Search results for: discrete radon transform
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The Effect of Laser Re-Solidification on Microstructure and Photo-Electrochemical Properties of Fe-Decorated TiO2 Nanotubes
PublicationFossil fuels became increasingly unpleasant energy source due to their negative impact on the environment; thus, attractiveness of renewable, and especially solar energy, is growing worldwide. Among others, the research is focused on smart combination of simple compounds towards formation of the photoactive materials. Following that, our work concerns the optimized manipulation of laser light coupled with the iron sputtering to...
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ASSESSMENT OF FINANCIAL SECURITY OF AN ENTERPRISE ON THE BASIS OF BEHAVIORAL ECONOMICS
PublicationThe article substantiates that the level of company’s financial security depends not so much on the indicators of its activity, but on its perception of decision-makers and other stakeholders. At the same time, this perception is formed due to the continuous participation of the stakeholder in operations, constant monitoring of financial indicators, the study of current approaches to enterprise management, changes in the environment,...
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FFT analysis of temperature modulated semiconductor gas sensor response for the prediction of ammonia concentration under humidity interference
PublicationThe increasing environmental contamination forces the need to design reliable devices for detecting of the volatile compounds present in the air. For this purpose semiconductor gas sensors, which have been widely used for years, are often utilized. Although they have many advantages such as low price and quite long life time, they still lack of long term stability and selectivity. Namely, environmental conditions have significant...
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Polyurethane/Silane-Functionalized ZrO2 Nanocomposite Powder Coatings: Thermal Degradation Kinetics
PublicationA polyurethane (PU)-based powder coating reinforced with vinyltrimethoxysilane (VTMS)-functionalized ZrO2 nanoparticles (V-ZrO2) for thermal stability was developed. Chemical structure, microstructure and thermal degradation kinetics of the prepared coatings were investigated. The peak of aliphatic C–H vibrating bond in the Fourier transform infrared (FTIR) spectrum of V-ZrO2 was a signature of VTMS attachment. Scanning electron...
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SYNTHESIS AND STRUCTURAL CHARACTERIZATION OF NIOBIUM-DOPED HYDROXYAPATITE CERAMICS
PublicationHydroxyapatite (HAp) ceramic materials are considered as one of the most promising implant materials in bone surgery and in dentistry. They exhibit unique biocompatibility, bioactivity, and osteoconductivity, which are the most desirable biomaterial features. However, HAp itself is brittle, has low strength, high degree of crystallinity and low solubility at physiological pH. Doping synthetic HAp with metal ions plays an important...
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Efficient Method for the Concentration Determination of Fmoc Groups Incorporated in the Core-Shell Materials by Fmoc–Glycine
PublicationIn this paper, we described the synthesis procedure of TiO2@SiO2 core-shell modified with 3-(aminopropyl)trimethoxysilane (APTMS). The chemical attachment of Fmoc–glycine (Fmoc–Gly–OH) at the surface of the core-shell structure was performed to determine the amount of active amino groups on the basis of the amount of Fmoc group calculation. We characterized nanostructures using various methods: transmission electron microscope...
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Experimental and theoretical studies on the Sulfamethazine-Urea and Sulfamethizole-Urea solid-liquid equilibria
PublicationThe miscibility of active pharmaceutical ingredients with excipients is an important aspect in pharmaceutical technology protocols. In this study, the differential scanning calorimetry (DSC) was used for Sulfamethazine-Urea (SI–U) and Sulfamethizole-Urea (SO–U) solid-liquid phase diagrams determination. Both sulfonamides form simple binary eutectics with Urea. The lack of new co-crystal phase formation was confirmed by inspection...
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The influence of different time durations of thermal processing on berries quality
PublicationBioactive compounds (polyphenols, flavonoids, flavanols, tannins, anthocyanins and ascorbic acid) and the level of antioxidant activity by ABTS, DPPH, FRAP and CUPRAC of water, acetone and hexane extracts of Chilean 'Murtilla' (Ugni molinae Turcz) and 'Myrteola' berries (Myrtaceae, Myrteola nummularia (Poiret) Berg.), Chilean and Polish blueberries (Vaccinium corymbosum), Chilean raspberries (Rubus idaeus), and Polish black chokeberry...
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Looking for New Ideas of Public Space – Public Space Projects in Gdansk Reinforced by Art Activities
PublicationRevitalization of public open spaces is a complex enterprise in Poland in terms of the art, cultural andinformation aspects of this process. Simultaneously the public space should play an important role whenbuilding the quality of revitalization programs and the quality of city development. The new art and culturalactivities are the revitalization tools, which are also the good examples of bottom up ideas helping to start aprocess...
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SHAPING PLACES THROUGH ART. THE ROLE OF CREATIVE PLACEMAKING IN PHILADELPHIA
PublicationThe aim of a paper is to examine the role of creative placemaking in shaping urban environment. Art and artists have a long history of contributing and changing cities. Nowadays art and cultural activities become the revitalization tools, helping to start and sustain the process of change in the areas in crisis. The process of creative placemaking brings art to people and people to art, enhancing creativity in lives to transform...
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The Influence of Calcium Glycerophosphate (GPCa) Modifier on Physicochemical, Mechanical, and Biological Performance of Polyurethanes Applicable as Biomaterials for Bone Tissue Scaffolds Fabrication
PublicationIn this paper we describe the synthesis of poly(ester ether urethane)s (PEEURs) by using selected raw materials to reach a biocompatible polyurethane (PU) for biomedical applications. PEEURs were synthesized by using aliphatic 1,6-hexamethylene diisocyanate (HDI), poly(ethylene glycol) (PEG), α,ω-dihydroxy(ethylene-butylene adipate) (Polios), 1,4-butanediol (BDO) as a chain extender and calcium glycerolphosphate salt (GPCa) as...
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Acetate-Induced Disassembly of Spherical Iron Oxide Nanoparticle Clusters into Monodispersed Core−Shell Structures upon Nanoemulsion Fusion
PublicationIt has been long known that the physical encapsulation of oleic acid-capped iron oxide nanoparticles (OA−IONPs) with the etyltrimethylammonium (CTA+) surfactant induces the formation of spherical iron oxide nanoparticle clusters (IONPCs). However, the behavior and functional properties of IONPCs in chemical reactions have been largely neglected and are still not well-understood. Herein, we report an unconventional ligand-exchange...
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On a 3D material modelling of smart nanocomposite structures
PublicationSmart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity...
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Facilitated water transport in composite reduced graphene oxide pervaporation membranes for ethanol upgrading
PublicationHigh purity ethanol is one of the most sought-after renewable energy sources. However, standard production methods yield ethanol of insufficient quality. Membrane processes such as pervaporation are recognized as a viable method for upgrading ethanol. Their performance and selectivity depend solely on membrane employed. Hydrophilic polyvinyl alcohol (PVA) membranes are used industrially for this purpose, but there is a trade-off...
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Enhanced cellulose extraction from agave plant (Agave americana Species) for synthesis of magnetic/cellulose nanocomposite for defluoridation of water
PublicationResearch on fluoride removal from water is currently focusing on the development of innovative materials for defluoridation water. The current study extracted and used enhanced cellulose from Agave americana species to synthesize a magnetic/cellulose nanocomposite for water defluoridation. Strong and light binary acids (H2SO4 and CH3COOH) were utilized to pretreat raw material to enhance cellulose extraction. Central composite...
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ZnO-decorated green-synthesized multi-doped carbon dots from Chlorella pyrenoidosa for sustainable photocatalytic carbamazepine degradation
PublicationThe promising green synthesis of carbon dots (CDs) from microalga Chlorella pyrenoidosa was achieved using simple hydrothermal and microwave-assisted methods. Doping of nanomaterials by nonmetals (N, S, and P) was confirmed by X-ray photoelectron spectroscopy (XPS), while the existence of metals in the CDs was confirmed by inductively coupled plasma optical emission spectroscopy (ICP-OES) and transmission electron microscopy (TEM),...
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Layer-by-layer polymer deposited fabrics with superior flame retardancy and electrical conductivity
PublicationSmart and multifunctional textiles and fabrics are progressively developing, such that multifunctional fabrics are becoming more widespread. We elaborated herein multi-layered flax fabrics with superior flame retardancy and conductivity, which revealed fireproof feature while keeping conductivity during burning. The flax fabric was reinforced by layer-by-layer (LbL) deposition of sodium polyacrylate (SPA), polyethylenimine (PEI),...
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Bio‑derived polyurethanes obtained by non‑isocyanate route using polyol‑based bis(cyclic carbonate)s—studies on thermal decomposition behavior
PublicationNon-isocyanate polyurethanes (NIPUs) constitute one of the most prospective groups of eco-friendly materials based on their phosgene-free synthesis pathway. Moreover, one of the steps of their obtaining includes the use of carbon dioxide (CO 2 ), which allows for the promotion of the development of carbon dioxide capture and storage technologies. In this work, non- isocyanate polyurethanes were obtained via three-step synthesis...
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Superhydrophobic sponges based on green deep eutectic solvents for spill oil removal from water
PublicationThe paper described a new method for crude oil-water separation by means of superhydrophobic melamine sponges impregnated by deep eutectic solvents (MS-DES). Due to the numerous potential of two-component DES formation, simple and quick screening of 156 non-ionic deep eutectic solvents using COSMO-RS (Conductor-like Screening Model for Real Solvents) computational model was used. DES which were characterized by high solubility...
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Conversion of waste biomass into activated carbon and evaluation of environmental consequences using life cycle assessment
PublicationIn this article, activated carbon was produced from Lantana camara and olive trees by H3PO4 chemical activation. The prepared activated carbons were analyzed by characterizations such as scanning electron microscopy, energy-dispersive X-ray spectroscopy, Brunauer–Emmett–Teller, X-ray diffraction, thermogravimetric analysis, and Fourier transform infrared spectroscopy. H3PO4 is used as an activator agent to create an abundant pore...
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Highly antifouling polymer-nanoparticle-nanoparticle/polymer hybrid membranes
PublicationWe introduce highly antifouling Polymer-Nanoparticle-Nanoparticle/Polymer (PNNP) hybrid membranes as multi-functional materials for versatile purification of wastewater. Nitrogen-rich polyethylenimine (PEI)-functionalized halloysite nanotube (HNT-SiO2-PEI) nanoparticles were developed and embedded in polyvinyl chloride (PVC) membranes for protein and dye filtration. Bulk and surface characteristics of the resulting HNT-SiO2-PEI...
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Nutritional and Pharmaceutical Properties of Bioactive Compounds in Organic and Conventional Growing Kiwifruit
PublicationThe bioactivity of two kiwifruit’s cultivars growing under organic and conventional conditions were studied and compared. The bioactive compounds were extracted with water and ethanol using similar conditions which are applied in pharmaceutical applications and for daily fruit consumption such as tea drink. Antioxidant radical scavenging assays [ferric-reducing/antioxidant power (FRAP); cupric reducing antioxidant capacity (CUPRAC);...
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Structure versus hydrolytic and thermal stability of bio-based thermoplastic polyurethane elastomers composed of hard and soft building blocks with high content of green carbon
PublicationNowadays, sustainability plays a key role in the design and synthesis of new materials. One of the methods for the preparation of green materials is incorporation into their structure the monomers with a high content of green carbon. Therefore, the aim of this work was to investigate the influence of the type and molecular mass of two bio-based polyester polyols and bio-glycol on the properties of aliphatic partially bio-based...
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Laser-textured cross-hatched surface topography analysis with evaluation of high-frequency measurement noise
PublicationThe precision of surface roughness determination using ISO 25178 parameters relies on various factors that directly impact the measurement process. In industry applications, the contactless roughness measurement reduces data collection time. However, it introduces several potential errors, including those stemming from the environment. One of the main types of errors encountered during topography analysis is measurement noise,...
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Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis
PublicationIn this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function...
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Polypropylene structure alterations after 5 years of natural degradation in a waste landfill
PublicationUp to 25% of plastic waste in Europe is still disposed of in landfills, despite recycling efforts. The plastic waste in the landfill plot may be exposed both to abiotic and biotic degradation processes, although it is thought that most of the plastic materials tend to be resistant to biodegradation or biodeterioration even after a long time. To verify if polypropylene (PP) can undergo the process of short-term biodegradation and...
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Chromatographic and Spectroscopic Identification and Recognition of Natural Dyes, Uncommon Dyestuff Components, and Mordants: Case Study of a 16th Century Carpet with Chintamani Motifs
PublicationA multi-tool analytical practice was used for the characterisation of a 16th century carpet manufactured in Cairo. A mild extraction method with hydrofluoric acid has been evaluated in order to isolate intact flavonoids and their glycosides, anthraquinones, tannins, and indigoids from fibre samples. High-performance liquid chromatography coupled to spectroscopic and mass spectrometric detectors was used for the identification of...
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Solar light driven degradation of norfloxacin using as-synthesized Bi 3+ and Fe 2+ co-doped ZnO with the addition of HSO 5 – : Toxicities and degradation pathways investigation
PublicationIn this study, solar light responsive Bi3+ and Fe2+ doped ZnO were synthesized and used for photocatalytic degradation of norfloxacin (NOR), an emerging water pollutant. Analysis with Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), selected area electron...
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Effect of bio-based components on the chemical structure, thermal stability and mechanical properties of green thermoplastic polyurethane elastomers
PublicationIt seems to be obvious that conditions changes during polyols synthesis have impact on the polyols properties. Even the chemical formula is the same or similar, physicochemical properties and also molecular weight of polyols might be different and are significant in term of future polyurethanes properties and processing. In this work, fully bio-based poly(propylene succinate)s synthesized at different temperature conditions were...
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From structure to luminescence investigation of oxyfluoride transparent glasses and glass-ceramics doped with Eu3+/Dy3+ ions
PublicationGlasses and glass-ceramics with nominal composition 73 TeO2– 4BaO– 3Bi2O3–18SrF2-2RE2O3 (where RE = Eu, Dy) have been synthesized by conventional melt-quenching technique and subsequent heat treatment at 370 °C for 24 h in air atmosphere. Various Eu3+ to Dy3+ molar ratio have been applied to investigate luminescence properties in both glass and glass-ceramic matrices. Especially, white light emission through simultaneous excitation...
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NUTRITIONAL AND PHARMACEUTICAL APPLICATIONS OF BIOACTIVE COMPOUNDS IN TROPICAL FRUITS
PublicationDuring the past two decades our international scientific group investigated in vitro the physicochemical and nutritional characteristics of some cultivars of durian at various stages of ripening, mangosteen and new cultivars of snake fruit in comparison with widely used avocado, kiwifruit and mango, and in vivo their influence on laboratory animals. The main objective of the present study was to screen and compare the properties...
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Comprehensive evaluation of physical properties and carbon dioxide capacities of new 2-(butylamino)ethanol-based deep eutectic solvents
PublicationThe aim of this research was to assess the impact of the components of alkanolamine deep eutectic solvents (DESs) on the physical properties of those DESs and their carbon dioxide capacity. To achieve this goal, novel deep eutectic solvents were synthesized by using 2-(butylamino)ethanol (BAE) as the hydrogen bond donor (HBD), along with tetrabutylammonium bromide TBAB), tetrabutylammonium chloride (TBAC), or tetraethy- lammonium...
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Bioactivation of Konjac Glucomannan Films by Tannic Acid and Gluconolactone Addition
PublicationWound healing is a dynamic process that requires an optimal extracellular environment, as well as an accurate synchronization between various cell types. Over the past few years, great efforts have been devoted to developing novel approaches for treating and managing burn injuries, sepsis, and chronic or accidental skin injuries. Multifunctional smart-polymer-based dressings represent a promising approach to support natural healing...
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Signature of Oxide-Ion Conduction in Alkaline-Earth-Metal-Doped Y3GaO6
PublicationWe have studied alkaline-earth-metal-doped Y3GaO6 as a new family of oxide-ion conductor. Solid solutions of Y3GaO6 and 2% −Ca2+-, −Sr2+-, and −Ba2+-doped Y3GaO6, i.e., Y(3−0.06)M0.06GaO6−δ (M = Ca2+, Sr2+, and Ba2+), were prepared via a conventional solid-state reaction route. X-ray Rietveld refined diffractograms of all the compositions showed the formation of an orthorhombic structure having the Cmc21 space group. Scanning electron...
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TiO2 /SrTiO3 and SrTiO3 microspheres decorated with Rh, Ru or Pt nanoparticles: Highly UV–vis responsible photoactivity and mechanism
PublicationA series of TiO2/SrTiO3 and SrTiO3 microspheres decorated by Rh, Ru or Pt NPs were prepared by facile hydrothermal method. The as-prepared samples were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM) with energy-dispersive Xray (EDX) spectroscopy, scanning electron microscopy (SEM), photoluminescence spectrometry (PL), Fourier transform infrared (FT-IR) and...
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The preparation and evaluation of core-shell magnetic dummy-template molecularly imprinted polymers for preliminary recognition of the low-mass polybrominated diphenyl ethers from aqueous solutions
PublicationThe design, preparation process, binding abilities, morphological characteristic and prospective field of application of dummy-template magnetic molecularly imprinted polymer (DMMIP) for preliminary recognition of the selected low-mass polybrominated diphenyl ethers (PBDE-47 and PBDE-99) from aquatic environment were investigated. The surface of iron oxide (Fe3O4) nanopowder (50-100 nm particles size) was modified with tetraethoxysilane...
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PREPARATION AND CHARACTERIZATION OF CoFe2O4/TiO2-PANI HYBRID NANOCOMPOSITE WITH MAGNETIC AND PHOYOCATALYTIC ACTIVITY
PublicationHybrid nanocomposites consisting of inorganic component and organic conducting polymer are promising materials, which can be applied in heterogeneous photocatalysis. Titanium(IV) oxide is widely used photocatalysts due to its non-toxicity, low cost and chemical stability. The main disadvantage of TiO2 is low photocatalytic activity under visible light. Conducting polymers, also known as conjugated polymers are polymer materials...
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Kinetics of Cross-Linking Reaction of Epoxy Resin with Hydroxyapatite-Functionalized Layered Double Hydroxides
PublicationThe cure kinetics analysis of thermoset polymer composites gives useful information about their properties. In this work, two types of layered double hydroxide (LDH) consisting of Mg2+ and Zn2+ as divalent metal ions and CO32− as an anion intercalating agent were synthesized and functionalized with hydroxyapatite (HA) to make a potential thermal resistant nanocomposite. The curing potential of the synthesized nanoplatelets in the...
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Synthesis and characterization of cycloaliphatic hydrophilic polyurethanes, modified with l-ascorbic acid, as materials for soft tissue regeneration
PublicationIn this paper we described synthesis and characteristic of obtained hydrophilic polyurethanes (PURs) modified with ascorbic acid (commonly known as vitamin C). Such materials may find an application in the biomedical field, for example in the regenerative medicine of soft tissues, according to ascorbic acid wide influence on tissue regeneration Flora (2009), Szymańska-Pasternak et al. (2011), Taikarimi and Ibrahim (2011), Myrvik...
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Increased inspiratory resistance affects the dynamic relationship between blood pressure changes and subarachnoid space width oscillations
PublicationBackground and objective Respiration is known to affect cerebrospinal fluid (CSF) movement. We hypothesised that increased inspiratory resistance would affect the dynamic relationship between blood pressure (BP) changes and subarachnoid space width (SAS) oscillations. Methods Experiments were performed in a group of 20 healthy volunteers undergoing controlled intermittent Mueller Manoeuvres (the key characteristic of the procedure...
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Great Resignation and Quiet Quitting as Post-pandemic Dangers to Knowledge Management
PublicationPurpose: COVID-19 pandemic aftermaths include the emergence of new tendencies, such as the Quiet Quitting, and continuation of trends such as the Great Resignation, both of which have multiple knowledge-related impacts on individual, organizational and even national level. The aim of this paper is to show the mechanisms behind the Quiet Quitting and the Great Resignation from individual and organizational perspectives. Understanding...
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Effect of temperature and composition on physical properties of deep eutectic solvents based on 2-(methylamino)ethanol – measurement and prediction
PublicationNovel deep eutectic solvents were synthesized using 2-(methylamino)ethanol as hydrogen bond donor with tetrabutylammonium bromide or tetrabutylammonium chloride or tetraethylammonium chloride as hydrogen bond acceptors. Mixtures were prepared at different molar ratios of 1:6, 1:8 and 1:10 salt to alkanolamine and then Fourier Transform Infrared Spectroscopy measurements were performed to confirm hydrogen bonds interactions between...
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High frequency oscillations are associated with cognitive processing in human recognition memory
PublicationHigh frequency oscillations are associated with normal brain function, but also increasingly recognized as potential biomarkers of the epileptogenic brain. Their role in human cognition has been predominantly studied in classical gamma frequencies (30-100 Hz), which reflect neuronal network coordination involved in attention, learning and memory. Invasive brain recordings in animals and humans demonstrate that physiological oscillations...
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Modelling of Asphalt Mixes under Long Time Creep at Low Temperatures
PublicationProper description of asphalt mixtures behavior under long time load is one of the most important factors in analyses of strain and stress relations at low temperatures both from traffic and environmental loads. For example different models of thermal stress accumulation require different approaches of description of asphalt concrete. But in all cases it is required to describe its behavior under long time loading, which in some...
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The health impact of urban parks along waterways
PublicationWell designed parks along waterways could promote health and well-being of local inhabitants. The way the human settlements meet water bodies can influence the habits of local population. How people spend their time have significant impact on their health. For example, a team of Japanese scientists has proven that a well designed walk-able green spaces are crucial for the longevity of elderly citizens (Takano T. et al, 2002). Nature...
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Effect of Maximal Apnoea Easy-Going and Struggle Phases on Subarachnoid Width and Pial Artery Pulsation in Elite Breath-Hold Divers
PublicationPurpose: The aim of the study was to assess changes in subarachnoid space width (sas-TQ), the marker of intracranial pressure (ICP), pial artery pulsation (cc-TQ) and cardiac contribution to blood pressure (BP), cerebral blood flow velocity (CBFV) and cc-TQ oscillations throughout the maximal breath hold in elite apnoea divers. Non-invasive assessment of sas-TQ and cc-TQ became possible due to recently developed method based on...
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Integracja danych przestrzennych z satelitarnych i lotniczych sensorów obrazujących w systemach czasu rzeczywistego
PublicationRozprawa dotyczy multidyscyplinarnego problemu integracji danych przestrzennych z sensorów lotniczych i satelitarnych w nowoczesnych systemach informatycznych zapewniających działanie w czasie niemal rzeczywistym. Zagadnienia poruszone w pracy obejmują m.in. systemy GIS, teledetekcję, fotogrametrię, rozpoznawanie wzorców jak również usługi sieciowe. W rozprawie omówiono oryginalne rozwiązania autora obejmujące opracowanie oraz...
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Study on polymer modified road asphalt mixture
PublicationThe formulation of ternary asphalt-additives blend composed of crumb rubber : low-density polyethylene (CR : LDPE) and crumb rubber : textile fiber (CR : TF) couples, and quaternary asphalt additives-blend composed of (CR : LDPE : TF) triplets on the virgin asphalt to optimize the asphalt basic and rheological properties and to use the extrusion process of two or three additives to obtain composite materials of them, as well as...
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Molecular transformation of dissolved organic matter in manganese ore-mediated constructed wetlands for fresh leachate treatment
PublicationThe organic matter (OM) and nitrogen in Fresh leachate (FL) from waste compression sites pose environmental and health risks. Even though the constructed wetland (CW) can efficiently remove these pollutants, the molecular-level transformations of dissolved OM (DOM) in FL remain uncertain. This study reports the molecular dynamics of DOM and nitrogen removal during FL treatment in CWs. Two lab-scale vertical-flow CW systems were...
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...