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Wyniki wyszukiwania dla: DISSOLVED OXYGEN CONCENTRATION
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The effect of paleo-environment on hydrocarbon generation potential: Example from Vaca Muerta Formation, Neuquén Basin, Argentina
PublikacjaA 137-m continuous core from the Jurassic-Early Cretaceous marine derived oil shale with the maturity Ro about 0.7 %, representing the oil window in the Vaca Muerta Formation, Neuquén Basin, Argentina, was examined using geological, mineralogical, petrographic, and geochemistry techniques. Three distinct intervals were identified within the core: the upper carbonate-rich section with intense bioturbation, indicating dysoxic to...
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Influence of Sb-substitution on ionic transport in lanthanum orthoniobates
PublikacjaThe results of ionic transport measurements for the lanthanum orthoniobate substituted with 10 and 30 mol% of antimony (LaNb0.9Sb0.1O4 and LaNb0.7Sb0.3O4) are presented and discussed. The influence of calcium co-doping on these properties has also been analysed. It has been shown that for the investigated material protonic conductivity predominates at temperatures up to 800 °C in oxidizing atmospheres under wet conditions. The...
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Mechanism-based inactivation of human cytochrome P450 1A2 and 3A4 isoenzymes by antitumor triazoloacridinone C-1305.
Publikacja5-Dimethylaminopropylamino-8-hydroxytriazoloacridinone, C-1305, is a promising antitumor therapeutic agent with high activity against several experimental tumors. It was determined to be a potent and selective inhibitor of liver microsomal and human recombinant cytochrome P450 (CYP) 1A2 and 3A4 isoenzymes. Therefore, C-1305 might modulate the effectiveness of other drugs used in multidrug therapy. The objective of this study was...
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The Influence of the Electrodeposition Parameters on the Properties of Mn-Co-Based Nanofilms as Anode Materials for Alkaline Electrolysers
PublikacjaIn this work, the influence of the synthesis conditions on the structure, morphology, and electrocatalytic performance for the oxygen evolution reaction (OER) of Mn-Co-based films is studied. For this purpose, Mn-Co nanofilm is electrochemically synthesised in a one-step process on nickel foam in the presence of metal nitrates without any additives. The possible mechanism of the synthesis is proposed. The morphology and structure...
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Evaluation of Partial Nitritation/Anammox (PN/A) Process Performance and Microorganisms Community Composition under Different C/N Ratio
PublikacjaA one-stage partial nitritation/anammox (PN/A) process with intermittent aeration is possible under sidestream conditions, but implementation in a mainstream is a challenge due to increased Carbon/Nitrogen (C/N) ratios in domestic wastewater. This study investigated the effect of C/N ratios on process efficiency and the effect of narrowing non-aeration time on process improvement at high chemical oxygen demand (COD) load. An increase...
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Occurrence and Levels of Biogenic Amines in Beers Produced by Different Methods
PublikacjaThe concentration of biogenic amines (BAs) in beer depends, among other factors, on the activity of microorganisms, in particular lactic acid bacteria. In this work an analytical method based on derivatization with tosyl chloride and high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) was used to determine 17 BAs in samples of commercially available beers, and to monitor the changes in concentration of...
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Oxidation kinetics of Zircaloy-4 alloy at 673 K determined by GDOES technique
PublikacjaOxidation of zirconium alloys is a process that takes place during the operation of nuclear reactors and is essential for assessing the durability of fuel claddings. The present study was aimed to determine the oxidation kinetics of the Zircaloy-4 alloy using GDOES (glow discharge optical emission spectroscopy) at temperature 673 K corresponding to the conditions of use of fuel pellets. The tests were performed on non-oxidized...
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Thermally activated natural chalcopyrite for Fenton-like degradation of Rhodamine B: Catalyst characterization, performance evaluation, and catalytic mechanism
PublikacjaIn this work, catalytic activity of natural chalcopyrite (CuFeS2) was improved by thermal activation. The modified chalcopyrite was used as efficient catalyst for degradation of organic dye Rhodamine B (RhB) through advanced oxidation process (AOP). Effects of catalyst dosage, H2O2 concentration, reaction temperature, solution pH, anions, and natural organic matter on the degradation efficiency of RhB were investigated. This study...
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The Unfolded Protein Response: A Double-Edged Sword for Brain Health
PublikacjaEfficient brain function requires as much as 20% of the total oxygen intake to support normal neuronal cell function. This level of oxygen usage, however, leads to the generation of free radicals, and thus can lead to oxidative stress and potentially to age-related cognitive decay and even neurodegenerative diseases. The regulation of this system requires a complex monitoring network to maintain proper oxygen homeostasis. Furthermore,...
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The sensitivity of bacteria to heavy metals in presence of mineral ship motor oil in coastal marine sediments and waters.
PublikacjaThe sensitivity of bacteria, isolated from coastal marine sediments and waters of Sopot beach, Gdańsk Bay (Poland), to heavy metals in the presence of mineral ship motor oil were studied. All isolated heterotrophic bacteria were resistant to the 0.1 mM lead concentration occurring in the environment. Metal resistance of bacteria isolated from coastal water was strongly related to mineral ship motor oil concentration. At 0.1% mineral...
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Preparation and Characterization of Defective TiO2. The Effect of the Reaction Environment on Titanium Vacancies Formation
PublikacjaAmong various methods of improving visible light activity of titanium(IV) oxide, the formation of defects and vacancies (both oxygen and titanium) in the crystal structure of TiO2 is an easy and relatively cheap alternative to improve the photocatalytic activity. In the presented work, visible light active defective TiO2 was obtained by the hydrothermal reaction in the presence of three different oxidizing agents: HIO3, H2O2, and...
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Evaluation of Ambient Air Odour Quality in Vicinity of Municipal Landfill Using Electronic Nose Technique
PublikacjaThe paper presents the results of investigation on ambient air quality evaluation with respect to concentration of odorants in a vicinity of municipal landfill. The investigation was carried out with a prototype of electronic nose and a team of panelists utilizing the Nasal Ranger field olfactometers. The prototype was equipped with a set of six semiconductor sensors by FIGARO Co. and one PID-type sensor. Performed measurements...
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Liniowe i nieliniowe modele wielowymiarowej kalibracji do predykcji stężenia substancji z pomiarów woltamperometrycznych
PublikacjaPomiary woltamperometryczne znajdują zastosowanie w wielu dziedzinach nauki i techniki, np. w przemyśle farmaceutycznym. Dane uzyskane w wyniku takich pomiarów zawierają informację odnośnie rodzaju i stężenia badanej substancji, jednakże są one często kłopotliwe w bezpośredniej interpretacji. Z tego powodu, istnieje konieczność wykorzystania odpowiednich metod matematycznych, które umożliwiają uzyskanie bezpośredniej i precyzyjnej...
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Investigation of RH effect on uncommon limonene ozonolysis products and SOA formation in indoor air with real time measurement techniques
PublikacjaScientific interest in SOA influence on indoor air quality increases since last 20 years. It is well known, that particles of nano-sized diameter pose a threat for human health causing, among others: eye, upper airway irritation, inflammatory response in cells, worsening asthma, hypertension, diabetes, and central nervous dysfunction. Terpenes are reactive VOCs, commonly emitted in indoor air and considered to be SOA precursors...
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Mercury in various components of the environment (Gulf of Gdańsk, southern Baltic Sea)
PublikacjaTotal mercury concentration was determined monthly form January 2012 to May 2013 in the water (microlayer and the surface), plankton, epilithon, epiphyton, benthos and sediment. The study was conducted in the coastal zone of the Gulf of Gdańsk. The abundance and biomass of plankton, benthos; the concentration of suspended particulate matter, particulate organic carbon and nitrogen; δ13C and δ15N in the suspended matter; sediment...
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Applying of Doped Graphene Oxide Coatings for Corrosion Prevention
PublikacjaINTRODUCTION Graphene is a carbonaceous material characterized by extraordinary properties (high electron mobility, high surface area, high mechanical strength of 1100 GPa, very dense network hindering the passage of even the smallest helium atoms) [1]. Therefore, it found many applications, also as an anti-corrosive layer [2]. Electrophoretic Deposition (EPD) is one of the methods to deposit coatings. However, due to slight solubility...
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Determination of isoprostanes in exhaled breath condensate samples by liquid chromatography coupled with tandem mass spectrometry
PublikacjaOxidative stress (OS) is a state of imbalance between continuously generating reactive oxygen species (ROS) during normal cell metabolism and mechanism of detoxifying oxygen radicals through a network of antioxidative enzymes. Isoprostanes are prostaglandin -like substances that are produced in vivo primarily by free radical-induced peroxidation of arachidonic acid. The measurement of isoprostanes in biological fluids and/or tissue...
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Model based evaluation of plant improvement at a large wastewater treatment plant (WWTP)
PublikacjaIn this work, the effect of the improvement carried out at a large-scale wastewater treatment plant (WWTP) was evaluated, by means of modelling works, with the aim to determine the influence of the modernization over the process performance. After modernization, the energy consumption due to the aeration decreased about a 20% maintaining the effluent quality. In order to double-check the good effluent quality, modelling works were...
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High-Temperature Structural and Electrical Properties of BaLnCo2O6 Positrodes
PublikacjaThe application of double perovskite cobaltites BaLnCo2O6−δ (Ln = lanthanide element) in electrochemical devices for energy conversion requires control of their properties at operating conditions. This work presents a study of a series of BaLnCo2O6−δ (Ln = La, Pr, Nd) with a focus on the evolution of structural and electrical properties with temperature. Symmetry, oxygen non-stoichiometry, and cobalt valence state have been examined...
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Monitoring the BTEX Volatiles during 3D Printing with Acrylonitrile Butadiene Styrene (ABS) Using Electronic Nose and Proton Transfer Reaction Mass Spectrometry
PublikacjaWe describe a concept study in which the changes of concentration of benzene, toluene, ethylbenzene, and xylene (BTEX) compounds and styrene within a 3D printer enclosure during printing with different acrylonitrile butadiene styrene (ABS) filaments were monitored in real-time using a proton transfer reaction mass spectrometer and an electronic nose. The quantitative data on the concentration of the BTEX compounds, in particular...
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Usługi ośrodków podregionalnych w Polsce
PublikacjaOśrodki podregionalne definiowane są jako miasta, w których skoncentrowane są takie usługi, które w Polsce mogą być w kilku miastach województwa, ale nie w każdym mieście powiatowym. Usługi zawsze miały tendencję do koncentracji, tworząc ośrodki różnych poziomów w hierarchicznej sieci osadniczej. Celem prezentowanych badań było: (1) określenie usług typowych dla poziomu podregionalnego; (2) rozpoznanie koncentracji tych usług,...
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Activation of N2O and SO2 by the P–B Bond System. Reversible Binding of SO2 by the P–O–B Geminal Frustrated Lewis Pair
PublikacjaHerein, we present the first transformation of borylphosphine into borylphosphinite using nitrous oxide. Borylphosphine reacts with N2O via insertion of a single oxygen atom into the P−B bond and formation of a P−O−B bond system. Borylphosphine and borylphosphinite capture SO2 and activate it in an irreversible and reversible manner, respectively.
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The Use of Artificial Neural Networks and Decision Trees to Predict the Degree of Odor Nuisance of Post-Digestion Sludge in the Sewage Treatment Plant Process
PublikacjaThis paper presents the application of artificial neural networks and decision trees for the prediction of odor properties of post-fermentation sludge from a biological-mechanical wastewater treatment plant. The input parameters were concentrations of popular compounds present in the sludge, such as toluene, p-xylene, and p-cresol, and process parameters including the concentration of volatile fatty acids, pH, and alkalinity in...
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Electroactive polymer/graphene oxide nanostructured composites; evidence for direct chemical interactions between PEDOT and GOx
PublikacjaThis work concerns electrochemical synthesis of nanocomposites consisting of conducting polymer and reduced graphene oxide (rGOx) as electrode materials for supercapacitors. The electrosynthesis was performed in an aqueous solution of the 3,4-ethylenedioxytiophene (EDOT) monomer and graphene oxide (GOx) without supporting electrolyte. The amount of GOx was optimized to obtain the best electrochemical performance of the nanocomposite...
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Characteristics of LaCo 0.4 Ni 0.6-x Cu x O 3-δ ceramics as a cathode material for intermediate-temperature solid oxide fuel cells
PublikacjaIn this study, the effects of Cu-ion substitution on the densification, microstructure, and physical properties of LaCo0.4Ni0.6-xCuxO3-δ ceramics were investigated. The results indicate that doping with Cu ions not only enhances the densification but also promotes the grain growth of LaCo0.4Ni0.6-xCuxO3-δ ceramics. The Cu substitution at x ≤ 0.2 can suppress the formation of La4Ni3O10, while the excess Cu triggers the formation...
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An effective method for studying intermolecular interactions in binary liquids with hydrogen bonds: FTIR spectra and ab initio calculations in the N-methylformamide - methanol system
PublikacjaMolecular complexes in methanol (MeOH)−N-methylformamide (NMF) mixtures were studied based on their FTIR-ATR spectra, to which two methods of analysis were applied: factor analysis and a quantitative version of the difference-spectra method. The mean composition of a complex between NMF and MeOH molecules over the whole range of mixture compositions was determined. Absorbing species differentiated with regard to the interaction...
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Enhanced solar light photocatalytic performance of Fe-ZnO in the presence of H2O2, S2O82−, and HSO5− for degradation of chlorpyrifos from agricultural wastes: Toxicities investigation
PublikacjaThis study reported Fe doped zinc oxide (Fe-ZnO) synthesis to degrade chlorpyrifos (CPY), a highly toxic organophosphate pesticide and important sources of agricultural wastes. Fourier transform infrared, X-ray diffraction, scanning electron microscope, and energy-dispersive X-ray spectroscopic analyses showed successful formation of the Fe-ZnO with highly crystalline and amorphous nature. Water collected from agricultural wastes...
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UV-Vis-Induced Degradation of Phenol over Magnetic Photocatalysts Modified with Pt, Pd, Cu and Au Nanoparticles
PublikacjaThe combination of TiO2 photocatalyst and magnetic oxide nanoparticles enhances the separation and recoverable properties of nanosized TiO2 photocatalyst. Metal-modified (Me = Pd, Au, Pt, Cu) TiO2/SiO2@Fe3O4 nanocomposites were prepared by an ultrasonic-assisted sol-gel method. All prepared samples were characterized by X-ray powder diffraction (XRD) analysis, Brunauer-Emmett-Teller (BET) method, X-ray photoelectron spectroscopy...
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Alternative methods for dark fermentation course analysis
PublikacjaDark fermentation course analysis is crucial, as complexed matrix of gaseous components may be formed and revealed during the process. The paper considers key issues related to the microbiological process in which complex organic substances are transformed into hydrogen. For the purposes of hydrogen generation, the application of wastewater mixed sludge pre-treated according to Faloye method (Faloye et al. in Int J Hydrog Energy...
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Metal ion directed template synthesis using 2-acetyl-1,3-indandione and ethylenediamine: steric and electronic restrictions
PublikacjaA template synthesis using 2-acetyl-1,3-indandione and ethylenediamine results in formation of octahedral Ni complex, whose crystal structure has been resolved using single crystal X-ray diffraction. The structure indicates that only exocyclic enolic oxygen atom of the triketone takes part in the condensation with ethylenediamine.
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Processing of Ce0.8Gd0.2O2-δ barrier layers for solid oxide cells: The effect of preparation method and thickness on the interdiffusion and electrochemical performance
PublikacjaCe0.8Gd0.2O1.9 (CGO) barrier layers are required to mitigate the chemical reactions between Sr-containing oxygen electrode materials and Zr-based oxygen ion conductors in high-temperature solid oxide cells. Barrier layers produced by different methods were studied in this work. As a reference, a cell with no barrier layer was measured. The application of the powder-processed barrier layers, considerably increases the performance....
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Determination Of Gas Mixture Components Using Fluctuation Enhanced Sensing And The LS-SVM Regression Algorithm
PublikacjaThis paper analyses the effectiveness of determining gas concentrations by using a prototype WO3 resistive gas sensor together with fluctuation enhanced sensing. We have earlier demonstrated that this method can determine the composition of a gas mixture by using only a single sensor. In the present study, we apply Least-Squares Support-Vector-Machine-based (LS-SVM-based) nonlinear regression to determine the gas concentration...
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Real-Time Monnitoring of Vegetable Oils' Thermal Degradation Using Proton Transfer Reaction Mass Spectrometry
PublikacjaThe volatile aldehydes, which are generated during frying, can be harmful to human health, therefore the concentration of these compounds in frying fumes should be monitored. In addition, aldehydes are markers of oils’ quality, and so it is possible to determine shelf-life or suitability for frying of these oils. Commonly, in order to determine aldehydes concentration gas chromatography is performed, however it does not allow for...
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Determination of benzo(a)pyrene content in PM10 using regression methods
PublikacjaThe paper presents an attempt of application of multidimensional linear regression to estimation of an empirical model describing the factors influencing on B(a)P content in suspended dust PM10 in Olsztyn and Elbląg city regions between 2010 and 2013. During this period annual average concentration of B(a)P in PM10 exceeded the admissible level 1.5-3 times. Conducted investigations confirm that the reasons of B(a)P concentration...
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Evaluation of the influence of grapevine growing conditions on wine quality
PublikacjaScientists are increasingly interested in the viticulture concept of terroir, which states that unique properties of wine are strictly related to the environmental conditions under which grapes are cultivated. The aim of the research was to compare the parameters characterizing wines produced in Poland, such as pH, conductivity, total organic carbon (TOC), and concentration of anions (F−, Cl−, NO2−, NO3−, PO43−, SO42−). It was...
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Chemically reduced graphene oxide based aerogels - Insight on the surface and textural functionalities dependent on handling the synthesis factors
PublikacjaEfficient adjusting of reduced graphene oxide aerogels properties requires information about experimental factor-aerogel property relationship. In this work, the reduced graphene oxide aerogels surface and textural functionalities in relation to precursor concentration, gelation time and hydrogel freezing temperature were studied in detail, with the use of dynamic adsorption method of gaseous organic probes and experimental design....
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Role of nitrogen in optical and electrical band gaps of hydrogenated/hydrogen free carbon nitride film
PublikacjaWe report the optical and electrical band gap energy of amorphous hydrogenated carbon nitride (a-HCNx) and carbon nitride (a-CNx) as a function of nitrogen concentration (N/C). The optical band gap of a-HCNx and a-CNx films has been determined by means of Ellipsometry and UV-VIS. Both optical and electrical band gaps increase with elevated nitrogen concentration. Experimentally obtained electrical band gap is compared with the...
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Investigation of thin perovskite layers between cathode and doped ceria used as buffer layer in solid oxide fuel cells
PublikacjaIn this paper, thin perovskite layers between cathode material of solid oxide fuel cells and gadolinia-doped ceria buffer layer are investigated. Thin layers made of LaNi0.6Fe0.4O3-δ (LNF), La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF), or SrTi0.65Fe0.35O3-δ (STF) were symmetrically deposited by spin coating method from metallo-organic polymer precursors on a Ce0.8Gd0.2O2-δ (CGO) substrate. Porous and about 40-μm-thick LNF cathodes were deposited...
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Influence of Osmolytes on Protein and Water Structure: A Step To Understanding the Mechanism of Protein Stabilization
PublikacjaResults concerning the thermostability of hen egg white lysozyme in aqueous solutions with stabilizing osmolytes, trimethylamine-N-oxide (TMAO), glycine (Gly), and its N-methyl derivatives, N-methylglycine (NMG), N,N-dimethylglycine (DMG), and N,N,N-trimethylglycine (betaine, TMG), have been presented. The combination of spectroscopic (IR) and calorimetric (DSC) data allowed us to establish a link between osmolytes’ influence on...
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Enhancement of PUR/PIR foam thermal stability after addition of Zostera marina biomass component investigated via thermal analysis and isoconversional kinetics
PublikacjaIn the present work, a thorough thermogravimetric (TG) analysis of bio-based polyurethane–polyisocyanurate (PUR–PIR) foams in both nitrogen and oxygen atmosphere is performed. A sustainable element of the foam is a biopolyol obtained via acid-catalyzed liquefaction of Zostera marina and Enteromorpha Algae biomass. Based on isoconversional analysis and apparent activation energies, several conclusions are obtained. In contradiction...
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Integrated Photocatalytic Advanced Oxidation System (TiO2/UV/O3/H2O2) for Degradation of Volatile Organic Compounds
PublikacjaSeveral advanced oxidation processes (AOPs) including photocatalytic processes were studied for effective treatment of complex model wastewater containing a wide variety of VOCs. The studies revealed synergistic effects of TiO2 based processes for improved degradation of the VOCs. A peroxone combined with TiO2/UV system (TiO2/UV/O3/H2O2) with a ratio between the oxygen source from the oxidant to chemical oxygen demand (COD) of...
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Modelization of Nutrient Removal Processes at a Large WWTP Using a Modified ASM2d Model
PublikacjaThe biodegradation of particulate substrates starts by a hydrolytic stage. Hydrolysis is a slow reaction and usually becomes the rate limiting step of the organic substrates biodegradation. The objective of this work was to evaluate a novel hydrolysis concept based on a modification of the activated sludge model (ASM2d) and to compare it with the original ASM2d model. The hydrolysis concept was developed in order to accurately...
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Electric and magnetic properties of Lanthanum Barium Cobaltite
PublikacjaThe cubic Ba0.5La0.5CoO3‐δ was synthesized using solid state reaction. The structural properties were determined by the simultaneous refinement of Synchrotron Powder X‐ray Diffraction and Neutron Powder Diffraction data. Iodometric titration was used to examine the oxygen stoichiometry and average cobalt oxidation state. Low‐temperature magnetic studies show soft ferromagnetic character of fully oxidized material, with θP = 198(3)...
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Tracking Fluorescent Dye Dispersion from an Unmanned Aerial Vehicle
PublikacjaCommercial unmanned aerial vehicles continue to gain popularity and their use for collecting image data and recording new phenomena is becoming more frequent. This study presents an effective method for measuring the concentration of fluorescent dyes (fluorescein and Rhodamine WT) for the purpose of providing a mathematical dispersion model. Image data obtained using a typical visible-light camera was used to measure the concentration...
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Influence of water salinity on corrosion risk - the case of the southern Baltic Sea coast.
PublikacjaWater corrosivity in Gdansk Bay, Poland, the southern part of the Baltic Sea, was investigated. The analysed region is heavily industrialized, and the coastline is very diverse. Twenty-seven test points along the coastline were selected. Water parameters such as salinity, total dissolved solids content, resistivity, conductivity, oxygenation, pH and corrosion rate were determined. The results of the investigation are presented....
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MOBILITY OF SHALE DRILL CUTTINGS CONSTITUENTS
PublikacjaThis study focuses on the abundance and mobility of metals and trace elements from shale drill cuttings into the water, being the main component of hydraulic fracturing fluid. The relationship between composition of the shale rock and the potential element release during standard water-based leaching tests was characterized by means of X-Ray Fluorescence spectroscopy (XRF). The XRF analysis confirmed the assumption of shales constituents...
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Rational method of grit chamber efficiency determination
PublikacjaAlthough grot chambers are designed with utmost care, they still remain difficuly to control. As concentration of grit is non-uniform, representative measurements of the sand concentration is a very complex issue. In the paper the results of measure,ents performed at WTP in Gdańsk and Gdynia were analyzed. The proposed method to determine grit chambers efficiency is based on comparison of suspension flow in the inlet and flux of...
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Effect of some organic solvent - water mixtures composion on precipitated calcium carbonate in carbonation process
PublikacjaPrecipitated calcium carbonate particles were obtained during carbonation of calcium hydroxide slurry with carbon dioxide. Aqueous solutions of isopropyl alcohol, n-butanol and glycerol were used as solvents. Concentration of organic additives in the reactive mixture was from 0 to 20 % (vol.). Precipitation process were performed in a stirred tank reactor equipped with gas distributor. Multimodal courses of particles size distribution...
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Occurrence of Cyanobacteria in the Gulf of Gdańsk (2008–2009)
PublikacjaBlooms of cyanobacteria develop each summer in the Baltic Sea. Collecting complete data on this phenomenon is helpful in understanding the changes taking place in the Baltic Sea and forecasting the occurrence of these phenomena in the future. This dataset includes unpublished information about the occurrence of cyanobacteria in the Gulf of Gdańsk (Southern Baltic) in 2008 and 2009. The presented data combines basic physic-ochemical...
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Mechanism of Solute and Thermal Characteristics in a Casson Hybrid Nanofluid Based with Ethylene Glycol Influenced by Soret and Dufour Effects
PublikacjaThis article models a system of partial differential equations (PDEs) for the thermal and solute characteristics under gradients (concentration and temperature) in the magnetohydrodynamic flow of Casson liquid in a Darcy porous medium. The modelled problems are highly non-linear with convective boundary conditions. These problems are solved numerically with a finite element approach under a tolerance of 10−8. A numerical algorithm...