactured by thermal annealing of thin metallic films. Structure and morphology were studied using scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HR-TEM) and X-ray photoelectron spectroscopy (XPS). SEM images show that the formation of nanostructures is influenced by the initial layer thickness as well as the...
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A Critical Reanalysis of Uncontrollable Washboarding Phenomenon in Metal Band Sawing
PublicationThe article analyzes the cutting process of hard bars. Investigations conducted in industrial conditions demonstrated the presence of surface errors in the machined workpieces in the form of washboard patterns. The purpose of this study was to analyze the results of cutting on band sawing machines with different band saw blades. The cutting processes were conducted on three different horizontal band sawing machine types. Analyzed...
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Analysis of the Dynamic Height Distribution at the Estuary of the Odra River Based on Gravimetric Measurements Acquired with the Use of a Light Survey Boat—A Case Study
PublicationLaCoste) for determining the dynamic height along the Odra River, in northwest Poland. The gravity measurement campaign described in this article was conducted on a small, hybrid-powered survey vessel (overall length: 9.5 m). We discuss a method for processing the results of gravimetric measurements performed on a mobile platform affected by strong external disturbances. Because measurement noise in most cases consists of signals...
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Heat exchange enhancement of jet impingement cooling with the novel humped-cone heat sink
PublicationJet impingement cooling technology is applicable to control temperature of devices, where very high heat flux is generated within a small area. This paper is about the improvement of the jet impingement cooling efficiency by the heat sink geometry modification. Two reference cases were sourced from the literature – flat heat sink and modified one with cone in the jet stagnation region. Such a change improves cooling capability...
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Latent fingerprint imaging by spectroscopic optical coherence tomography
PublicationOptical coherence tomography (OCT) is a non-contact and non-invasive optical method for evaluating semitransparent and scattering objects. Its unique features, such as non-destructive 3D measurements of tested objects with a fast scanning rate, make this technique interesting for latent fingerprint reading, which is the subject of this paper. So far, OCT has not found widespread use for reading fingerprints directly from surfaces...
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DETERMINATION OF THE AERODYNAMIC DRAG OF PNEUMATIC LIFE RAFTS AS A FACTOR FOR INCREASING THE RELIABILITY OF RESCUE OPERATIONS
PublicationEnsuring the safety of ship crews at sea is of the utmost importance. Life rafts are one of the basic components of any seagoing vessel and ensuring their stability is an important component of maritime research. This study concerns the determination of the aerodynamic drag coefficients of pneumatic life rafts in a full range of wind speed and directions. The drag coefficients are based on full-scale experimental studies and numerical...
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Teoria systemów i Teoria Organizacji i Zarządzania
e-Learning CoursesZajęcia odbywają się co tydzień w środę w godzinach 13:15-16:00 w MsTeams pod linkiem: https://teams.microsoft.com/dl/launcher/launcher.html?url=%2F_%23%2Fl%2Fmeetup-join%2F19%3Ameeting_NjAxZTY2ZjktODI0MS00YjljLWE3NjgtMWQxMDliODRlMDAz%40thread.v2%2F0%3Fcontext%3D%257b%2522Tid%2522%253a%2522b2b950ec-1ee3-4d9d-ac5e-4dd9db5e0b73%2522%252c%2522Oid%2522%253a%252233f97504-8676-4b87-96ad-a9394d16b3b2%2522%257d%26anon%3Dtrue&type=meetup-join&deeplinkId=2fee9fd8-de07-42a7-b754-8ed19d269a8a&directDl=true&msLaunch=true&enableMobilePage=true&suppressPrompt=true
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Wykorzystanie narzędzi pracy zdalnej w działaniach Koła Naukowego Konstruktorów Pojazdów
PublicationNiniejszy artykuł stanowi opis działalności Koła Naukowego Konstruktorów Pojazdów, w którego działaniach wykorzystywane są nowoczesne narzędzia pracy zdalnej. Dzięki takiemu podejściu, możliwe staje się wyeliminowanie niedogodnień, z którymi borykano się stosując standardowe, starsze podejście do realizacji zadań projektowych w jednostkach badawczo-rozwojowych. Podane przykłady ilustrują, w jaki sposób powszechny obecnie dostęp...
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Grafika inżynierska
e-Learning CoursesKurs łączy w sobie elementy kształcenia tradycyjnego z e-nauczaniem. Przeznaczony jest dla studentów kierunku GOSPODARKA PRZESTRZENNA, semestr 1, studia inżynierskie I stopnia. Celem nauczania jest zdobycie przez studentów wiedzy i umiejętności z zakresu graficznej prezentacji obiektów 3D na płaszczyźnie, ich restytucji na podstawie rzutów (umiejętność sprawnego odczytania rzutów) oraz rozwiązywania prostych problemów przestrzennych. Treść...
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Oprzyrządowanie technologicznych systemów wytwarzania (PG_00050175)
e-Learning CoursesWYKŁAD: Rola oprzyrządowania w systemach wytwarzania części maszyn. Błędy wpływające na dokładność wykonania w uchwytach obróbkowych. Ustalenie przedmiotu w uchwycie. Zamocowanie przedmiotu w uchwycie. Ustalenie i zamocowanie uchwytu na obrabiarce. Uchwyty tokarskie. Uchwyty wiertarskie. Uchwyty frezarskie. Uchwyty modułowe. Uchwyty narzędziowe. Oprzyrządowanie montażowe. Zasady użytkowania uchwytów uniwersalnych. Koszty stosowania...
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Structural analysis and physico-chemical characterization of mononuclear manganese(II) and polynuclear copper(II) complexes with pyridine-based alcohol
PublicationTwo novel manganese(II) and copper(II) complexes, mononuclear [Mn(H2O)2(2-(CH2)2OHpy)2](NO3)2 (1) and polynuclear [Cu(SO4)(2-(CH2)2OHpy)2]n (2), based on 2-(hydroxyethyl)pyridine (2-(CH2)2OHpy) were synthesised and fully characterised using X-ray structure analysis as well as spectroscopic, magnetic and thermal methods. Both central metal ions Mn(1) and Cu(1) are coordinated by two N,O-donor 2-(CH2)2OHpy ligands and possess an...
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Optical profilometer
PublicationThe profilometry plays a huge role in the most fields of science and technology. It allows to measure the profile of the surface with high-resolution. This technique is used in the fields like optic, electronic, medicine, automotive, and much more. The aim of the current work was to design and build optical profilometer based on the interference phenomena. The developed device has been working with He-Ne laser (632.8 nm). The optical...
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Modeling the debonding process of osseointegrated implants due to coupled adhesion and friction
PublicationCementless implants have become widely used for total hip replacement surgery. The long-term stability of these implants is achieved by bone growing around and into the rough surface of the implant, a process called osseointegration. However, debonding of the bone–implant interface can still occur due to aseptic implant loosening and insufficient osseointegration, which may have dramatic consequences. The aim of this work is to...
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Vascular stents - materials and manufacturing technologies
PublicationThe objective of this article is to present materials and technology for the manufacture of vascular stents with appropriate design requirements. The use of the right material is very important in implantology. A biomaterial introduced into the circulatory system must be biocompatible and hemocompatible. At the same time, it should not initiate toxic, mutagenic, or immunological reactions. Currently, 316L stainless steel (316L...
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INVESTIGATION OF THE EFFECT OF THE ROCKET'S SUBORBITAL FLIGHT ON BIOFILM, ENZYMES AND BIOSYNTHESIS ON AUTONOMOUS, MODULAR AND SCALABLE PLATFORM FOR CONDUCTING EXPERIMENTS OF AN ASTROBIOTECHNOLOGICAL NATURE
PublicationWith new incentives for human space exploration, biotechnological experiments in orbit became imperative.Answering this need, we build an autonomous, modular, and scalable platform that enables those experiments onrockets. We called it AMBER. The aim of the payload of the R6 suborbital rocket is to perform an experiment tostudy the influence of rocket flights on biofilm, molecular...
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Synthesis and modification of reduced graphene oxide aerogels for biofuel cell applications
PublicationWe have carried out the preparation of reduced graphene oxide aerogels using eco-friendly method that is based on the Hummers method of graphite oxidation without the use of NaNO3 that produces toxic gases. To obtain a porous 3D structure of reduced graphene oxide, we performed the hydrothermal reduction at elevated temperature. We also prepared the rGO aerogel/CNT composite using multiwalled carbon nanotubes as linkers. The rGO...
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Ionic liquids for nano- and microstructures preparation. Part 1: Properties and multifunctional role
PublicationIonic liquids (ILs) are a broad group of organic salts of varying structure and properties, used in energy conversion and storage, chemical analysis, separation processes, as well as in the preparation of particles in nano- and microscale. In material engineering, ionic liquids are applied to synthesize mainly metal nanoparticles and 3D semiconductor microparticles. They could generally serve as a structuring agent or as a reaction...
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Seafloor Characterisation and Imaging Using Multibeam Sonar Data
PublicationThe approach to seafloor characterisation and imaging is presented. It relies on the combined, concurrent use of several techniques of multibeam sonar data processing. The first one is based on constructing the grey-level sonar images of seabed using the backscattering strength calculated for the echoes received in the consecutive beams. Then, the set of parameters describing the local region of sonar image is calculated. The second...
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Investigation of tracking systems properties in CAVE-type virtual reality systems
PublicationIn recent years, many scientific and industrial centers in the world developed a virtual reality systems or laboratories. One of the most advanced solutions are Immersive 3D Visualization Lab (I3DVL), a CAVE-type (Cave Automatic Virtual Environment) laboratory. It contains two CAVE-type installations: six-screen installation arranged in a form of a cube, and four-screen installation, a simplified version of the previous one. The...
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Cast Iron Staircase in Aleksandrów Kujawski (Poland) - History, Construction, Architectural Form
PublicationThe text presents historic cast iron staircase, which is situated inside the railway station building in Aleksandrów Kujawski. Since the moment of creation in the 19th century for a long time that station, located at the border of Prussia and Kingdom of Poland, was an important transit point. Nowadays it is situated in the central of Poland. The staircase was built in 1870’s as a result of an extension of the railway station building...
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The Effect of Cobalt Incorporation into Nickel–Iron Oxide/(oxy)hydroxide Catalyst on Electrocatalytic Performance Toward Oxygen Evolution Reaction
PublicationThis work presents a study on the influence of the addition of cobalt into state-of-the-art nickel–iron (NiFe) mixed oxides/hydroxides/(oxy)hydroxides on their structural and morphological properties, and oxygen evolution reaction (OER) catalytic activity. A one-step electrodeposition process is performed without any additives to fabricate NiFe and x cobalt-doped nickel/iron (xCoNiFe) layer-double-hydroxide catalysts directly on...
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Bioactivities of Phenolic Compounds from Kiwifruit and Persimmon
PublicationFruit used in the common human diet in general, and kiwifruit and persimmon particularly, displays health properties in the prevention of heart disease. This study describes a combination of bioactivity, multivariate data analyses and fluorescence measurements for the differentiating of kiwifruit and persimmon, their quenching and antioxidant properties. The metabolic differences are shown, as well in the results of bioactivities...
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Acid–Base Equilibrium and Self-Association in Relation to High Antitumor Activity of Selected Unsymmetrical Bisacridines Established by Extensive Chemometric Analysis
PublicationUnsymmetrical bisacridines (UAs) represent a novel class of anticancer agents previously synthesized by our group. Our recent studies have demonstrated their high antitumor potential against multiple cancer cell lines and human tumor xenografts in nude mice. At the cellular level, these compounds affected 3D cancer spheroid growth and their cellular uptake was selectively modulated by quantum dots. UAs were shown to undergo metabolic...
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An unusual four-nuclear Pb(II)-pyrrole-2-carboxylato polymer: The effect of the lone pair and non-covalent interactions on the supramolecular assembly and fluorescence properties
PublicationThe reaction of Pb(NO3)2 with 1H-pyrrole-2-carboxylic acid (2prCOOH) leads to the formation of a new four-nuclear Pb(II) polymer, [Pb4(2prCOO)8(H2O)]n, which has been characterized by CHN, FT-IR, TG, PL and single-crystal X-ray diffraction methods. In view of the primary Pb–O bonds, Pb1 and Pb3 show hemidirected pentagonal pyramidal geometries, while Pb2 and Pb4 display hemidirected octahedral geometries. The topology of the strongest...
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Wpływ namagnesowania obiektu ferromagnetycznego na rozkład pola magnetycznego.
PublicationObiekt ferromagnetyczny znajdujący się w ziemskim polu magnetycznym zaburza w swoim otoczeniu równomierność tego pola. W dalszym ciągu, zaburzenie to nazywane jako "anomalia". Anomalia związana jest z namagnesowaniem stałym i indukowanym obiektu ferromagnetycznego.W pracy przedstawiono wyniki badań symulacyjnych dotyczące anomalii magnetycznej od namagnesowanego obiektu ferromagnetycznego. Namagnesowany obiekt znajduje się w ziemskim...
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A Closed Bipolar Electrochemical Cell for the Interrogation of BDD Single Particles: Electrochemical Advanced Oxidation
PublicationA closed bipolar electrochemical cell containing two conductive boron-doped diamond (BDD) particles of size 250 – 350 m, produced by high-pressure high-temperature (HPHT) synthesis, has been used to demonstrate the applicability of single BDD particles for electrochemical oxidative degradation of the dye, methylene blue (MB). The cell is fabricated using stereolithography 3D printing and the BDD particles are located at either...
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Development of novel optoelectronic sensory structures utilising colour centres in nanodiamonds and their interactions with analytes
PublicationThe goal of this dissertation was to develop and assess surface modifications of fluorescent nanodiamonds (NDs) for optical sensing. Three modification routes were tested, each aimed at a different application. Modification with poly-L-lysine (pLys) was verified for optical sensing of pH via an interrelationship between electrically negative (NV¯) and neutral (NV0) nitrogen-vacancy centres. Immobilisation of Ochratoxin A (OTA),...
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Green engineered biomaterials for bone repair and regeneration: Printing technologies and fracture analysis
PublicationDespite the exceptional self-regeneration properties of bone, severe injuries often require additional surgical intervention such as using artificial bone constructs. These structures need to meet a number of criteria regarding their structure, performance, alongside the rate and the mechanism of erosion and fracture when implanted, for stimulating the regeneration of defected bone and, more critically providing support in the...
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The fracture behaviour of notched PMMA specimens under simple loading conditions – Tension and torsion experimental tests
PublicationThis paper presents the results of experimental testing of flat PMMA specimens during uniaxial loading conditions. Two separate tests were conducted: tensile and torsion. The specimens were weakened with V-type edge notches with different root radii: 0.5; 2 and 10 mm. The specimens were made in two thickness variants: 5 and 15 mm. Monotonic tensile and torsion tests were carried out while keeping the averaged strain rate constant,...
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The In-House Method of Manufacturing a Low-Cost Heat Pipe with Specified Thermophysical Properties and Geometry
PublicationVarious types of heat pipes are available to purchase off the shelf, from various manufacturers, but most of them have strictly defined geometry and technical parameters. However, when there is a need to use a heat pipe (HP) with an unusual size and shape or working conditions other than the standard ones, it becomes very costly to order them from manufacturers, especially in small quantities, and only a few producers are willing...
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Komputerowe modelowanie geometryczne w kształceniu architektonicznym I stopnia
PublicationDynamiczny rozwój technik cyfrowych i wynikające stąd postępujące zmiany w oprogramowaniu powodują wzrost znaczenia znajomości komputerowych metod wspomagania projektowania w warsztacie zawodowym architekta. W trosce o zapewnienie studentom możliwości rozwijania kompetencji w tym zakresie, konieczna jest stała analiza oraz potrzeba rozszerzania i wzbogacania treści programowych w ramach istniejąch programów kształcenia. Tematyka...
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Post processing and selecting data obtain with parametric sub-bottom profiler SES-2000 Standard during sounding the Gulf of Gdansk
PublicationThe main goal of the paper is to describe the results of sounding the Gulf of Gdansk seabed using a parametric sub-bottom profiler SES-2000 Standard. Quality of obtained during trials data depends inter alia on proper location of antenna to reduce influence of pitch, roll, heave and ship noise (bubbles from propeller and a hull flow, vibration from main engine and peripheral devices). Furthermore calibration of complementary units...