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Search results for: 1,4-naftochinony
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Open-transistor fault diagnostics in voltage-source inverters by analyzing the load current
PublicationA novel method is presented for the detection andisolation of open-transistor faults in voltage-source invertersfeeding low-power AC motors. The method is based onmonitoring two diagnostic signals, one indicating sustained nearzerovalues of output current and thus permitting fault detection,the other permitting the isolation of the particular transistorwhich went faulty. The latter signal is the ratio of the averagephase current...
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Linia metra nr 4 w São Paulo
PublicationSão Paulo w Brazylii to jedna z największych metropolii swiata. Ogromne potrzeby transportowe spowodowały, że w komunikacji zbiorowej bardzo duży nacisk kładziony jest na transport szynowy - zarówno naziemny jak i podziemny (metro). Jego stan obecny oraz perspektywy rozwoju, ze szczególnym uwzględnieniem oddanej do użytku w bieżacym roku linii metra nr 4, przedstawiono w niniejszym artykule.
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Edge coloring of graphs of signed class 1 and 2
PublicationRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Projekt Sachalin 1. Rosja - Daleki Wschód
PublicationPrzedstawiono podstawowe rozwiązania w zakresie projektu Sachalin 1. Omówiono warunki budowlane i ich wpływ na przebieg projektu. Logistyka, wsparcie, element międzynarodowy.
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Mixed 4-node shell element with assumed strain and stress in 6-parameter theory
PublicationWe propose a mixed hybrid 4-node shell elements based on Hu-Washizu principle. Apart from displacements both strains and stress fields are treated as independent fields. The element is derived in the framework of a general nonlinear 6-field shell theory with drilling rotation which is dedicated to the analysis of multifold irregular shells with intersections. The novelty of the presented results stems from the fact that the measures...
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Mixed 4-node shell element with assumed strain and stress in 6-parameter theory
PublicationWe propose a mixed hybrid 4-node shell elements based on Hu-Washizu principle. Apart from displacements both strains and stress fields are treated as independent fields. The element is derived in the framework of a general nonlinear 6-field shell theory with drilling rotation which is dedicated to the analysis of multifold irregular shells with intersections. The novelty of the presented results stems from the fact that the measures...
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Structure, Physicochemical and Biological Properties of an Aqua (2,2′,2′′-Nitrilotriacetato)-oxidovanadium(IV) Salt with 4-Methylpyridinium Cation
PublicationThe crystal structure of a nitrilotriacetate (nta) oxidovanadi-um(IV) salt with 4-methylpyridinium cation, [4-Me(Py)H]+, of [4-Me(Py)H][VO(nta)(H2O)] stoichiometry was determined. The com-plex comprises a discrete mononuclear [VO(nta)(H2O)]–coordinationentity that can be rarely found among other known compounds con-taining nitrilotriacetate oxidovanadium(IV) moieties. The complex wascharacterized by spectroscopic (IR and EPR) methods,...
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On simplification of residue scaling process in pipelined Radix-4 MQRNS FFT processor
PublicationResidue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and generates four complex residue numbers. In order to prevent arithmetic overflow intermediate results after each butterfly have to be...
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On configuration of residue scaling process in pipelined radix-4 MQRNS FFT processor
PublicationResidue scaling is needed in pipelined FFT radix-4 processors based on the Modified Quadratic Residue Number System (MQRNS) at the output of each butterfly. Such processor uses serial connection of radix-4 butterflies. Each butterfly comprises n subunits, one for each modulus of the RNS base and outputs four complex residue numbers. In order to prevent the arithmetic overflow in the succesive stage, every number has to be scaled,...
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Z cyklu: Cyrkulacje (1), akwarela
PublicationRada Miasta Krakowa oraz Prezydent Krakowa objęli honorowym patronatem XXIX Aukcję Wielkiego Serca (Internetową) na rzecz młodzieży niepełnosprawnej. Aukcja rozpoczęła się 16 listopada 2020 r.Czas pandemii spowodował, że aukcja po raz pierwszy w historii odbędzie się w formie internetowej na stronie artinfo.pl. Aukcja będzie trwała prawie dwa tygodnie. W tym roku organizatorom udało się nam pozyskać190 prac od znakomitych artystów....
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Lower rim substituted tert-butylcalix[4]arenes (Part VI). Synthesis and ionophoric properties of 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrakis(3-diethoxyphosphorylpropoxy)calix[4]arene.
PublicationSyntezowano nowy związek: 5,11,17,23-tetra-tert-butylo-25,26,27,28-tetrakis(3-dietoksyfosforylopropoksy)kaliks[4]aren i badano jego właściwości kompleksujące w membranowych elektrodach jonoselektywnych. Związek wykazuje selektywność na jony wapnia oraz na kationy litu. Wyznaczono stałe tworzenia kompleksów z wymienionymi jonami w membranie elektrody.
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A note on polynomial algorithm for cost coloring of bipartite graphs with Δ ≤ 4
PublicationIn the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree ∆≤4 can be solved in O(n^2) time. This extends Jansen’s result [K.Jansen,The optimum cost chromatic partition problem, in:...
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Radix-4 dft butterfly realization with the use of the modified quadratic residue number system
PublicationW pracy zaprezentowano projektowanie i realizację obliczenia motylkowego dft dla podstawy 4 z użyciem zespolonego systemu resztowego (CRNS) i zmodyfikowanego kwadratowego systemu resztowego (MQRNS). System MQRNS oprócz własności dekompozycyjnych pozwala na realizację mnożenia zespolonego przy zastosowaniu trzech mnożeń rzeczywistych. Przedstawiono konwertery wejściowy CRNS/MQRNS i wyjściowy MQRNS/CRNS, mnożenie zespolone w MQRNS,...
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Calix[4]arene-Thioamides as Ionophores for Transition and Heavy Metal cations
PublicationCalix[4]arene derivatives play an important role as sensing materials in Ion Selective Electrodes(ISEs). Nowadays a high impact is put to control in natural waters the level of toxic heavy metals, like Pb ,Cd, Hg or Cu which may cause the great risk to human health. Our goal was to design and to synthesize ligands possessing ability to bind transition and heavy metal cations. The synthesis, crystal structures,extractive and ionophoric...
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Improved Performance of 1-Ethyl-3-Methylimidazolium Tetrafluoroborate at Steel/HCl Interface by Iodide Ions
PublicationThe corrosion and corrosion inhibition of St37 steel in 0.1 M HCl solution by 1-ethyl-3-methylimidazolium tetrafluoroborate (EMITFB) and the effect of addition of KI on the inhibitive performance of EMITFB have been examined by electrochemical [electrochemical impedance spectroscopy, potentiodynamic polarization, and dynamic electrochemical impedance spectroscopy (DEIS)] and surface examination [scanning electron microscope (SEM)...
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Calix[4]arene-Thioamides as Ionophores for Transition and Heavy Metal Cations.
PublicationPochodne kaliks[4]arenów odgrywają ważną rolę jako materiał aktywny w membranowych elektrodach jonoselektywnych. Obecnie duży nacisk kładzie się na kontrolę stężeń kationów metali ciężkich, takich jak Pb, Cd, Hg, Cu w wodach naturalnych. Naszym zadaniem było zaprojektować i zsyntezować ligandy, które wykazują zdolność do wiązania kationów metali ciężkich i przejściowych. Synteza, struktury krystaliczne, ekstrakcja i właściwości...
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Szerokość rozwarcia rys w konstrukcjach żelbetowych według PN-EN 1992-1-1:2008 oraz PN-B 03264:2002
PublicationW referacie przedstawiono zalecenia normowe związane z ograniczeniem szerokości rozwarcia rys w konstrukcjach żelbetowych. Przeanalizowano wytyczne projektowe podane w PN-EN 1992-1-1:2008 [1] oraz PN-B 03264:2002 [2]. W przykładzie obliczeniowym dołączonym do referatu sprawdzono rozwarcie rys w płycie żelbetowej pod obciążeniem długotrwałym dla różnych wariantów: obliczeń elementu według założeń PN-EN 1992-1-1:2008 – m. in. z...
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Szerokość rozwarcia rys w konstrukcjach żelbetowych według PN-EN 1992-1-1:2008 oraz PN-B 03264:2002
PublicationW referacie przedstawiono zalecenia normowe związane z ograniczeniem szerokości rozwarcia rys w konstrukcjach żelbetowych. Przeanalizowano wytyczne projektowe podane w PN-EN 1992-1-1:2008 [1] oraz PN-B 03264:2002 [2]. W przykładzie obliczeniowym dołączonym do referatu sprawdzono rozwarcie rys w płycie żelbetowej pod obciążeniem długotrwałym dla różnych wariantów: obliczeń elementu według założeń PN-EN 1992-1-1:2008 – m. in. z...
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Wykorzystanie termowizji w badaniach odporności na udary wg EN61000-4-5
PublicationPrzedstawiono wyniki badań konstrukcyjnych urządzeń elektronicznych z zastosowaniem kamery podczerwieni do obserwacji obiektu badanego podczas badań odporności na udary napięciowe wykonywane wg normy EN61000-4-5.
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Rhenium Nanostructures Loaded into Amino-Functionalized Resin as a Nanocomposite Catalyst for Hydrogenation of 4-Nitrophenol and 4-Nitroaniline
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The LaPdIn 4 indide and elementary properties of the LaTIn 4 ( T = Ni, Pd, Pt) materials family
PublicationThe indium-rich intermetallic compound LaPdIn4 is reported, prepared by arc-melting and annealing at 600 C. Single crystal X-ray diffraction found the material to be orthorhombic, space group Cmcm (No. 63), with lattice parameters a ¼ 4.5462(3) Å, b ¼ 16.9208(10) Å, and c ¼ 7.3100(5) Å. This previously unreported indide is isostructural with LaNiIn4 and LaPtIn4. It is demonstrated that all three compounds in the LaTIn4 (T ¼ Ni,...
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Numerical analyses of novel prefabricated structural wall panels in residential buildings based on laboratory tests in scale 1:1
PublicationThe paper presents experimental and numerical investigations on novel prefabricated composite building wall panels for residential building constructions. The wall panels were composed of reinforced concrete ribbed elements with the core from the EPS foam as the thermal insulation. The wall panels in the full-scale 1:1 were subjected to vertical loads. In the first step, the experiments were analysed with simple usual static methods....
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Chitosan/poly(4-vinylpyridine) coatings formed on AgNPs-decorated titanium
PublicationElectrophoretic deposition (EPD) of chitosan/poly(4-vinylpyridine) (chit/P4VP) coatings on titanium substrates previously decorated with silver nanoparticles (AgNPs) was performed at different content of P4VP in the suspension and different voltage values. The results revealed that the composite coatings were formed, well-adjacent to the titanium substrate, of suitable roughness, hydrophilicity, and corrosion resistance. The voltage...
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A Convenient Synthesis of Monocationic 1-[(Cyclic amidino)methyl]thymines
Publication1-[(Cyclic amidino)methyl]thymines have been conveniently synthesized from thymine in a three-step procedure via 1-cyanomethyl- and 1-[(thiocarbamoyl) methyl]thymines. The above synthetic intermediates were obtained in good yields by improved methods.
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Exact analytical scattering lengths for a class of long-range potentials with r(-4) asymptotics.
PublicationWyprowadzono analityczne wyrażenie dla długości rozpraszania dla pewnej klasy potencjałów zanikających asymptotycznie jak r do (-4). Wpływ rdzenia potencjału uwzględniono poprzez dwa parametry: promień rdzenia oraz krótkozasięgową długość rozpraszania.
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Formation of chlorinated breakdown products during degradation of sunscreen agent, 2-ethylhexyl-4-methoxycinnamate in the presence of sodium hypochlorite
PublicationIn this study, a new degradation path of sunscreen active ingredient, 2-ethylhexyl-4-methoxycinnamate (EHMC) and 4-methoxycinnamic acid (MCA) in the presence of sodium hypochlorite (NaOCl), was discussed. The reaction products were detected using gas chromatography–mass spectrometry (GC-MS). Since HOCl treatment leads to more polar products than EHMC, application of polar extracting agents, dichloromethane and ethyl acetate/n-hexane...
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Implication of the disulfide bridge in trypsin inhibitor SFTI-1 in its interaction with serine proteinases
PublicationFourteen monocyclic analogues of trypsin inhibitor SFTI-1 isolated from sunflower seeds were synthesized by the solid-phase method. The purpose of this work was to establish the role of a disulfide bridge present in inhibitor's side chains of Cys3 and Cys11 in association with serine proteinases. This cyclic fragment was replaced by the disulfide bridges formed by L-pencillamine (Pen), homo-L-cysteine (Hcy), N-sulfanylethylglycine...
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Synthesis and ionophoric properties of functionalized p-tert-butyl-calix[4]arenes
PublicationProjektowanie struktury związków o właściwościach jonoforowych stanowi ważny element chemii supramolekularnej. W pracy przedstawiono wyniki badań nad funkcjonalizacją makrocyklicznych kaliks[4]arenów prowadzacą do nowych związków o zróżnicowanych właściwościach kompleksujących. Syntezowane przez nas jonofory badane były w membranowych elektrodach jonoselektywnych. Wyznaczono potencjometryczne współczynniki selektywności oraz stałe...
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4. Charakterystyka hydrograficzna zlewni Raduni
PublicationW rozdziale przedstawiono charakterystykę zlewni i rzeki Raduni. Szczególną uwagę zwrócono na profil podłużny rzeki, zabudowę, gęstość sieci rzecznej oraz przepływy charakterystyczne. Przedstawiono również problem obliczenia przepływów nienaruszalnych i zmiany antropogeniczne w zlewni. Na koniec dokonano identyfikacji obecnego stanu wód w świetle Ramowej Dyrewktywy UE, odnosząc się zarówno do stanu ekologicznego rzeki, jak i do...
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Diminished toxicity of C-1748, 4-methyl-9-hydroxyethylamino-1-nitroacridine, compared with its demethyl analog, C-857, corresponds to its resistance to metabolism in HepG2 cells
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Differential Response of MDA-MB-231 and MCF-7 Breast Cancer Cells to In Vitro Inhibition with CTLA-4 and PD-1 through Cancer-Immune Cells Modified Interactions
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Radix-4 dft butterfly realization with the use of the modified quadratic residue number system
PublicationW pracy przedstawiono algorytm realizacji mnożenia zespolonego z użyciem zmodyfikowanego kwadratowego zmodyfikowanego systemu liczbowego (mqrns) oraz jego zastosowanie do wykonania obliczenia motylkowego dft dla podstawy 4. pokazano też wstępne rezultaty implementacji w układzie xilinx fpga.
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Potassium Tri-tert-butoxysilanethiolates: Synthesis, Properties, and Crystal and Molecular Structures of [(tBuO)3SiSK]6[THF]2·2THF, {[(tBuO)3SiS]2K2}n, and [(tBuO)3SiSK]4[H2O]4·C6H6
PublicationW reakcji tri-tert-butoksysilanotiolu z potasem otrzymano trzy nowe związki:[(tBuO)3SiSK]6[THF]2·2THF, {[(tBuO)3SiS]2K2}n, i[(tBuO)3SiSK]4[H2O]4·C6H6. Stanowią one dogodne substraty w syntezach kompleksów silanotiolanowych metali przejściowych. Charakteryzują się one również różnorodnością tworzonych układów. Rentgenowska analiza strukturalna wykazała, iż tworzą one trzy typy makrocząsteczkowych układów, w których...
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Perfusion computed tomography: 4 cmversus8 cm coverage size in subjects with chronic carotid artery stenosis
PublicationOBJECTIVE: The impact of coverage size on global cerebral blood flow (CBF), cerebral blood volume (CBV), mean transit time (MTT) and time to peak (TTP) parameters has not been investigated in patients with chronic carotid artery stenosis. METHODS: 63 patients with stenosis of >70% within a single internal carotid artery and neurological symptoms were randomly assigned to two well-matched groups. Differences in CT perfusion scan...
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Role of methylation in electron scattering on X(CH3)4 (X= C, Si, Ge) molecules (2)
PublicationTo investigate how replacement of H atom with methyl group (CH3) – in tetrahedral compounds of carbon, silicon and germanium – affects electron scattering process, total cross sections (TCS) for electron scattering from C(CH3)4, Si(CH3)4 and Ge(CH3)4 molecules have been compared with data for CH4, SiH4 and GeH4 molecules. All examined data have been obtained with the same experimental setup. The shape of all discussed TCS energy...
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Identification of novel psychoactive substances 25B-NBOMe and 4-CMC in biological material using HPLC-Q-TOF-MS and their quantification in blood using UPLC–MS/MS in case of severe intoxications
PublicationThis paper describes cases of poisoning caused by new psychoactive substances such as: 25BNBOMe (2-(4-bromo-2,5-dimethoxyphenyl)-N-[(2-methoxyphenyl)methyl]ethanamine) and 4-CMC (1-(4-chlorophenyl)-2-(methylamino)-1-propanone). The analytical procedure includes rapid and selective method for the extraction and determination of 4-CMC and 25B-NBOMe in blood samples using UPLC–MS/MS technique. To the best of our knowledge,this is...
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Transport of lead across polymer inclusion membrane with p-tert-butylkalix[4]arene derivative
PublicationOpisane zostały ułatwienia w transporcie jonów ołowiu (II) przez polimerową membranę inkluzyjną (PIMs),która składała się z trój octanu celulozy jako polimerowego suportu, eteru o-nitrofenylooktylu jako plastyfikatora i 25,26,27,28, tetra-(N-hydroksy-N-metylokarbonylo metoksy)-p-tert-butylokaliks[4]arenu jako nośnika jonów. Polimerowa membrana inkluzyjna została scharakteryzowana przy pomocy mikroskopu sił atomowych (AFM). Otrzymane...
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Lower rim substituted p-tert-butyl-calix[4]arene. Part 17. synthesis, extractive and ionophoric properties of p-tert-butylcalix[4]arene appended with hydroxamix acid moieties
PublicationThe synthesis and characterization of four p-tert-butylcalix[4]arene-hydroxamic acidc are reported. The dependence of the metal ion binding, assessed by liquid extraction of the metal nitrates from water into dichloromethane in individual and competitive experiments, on the ligand structure, is presented. The results showed that those ligands could be successfully used in separation process of trnasition and heavy metals often...
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Manifestation of Intermolecular Interactions in the IR Spectra of 2- and 4-Methylmethcathinones Hydrochlorides: DFT Study and Hirshfeld Surfaces Analysis
PublicationThis paper reports a Hirshfeld surfaces analysis of crystalline 2- and 4-methylmethcathinone (2-MMC and 4-MMC) hydrochlorides to analyze NH∙Cl and CH∙∙∙Cl intermolecular interactions and approve the formation of the NН2+–Cl– salt fragment in both 2-MMC∙HCl and 4-MMC∙HCl crystals. Two isomeric dimers were separated from the corresponding crystal packing to model IR spectra of the crystalline 2-MMC∙HCl...
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Comparison of hydrogen bonds and diverse weak interactions of the nitro group in 2-methyl-4-nitroanilinium nitrate, bisulfate and two hexafluoridosilicates: elementary graph-set approach
PublicationCrystal structures of (H2m4na)NO3 (1), (H2m4na)HSO4 (2), (H2m4na)2SiF6 (3) and (H2m4na)2SiF6*2H2O (4), where 2m4na = 2-methyl-4-nitroaniline, are presented. Two layers of interactions occur in the structures, N—H...O/F hydrogen bonds and interactions with the nitro group. Although diverse, hydrogen-bonding patterns are compared with each other by means of interrelations among elementary graph-set descriptors and descriptors of hydrogen-bonding...
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Preparation of 1-[Ω-(1,4,5,6-Tetrahydropyrimidin-2-yl)alkyl]thymines
PublicationOne-stage prepn. of the hydrochloride salts of 1-[ω-(1,4,5,6-tetrahydropyrimidin-2-yl)alkyl]-thymines, e.g. I, from 1-(ω-cyanoalkyl)thymines and a 1:1-mixt. of 1,3-diaminopropane and ethanol satd. with hydrogen sulfide is described. 1-(2-Cyanoethyl)-thymine gave a facile reversal of the Michael reaction to thymine under the conditions used. The reaction of 1,3-bis(3-cyanobenzyl)thymine with the above reagent produced 1,3-bis[3-(1,4,5,6-tetrahydropyrimidin-2-yl)benzyl]thymine.
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Oxidation kinetics of Zircaloy-4 alloy at 673 K determined by GDOES technique
PublicationOxidation 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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Dichlorido-1Cl,3Cl-hexakis[1,1,2,2,3,3(n5)-methylcyclopentadienyl]di-μ2-oxido-1:2κ2O:O;2:3κ2O:O-trihafnium(IV)
PublicationTytułowy związek jest trójrdzeniową cząsteczką. Dwie jednostki (MeCp)2HfCl połączone są z (MeCp)2Hf przez mostki tlenowe. Mostki Hf-O-Hf są prawie liniowe. Geometria trzech atomów Hf jest tetraedryczna.
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Unassisted formation of hemiaminal ether from 4-aminopyridine and o-vanillin - experimental and theoretical study
PublicationThe reactions between o-vanillin and three isomeric aminopyridines lead to imines of diverse spatial conformation and reactivity. The direct products of these simple reactions carried out in methanol are either imine compounds formed in the reactions of 2- amino- and 3-aminopyridine with o-vanillin or the α-aminoether formed in the reaction of o-vanillin with 4-aminopyridine. The Schiff-type derivative of 4-aminopyridine and o-vanillin,...
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The influence of food phytochemicals on cyclic phosphodiesterase 4 (PDE4) activity
PublicationCyclic phosphodiesterase 4 (PDE4) belongs to family of cyclic phosphodiesterases, which are expressed predominantly in inflammatory cells, airway smooth muscles, cardiovascular tissues and brain. Inhibitors of this family of enzymes found medicinal applications as antidepressants, antiinflamatory drugs (mainly in airway diseases) or antiasthmatics (Ibudilast). PDE4 inhibitors are also being tested for preventing the development...
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The influence of the type of halogen substituent and its position on the molecular conformation, intermolecular interactions and crystal packing for a series of 1-benzoyl-3-(halogenophenyl)thioureas
PublicationBy the reaction of benzoyl chloride, potassium isothiocyanate and the appropriate halogenoaniline, i.e. 2/3/4-(bromo/iodo)aniline, we have obtained five new 1-benzoyl-3-(halogenophenyl)thioureas, namely, 1-benzoyl-3-(2-bromophenyl)- thiourea and 1-benzoyl-3-(3-bromophenyl)thiourea, C14H11BrN2OS, and 1-benzoyl-3-(2-iodophenyl)thiourea, 1-benzoyl-3-(3-iodophenyl)thiourea and 1-benzoyl-3-(4-iodophenyl)thiourea, C14H11IN2OS. Structural...
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Antimicrobial Activity of Chimera Peptides Composed of Human Neutrophil Peptide 1 (HNP-1) Truncated Analogues and Bovine Lactoferrampin
PublicationThree chimera peptides composed of bovine lactoferrampin and the analogue of truncated human neutrophil peptide 1 were synthesized by the solid-phase method. In two compounds peptide chains were connected via isopeptide bond, whereas in the third one disulfide bridge served as a linker. All three chimeras displayed significantly higher antimicrobial activity than the constituent peptides as well as their equimolar mixtures. The...
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Witaminy. Rozdział 1
PublicationPrzedstawiono budowę chemiczną i omówiono własności witamin rozpuszczalnych w tłuszczach (wit. A, D, E, K) oraz w wodzie (wit. B1, B2, PP, B5, B6, B12, H, C, P, kwas foliowy).
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Sztywne złącza (1)
PublicationWarunki posadowienia rur, problemy oddziaływań na złącza.Obciążenia złączy rurowych. Różnice między wodoszczelnością a wytrzymałością. Normowe złącze sztywne
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.