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Search results for: N-ACETYL-L-CYSTEINE
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Efficient synthesis of N-benzyloxycarbonyl- and N-tert-butoxycarbonyl-(S)-isoserine and their derivatives
PublicationOpisano wydajną metodę syntezy N-benzyloksykarbonylo- i N-tert-butoksykarbo-nylo-(S)-izoseryny i jej pochodnych z kwasu L-jabłkowego poprzez odpowiednie oksazolidinony i hydrolizę tych połączeń za pomocą wodorotlenku benzylowo-trimetyloamoniowego.
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ADAPTATION OF THE ACTIVATED SLUDGE TO THE DIGESTATE LIQUORS DURING THE NITRIFICATION AND DENITRIFICATION PROCESSES
PublicationThe activated sludge process of the digestate liquors after chemical separation was conducted using a 10 L lab-scale sequencing batch reactor (SBR) and a 0.50 m3 pilotscale SBR independently (with pH control). Due to the relatively high concentration of free ammonia (FA), clear inhibitory effects of the digestate liquors on the nitrifying bacteria were observed. The adaptation of the activated sludge to the toxicity was evaluated...
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Desensitization of glucosamine-6-phosphate synthase to inhibition by UDP-GlcNAc
PublicationGlucosamine-6-phosphate (GlcN-6-P) synthase, known also as L-Glutamine: D-fructose-6-phosphate amidotransferase, catalyzes the first committed step in the pathway leading to the ultimate formation of UDP-GlcNAc. The final product of this pathway is an activated precursor of numerous macromolecules containing amino sugars, including chitin and mannproteins in fungi, peptidoglycan and lipopolysaccharides in bacteria, and glycoproteins...
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BASECOL2023 scientific content
PublicationContext. The global context of making numerous data produced by researchers available requires collecting and organising the data, assigning meaningful metadata, and presenting the data in a meaningful and homogeneous way. The BASECOL database, which collects inelastic rate coefficients for application to the interstellar medium and to circumstellar and cometary atmospheres, meets those requirements. Aims. We aim to present the...
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An upper bound on the 2-outer-independent domination number of a tree
PublicationA 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
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Experimental guinea pig model of dermatophytosis: a simple and useful tool for the evaluation of new diagnostics and antifungals
PublicationCelem badań było opracowanie prostego modelu zwierzęcego (świnki morskie) odpowiedniego do sprawdzania systemów diagnostycznych oraz terapii infekcji dermatofitów. Następujące zmienne były analizowane: przygotowanie skóry przez golenie versus użycie taśmy, testowy szczep Microsporum canis czy Trichophyton mentagrophytes jako czynnik etiologiczny, sposób inokulacji. Przebieg infekcji był oceniany poprzez ocenę zaczerwienienia i...
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Hydration of Simple Model Peptides in Aqueous Osmolyte Solutions
PublicationThe biology and chemistry of proteins and peptides are inextricably linked with water as the solvent. The reason for the high stability of some proteins or uncontrolled aggregation of others may be hidden in the properties of their hydration water. In this study, we investigated the effect of stabilizing osmolyte–TMAO (trimethylamine N-oxide) and destabilizing osmolyte–urea on hydration shells of two short peptides, NAGMA (N-acetyl-glycine-methylamide)...
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Synthesis, Antimicrobial and Mutagenic Activity of a New Class of d-Xylopyranosides
PublicationEight N-[2-(2′,3′,4′-tri-O-acetyl-α/β-d-xylopyranosyloxy)ethyl]ammonium bromides, a new class of d-xylopyranosides containing a quaternary ammonium aglycone, were obtained. Their complete structure was confirmed using NMR spectroscopy (1H, 13C, COSY and HSQC) and high-resolution mass spectrometry (HRMS). An antimicrobial activity against fungi (Candida albicans, Candida glabrata) and bacteria (Staphylococcus aureus, Escherichia...
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(R,R)-1-Acetyl-1'-(2,4,6-trinitrophenyl)-2,2'-bipyrrolidine
Publication(R,R)-1-Acetyl-1'-(2,4,6-trinitrophenyl)-2,2'-bipyrrolidine has been synthesized and its rentgenostructure has been determined. The structure of the title molecule, C16H19N5O7, is mainly determined by the steric effect of a bulky 2,4,6-trinitrophenyl group attached to the N atom of a pyrrolidine ring. Both pyrrolidine rings adopt an envelope conformation, with one of the methylene C atoms as the flap in each case, and the N-C-C-N...
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Comparison of the Efficiency of Deammonification under Different DO Concentrations in a Laboratory-Scale Sequencing Batch Reactor
PublicationThe efficiency of deammonification depends on the cooperation of ammonium oxidizing bacteria and archaea (AOB/AOA), anaerobic ammonium oxidizing bacteria (AnAOB) and the effective suppression of nitrite oxidizing bacteria (NOB) that compete with AnAOB for nitrite (NO2 -N). One of the effective NOB suppression strategies is intermittent aeration. However, it is important to have a good understanding of the optimum dissolved oxygen...
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Modelling the impact of the agricultural holdings and land-use structure on the quality of inland and coastal waters with an innovative and interdisciplinary toolkit
PublicationThe changes taking place in the marine coastal zones are extremely important, as about 40% of the human population currently lives in the coastal areas (within 100 kilometres of the coastline) increasing anthropogenic pressure on the marine ecosystems. Agriculture is a significant source of nutrients to the marine environment that increase hypoxia, eutrophication and may pose a threat to the services provided by ecosystems. In...
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Almost homoclinics for nonautonomous second order Hamiltonian systems by a variational approach
PublicationW artykule badamy problem istnienia rozwiązań prawie homoklinicznych dla nieautonomicznych układów Hamiltona w R^n z potencjałem V(t,x) postaci -1/2(L(t)x,x)+W(t,x) oraz zaburzeniem f(t) (ang. forcing term) z L^2. Zakładamy, że L jest funkcją ciągłą z prostej w zbiór macierzy kwadratowych nxn taką, że macierze L(t) są symetryczne i dodatnio określone jednostajnie względem zmiennej t. Potencjał W(t,x) jest klasy C^1 i nadkwadratowy...
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Immediate and late benefits of treating very elderly people with hypertension: results from active treatment extension to Hypertension in the Very Elderly randomised controlled trial
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1,3,4-Thiadiazole-based diamides: Synthesis and complexation properties
PublicationAromatic diamides, derivative of 2,6-pyridinedicarboxylic acid and isophthalic acid, bearing 1,3,4-thiadiazole residue were prepared with satisfactory yields in conventional procedures and microwave stimulated reactions. X-ray structure of N,N-bis (1,3,4-thiadiazol-2-yl)-2,6-pyridinedicarboxamide (2) DMSO solvate (2DMSO) was described. Selective zinc(II), lanthanum(III), terbium(III) and L-tyrosine recognition was found for N,N-bis(1,3,4-thiadiazol-2-yl)-2,6-pyridinedicarboxamide...
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Ammonia amendment promotes high rate lactate production and recovery from semi-continuous food waste fermentation
PublicationIn this study, a reliable approach using ammonia nitrogen was proposed to increase lactate production during semi-continuous food waste (FW) fermentation under mesophilic conditions. Both free ammonia nitrogen (FAN) and ammonium ion (NH4+-N) were present in mesophilic reactors, with a wide FAN/NH4+-N ratio variation due to the intermittent pH control. The investigation of responsible mechanisms revealed that the increased production...
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Systemic modulation of stress and immune parameters in patients treated for prostate adenocarcinoma by intensity-modulated radiation therapy or stereotactic ablative body radiotherapy
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Enhancing chain-elongating microbiomes: Sequential fungi-bacteria cooperation for efficient food waste upgrading using endogenous electron donors
PublicationThe upgrading of organic waste such as food waste (FW) into medium-chain carboxylates (MCC) is within a bio-based circular economy concept. An efficient chain elongation (CE) microbiome is difficult to obtain, which normally requires long-term acclimatization and an exogenous supplement of electron donor (ED, especially ethanol). In this study, the CE microbiome was rapidly shaped within 18 days and an efficient endogenous ethanol-based...
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Anticancer Study on IrIII and RhIII Half-Sandwich Complexes with the Bipyridylsulfonamide Ligand
PublicationTwo non-platinum compounds, organometallic half-sandwich complexes [(η 5 -Cp)IrCl(L)]PF 6 (1) and [(η 5 -Cp)RhCl(L)]PF 6 (2) were prepared by treating pentamethylcyclopentadienyl chloride dimers of iridium(III) or rhodium(III) with the obtained 4-amino-N-(2,2'-bipyridin-5- yl)benzenesulfonamide ligand (L) and ammonium hexafluorophosphate. The crystal structures of ligand (L) and complexes 1 and 2 were obtained and then analyzed. Coordination...
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Fecal indicators resistance to antimicrobial agents present in municipal wastewater
PublicationIn this study removal rate of six antimicrobial compounds (belonging to folate pathway inhibitors and macrolides class) was analyzed in processes of local wastewater treatment plant (WWTP) together with susceptibility patterns of erythromycin (E) resistant Enterococcus spp. and trimethoprim/sulfamethoxazole (SXT) resistant Escherichia coli. According to the obtained data, six of tested antimicrobial agents, namely erythromycin,...
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Własności kwantowe przemian energetycznych zachodzących w silnikach o zapłonie samoczynnym = Quantum properties of energy transformation in diesel engines
PublicationW pracy uzasadniono, że w badaniach własności energetycznych silników spalinowych o zapłonie samoczynnym należy uwzględnić istniejącą w ich eksploatacji przypadkowość i nieprzewidywalność zdarzeń. Nawiązano do osiągnięć mechaniki kwantowej wskazując na wynikający z nich postulat, że wielkości nazywane komplementarnymi, mają istotną własność, która polega na tym, że niemożliwy jest jednoczesny i zarazem dokładny pomiar ich wartości....
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Concentrations of alfa- and gamma- tocopherols in human breast milk during the first months of lactation and in infant formulas
PublicationThe aim of this study was to determine the concentrations of alpha- and gamma-tocopherols in human breast milk samples from different periods of lactation and to compare them with tocopherol content in commercially available formulas for infants at corresponding ages. The study included 93 breast milk samples obtained on the 2nd (colostrum, n=17), 14th (n=30), 30th (n=27) and 90th day of lactation (n=19), along with 90 samples...
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The effect of an active force while slide diamond burnishing of wooden shafts upon process quality
PublicationThe quality of the surface of wooden elements that have been turned and burnished has got a crucial meaning in the whole production process flow, since the obtained effects affect the quality of the wooden surface after finishing (coating, painting). In the paper, selected results of the investigation of the effect of the burnishing process on the surface quality of the elements after turning are presented. Research experiments...
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Elucidation of chemical compounds in different extracts of two Lavandula taxa and their biological potentials: Walking with versatile agents on the road from nature to functional applications
PublicationDue to their health-promoting and nutraceutical properties, lavenders are frequently employed in the food and pharmaceutical industries. Here, we focused on investigate the chemical profile of hexane, MeOH, and water extracts of leaf, flower, and root of L. pedunculata and L. stoechas and to assess their antioxidant, enzyme inhibitory, and antibacterial properties. The highest total polyphenolic and flavonoids contents were recorded...
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Glucosamine-6-phosphate synthase with an oligoHis insert
PublicationGlucosamine-6-phosphate (GlcN-6-P) synthase known also as L-Glutamine: D-fructose-6-phosphate aminotransferase (EC 2.6.1.16), catalyzes the first committed step in the amino sugar biosynthetic pathway in prokaryotic and eukaryotic organisms. The final product of this pathway is an activated precursor of numerous macromolecules containing amino sugars, including chitin and mannproteins in fungi, peptydoglican and lipopolysaccharides...
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Sources and composition of chemical pollution in Maritime Antarctica (King George Island), part 2: Organic and inorganic chemicals in snow cover at the Warszawa Icefield
PublicationThe study area is located on King George Island, where 90% of the area is permanently glaciated. This study provides a comprehensive analysis of the inorganic and organic chemistry of snow cover in the icefield and a comparison against previous results obtained in fresh water. Snow samples were collected in the summer of 2017 in the Warszawa Icefield area. Sampling points are located along two transects: between the Arctowski Polish...
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An upper bound on the total outer-independent domination number of a tree
PublicationA total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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The effects of different aeration modes on ammonia removal from sludge digester liquors in the nitritation–anammox proces
PublicationThe aim of this study was to determine the impact of continuous and intermittent aeration on the rate of ammonia removal in the combined nitritation–anammox process. This process was run in two parallel sequencing batch reactors (SBRs), with a working volume V = 10 L, treating sludge digester liquors from the Gdansk (Poland) wastewater treatment plant (WWTP). The ammonia oxidizing bacteria were cultivated from activated sludge...
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An upper bound for the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove...
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Recovery of Anammox Biomass at Short Hydraulic Retention Time in a MBR Reactor
PublicationThe anammox system has been consider as an economical option for treating high concentration of nitrogen and poor in biodegradable orgaednic carbon wastewaters. This process is attractive option compared with conventional nitrogen removal because it provides a significant saving in aeration and organic addition for denitrification. The anammox technology has been applied mostly for concentrated nitrogenous wastewater containing...
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Integration of the sulfate reduction and anammox processes for enhancing sustainable nitrogen removal in granular sludge reactors
PublicationThe Anammox and Sulfate Reduction Ammonium Oxidation processes were compared in two granular sequencing batch reactors operated for 160 days under anammox conditions. It was hypothesized that increasing the concentration of SO42− may positively influence the rate of N removal under anaerobic conditions and it was tested whether SO42− reduction and anammox occur independently or are related to each other. The cooperation of N-S...
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Estimation of platinum in environmental water samples with solid phase extraction technique using inductively coupled plasma mass spectrometry
PublicationZoptymalizowano metodykę oznaczania śladowych poziomów stężeń platyny (IV) w oparciu o technikę ekstrakcji do fazy stałej w połączeniu ze spektrometrią mas z plazmą wzbudzoną indukcyjnie. Na etapie wzbogacania platyny wykorzystano żel krzemionkowy modyfikowany grupami aminopropylowymi. Ilościowy odzysk platyny uzyskano poprzez wykorzystanie 1.0 mol L-1 roztworu tiomocznika jako eluenta. Odchylenie standardowe wyników (RSD) było...
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Chromium (III) removal by perennial emerging macrophytes in floating treatment wetlands
PublicationFloating treatment wetlands (FTWs) are a sustainable solution to treat polluted water, but their role in chromium (Cr(III)) removal under neutral pH conditions remains poorly understood. This study evaluated the potential of FTWs planted with two perennial emergent macrophytes, Phragmites australis and Iris pseudacorus, to remove Cr(III) and nutrients (N and PO4-P) from water containing 7.5 mg/L TN, 1.8 mg/L PO4-P, and Cr(III)...
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Higher Absorption of Vitamin C from Food than from Supplements by Breastfeeding Mothers at Early Stages of Lactation
PublicationThe aim of the present study was to determine the effect of vitamin C supply in the diet of lactating women on vitamin C concentra¬tions in human milk (n = 97) sampled at different stages of lactation. Vitamin C levels were measured by liquid chromatography. Dietary intake of vitamin C was determined based on 3-day food dairies kept by breastfeeding mothers. Maternal dietary intakes of vitamin C from natural sources on lactation...
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Synthesis of N-doped TiO2 nanoparticles with enhanced photocatalytic activity for 2,4-dichlorophenol degradation and H2 production
PublicationNitrogen-doped titanium dioxide (N-TiO2) nanoparticles were prepared using a modified sol-gel method. The as-prepared nanoparticles were characterized by state-of-the-art techniques for their optical, structural and morphological properties. The crystallite size, surface area and bandgap energy of reference TiO2 and N-TiO2 nanoparticles were found to be 16.1 and 10.9 nm, 83.6 and 131.8 m2 g−1 and 3.23 and 2.89 eV, respectively....
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Nondestructive Optical Sensing of Flavonols and Chlorophyll in White Head Cabbage ( Brassica oleracea L. var. capitata subvar. alba ) Grown under Different Nitrogen Regimens
PublicationA multiparametric optical sensor was used to nondestructively estimate phytochemical compounds in white cabbage leaves directly in the field. An experimental site of 1980 white cabbages (Brassica oleracea L. var. capitata subvar. alba), under different nitrogen (N) treatments, was mapped by measuring leaf transmittance and chlorophyll fluorescence screening in one leaf/cabbage head. The provided indices of flavonols (FLAV) and...
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Przebieg wpracowywania kwarcowych złóż filtracyjnych przeznaczonych do usuwania manganu i azotu amonowego z wód podziemnych.The course of ripenining of quartz sand filter beds used for manganese and ammonium nitrogen removal from the groundwaters.
PublicationPrzeprowadzone badania wykazały, ze czas wpracowywania się kwarcowego złoża filtracyjnego w procesie odmanganiania i nitryfikacji trwał od 7 do 8 tygodni (złoże wpracowywało się jednocześnie w obu procesach) Wpracowanie uzyskano filtrując napowietrzoną wodę podziemną o stosunkowo wysokich stężeniach manganu (0,6 - 1,1 mg/l) i azotu amonowego (0,4 - 1,4 mgN/l) i niewielkich stężeniach żelaza (poniżej 0,5 mg/l). Po wpracowaniu...
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A lower bound on the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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The coexistence and competition of canonical and comammox nitrite oxidizing bacteria in a nitrifying activated sludge system – Experimental observations and simulation studies
PublicationThe second step of nitrification can be mediated by nitrite oxidizing bacteria (NOB), i.e. Nitrospira and Nitrobacter, with different characteristics in terms of the r/K theory. In this study, an activated sludge model was developed to account for competition between two groups of canonical NOB and comammox bacteria. Heterotrophic denitrification on soluble microbial products was also incorporated into the model. Four 5-week washout...
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Cadmium accumulation by Phragmites australis and Iris pseudacorus from stormwater in floating treatment wetlands microcosms: Insights into plant tolerance and utility for phytoremediation
PublicationEnvironmentally sustainable remediation is needed to protect freshwater resources which are deteriorating due to severe industrial, mining, and agricultural activities. Treatment by floating wetlands could be a sustainable solution to remediate water bodies. The study aimed to examine the effects of Cd on Phragmites australis and Iris pseudacorus growth (height, biomass, root length and chlorophyll contents), anatomy, Cd accumulation...
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The electronic excited states of dichloromethane in the 5.8-10.8 eV energy range investigated by experimental and theoretical methods
PublicationWe present a comprehensive experimental high-resolution vacuum ultraviolet (VUV) photoabsorption spectrum of dichloromethane, CH 2 Cl 2 , with absolute cross sections determined for the full 5.8–10.8 eV energy-range. The calculations on the vertical excitation energies and oscillator strengths were performed using the equation-of-motion coupled cluster method, restricted to the single and double excitations level (EOM-CCSD), and...
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The influence of selenium addition during seeds' germination on the biological properties of obtained sprouts
PublicationSelenium plays a vital role in human body, because in the form of aminoacids (Se-methionine, Se-cysteine) it is found in the active centres of over 25 enzymes, including those regarded as 'cytoprotective'. Unfortunatelly, its daily intake in Poland and other European countries is lower than predicted by dietary recommendations. The consequences of selenium deficiency in diet might be severe, including higher susceptibility to cardio-vascular...
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Impact of soluble organic matter and particulate organic matter on anammox system: Performance, microbial community and N2O production
PublicationIn this study, the effects of soluble readily biodegradable COD (sCOD) and particulate slowly biodegradable COD (pCOD) on anammox process were investigated. The results of the longterm experiment indicated that a low sCOD/N ratio of 0.5 could accelerate the anammox and denitrification activity, to reach as high as 84.9% ±2.8% TN removal efficiency. Partial denitrification-anammox (PDN/anammox) and denitrification were proposed...
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Binuclear Co(II), Zn(II) and Cd(II) tri-tert-butoxysilanethiolates. Synthesis, crystal structure and spectroscopic studies.
PublicationA series of Co(II), Zn(II) and Cd(II) complexes have been synthesized in reaction of respective metal tri-tert-butoxysilanethiolates with pyrazine 1 and 2 and 1,2-bis(2-pyridyl)ethylene 3–5. All compounds have been characterized by single-crystal X-ray structure determination, elemental analysis, FT-IR and thermogravimetry. Obtained complexes are bimetallic with the formula of [M{SSi(OtBu)3}2(μ-L)]2 and metal ions bridged by N,N′-spacer....
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Analogues of trypsin inhibitor SFTI-1 modified in the conserved P1′ position by synthetic or non-proteinogenic amino acids retain their inhibitory activity
PublicationA series of linear and monocyclic (with a disulfide bridge only) analogues of trypsin inhibitor SFTI-1 modified in the P-1 and/or P-1' positions were synthesized by the solid-phase method. In the substrate specificity P-1 position, Phe or N-benzylglycine (Nphe) were introduced, whereas the conserved Ser6 in Bownam-Birk (BBI) inhibitors was replaced by Hse (L-homoserine), Nhse [N-(2-hydroxyethyl)glycine], Sar, and Ala. Kinetic studies...
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Influence of the boron doping level on the electrochemical oxidation of raw landfill leachates: advanced pre-treatment prior to the biological nitrogen removal
PublicationThe electrochemical oxidative treatment of landfill leachates (LLs) containing high amounts of ammonia nitrogen and organic matter was used as a promising method, prior to biological processes, to achieve the final effluent quality that would be acceptable by current regulations. The deposited boron-doped diamond electrodes (BDDs) with different boron doping concentrations (10000, 5000 and 500 ppm of B) were applied as anodes....
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Effects of different external carbon sources and electron acceptors on interactions between denitrification and phosphorus removal in BNR processes
PublicationThe effects of two different external carbon sources (acetate, ethanol) and electron acceptors (dissolved oxygen, nitrate and nitrite) were investigated under aerobic and anoxic conditions with non-acclimated process biomass from a full-scale biological nutrient removal activated sludge system. When acetate was added as an external carbon source, phosphate release was observed even in the presence of electron acceptors. The release...
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Redundant information encoding in QED during decoherence
PublicationBroadly understood decoherence processes in quantum electrodynamics, induced by neglecting either the radiation [L. Landau, Z. Phys. 45, 430 (1927)] or the charged matter [N. Bohr and L. Rosenfeld, K. Danske Vidensk. Selsk, Math.-Fys. Medd. XII, 8 (1933)], have been studied from the dawn of the theory. However, what happens in between, when a part of the radiation may be observed, as is the case in many real-life situations, has...
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Kinetics of the Organic Compounds and Ammonium Nitrogen Electrochemical Oxidation in Landfill Leachates at Boron-Doped Diamond Anodes
PublicationElectrochemical oxidation (EO) of organic compounds and ammonium in the complex matrix of landfill leachates (LLs) was investigated using three different boron-doped diamond electrodes produced on silicon substrate (BDD/Si)(levels of boron doping [B]/[C] = 500, 10,000, and 15,000 ppm—0.5 k; 10 k, and 15 k, respectively) during 8-h tests. The LLs were collected from an old landfill in the Pomerania region (Northern Poland) and were...
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Almost homoclinic solutions for the second order Hamiltonian systems
PublicationW niniejszej pracy badam istnienie rozwiązań prawie homoklinicznych (almost homoclinic) dla układu Hamiltona rzędu drugiego (układu Newtona): ü(t) + V_{u}(t,u) = f(t), gdzie t є R, u є R^{n}, V(t,u) = -K(t,u) + W(t,u), K,W: R x R^{n} → R są klasy C^{1}, K spełnia warunek ''pinching'', W_{u}(t,u)=o(|u|), gdy |u| → 0 jednostajnie względem t, f: R → R^{n} jest funkcją ciągłą, niezerową i odpowiednio małą w L^{2}(R,R^{n}). Przy tych...
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Note on the variance of the sum of gaussian functonals
PublicationDowodzi się oszacowania wariancji sum funkcjonałów losowych, konstruowanych dla zależnego ciągu gaussowskiego.Let (Xi; i = 1; 2; : : :) be a Gaussian sequence with Xi 2 N(0; 1) for each i and suppose its correlation matrix R = (ij)i;j1 is the matrix of some linear operator R : l2 ! l2. Then for fi 2 L 2(), i = 1; 2; : : : ; where is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals...