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Wyniki wyszukiwania dla: 2-OXOPROPANOIC ACID
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Easy formation of acyl-Meldrum's acid anhydride
PublikacjaAcyl Meldrum's acid are usually a good source of ketenes upon definite thermal composition. However we treated acyl-Meldrum's acid with the Lewis acid and we observed formation of 5[[(2,2-dimethyl-4,6-dioxo-1,3-dioxan 5 ylidene)(acyl/arylamino)mathoxy](acyl/arylamino)methylene]-2,2dimethyl-1,3-dioxane-4,6 dione which means acyl-Meldrum's acid anhydride. The chemical properities of acyl-Meldrum's acid anhydride were explored.
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Thermal and mechanical properties of polyurethanes modified with L-ascorbic acid
PublikacjaIn this study we report the thermal and mechanical properties of polyurethanes modified with ascorbic acid (AA). Ascorbic acid was used as a modifier at concentration of 1 or 2 mass%. The antioxidative properties of AA may improve the biocompatibility of the obtained materials, which were designed for biomedical applications. In this paper we describe characterization of obtained unmodified and ascorbic acid modified polyurethanes...
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New Analogues of Mycophenolic Acid
PublikacjaMycophenolic acid (MPA) possesses antibacterial, antifungal, antiviral, immunosuppressive and anticancer properties. It is a non-competitive and reversible inhibitor of dehydrogenase inosine-5'-monophosphate (IMPDH). This compound belongs to the immunosuppressive drugs used for the prevention of both acute and chronic transplant rejection. Until now, two derivatives of MPA have been used clinically: mycophenolate mofetil (MMF,...
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A novel luminescent chemical sensor for the determination of Pb 2+ and Cu 2+ ions
PublikacjaSilica xerogel surface grafted with aminopropyl (PrNH2) groups was additionally treated by cetyltrimethylammonium bromide (CTAB) surfactant and ascorbic acid (asc) in alkaline solution. This material symbolized as SiO2-PrNH2-CTAB/asc, proved to be a stable luminescent material, exhibited an emission band peaked at 393 nm under excitation wavelength 335 nm. Time evolution of the band intensity suggests changes of defect concentration...
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Synthesis, structure characterization and thermal propertiesof [Zr<sub>6</sub>(μ<sub>3</sub>-O)<sub>4</sub>(μ<sub>3</sub>-OH)<sub>4</sub>(OOCCH<sub>2</sub><sup>t</sup>Bu)<sub>9</sub>(μ<sub>2</sub>-OH)<sub>3</sub>]<sub>2</sub>
PublikacjaTytułowy związek otrzymano w reakcji Zr(OiPr)4 z nadmiarem kwasu 3,3-dimetylobutyrowego. Rentgenowska analiza strukturalna została wykonana w temperaturze 103 i 153K. Struktury zawierają dimery podjednostek o wzorze: [Zr6(μ3-O)4(μ3-OH)4-(OOCCH2tBu)9] połączonych 6 mostkującymi grupami μ2-OH. Analiza zmiennotemperaturowych...
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Topochemical, Single‐Crystal‐to‐Single‐Crystal [2+2] Photocycloadditions Driven by Chalcogen‐Bonding Interactions
PublikacjaThe face-to-face association of (E)-1,2-di(4-pyridyl)ethylene (bpen) molecules into rectangular motifs stabilized for the first time by chalcogen bonding (ChB) interactions is shown to provide photoreactive systems leading to cyclobutane formation through single-crystal-to-single-crystal [2+2] photodimerizations. The chelating chalcogen bond donors are based on original aromatic, ortho-substituted bis(selenocyanato)benzene derivatives...
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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)
PublikacjaTytułowy 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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Photoresponsive, amide-based derivative of embonic acid for anion recognition
PublikacjaThe synthesis and ion-binding properties of amide-based derivative of embonic acid andp-aminoazobenzenewere described. The new compound was characterized by X-ray structural analysis and spectroscopic methods.Ligand interacts in acetonitrile with Y-shaped anions (benzoates and acetates) and dihydrogen phosphatesforming complexes of 1:1 stoichiometry. In more polar DMSO the complexes stoichiometry changes to 2:1(L:anion). Light-inducedtranstocisisomerization...
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4-[(tert-Butyldimethylsilyl)oxy]-6-methoxy-7-methyl-5-(oxiran-2-ylmethyl)-2-benzofuran-3(1H)-one
PublikacjaThe title compound, C19H28O5Si, was obtained in the reaction of 1,3-dihydro-4-[(tert-butyldimethylsilyl)oxy]-6-methoxy-7-methyl-3-oxo-5-(prop-2-enyl)isobenzofuran with meta-chloroperbenzoic acid. This reaction is one of the stages of the total synthesis of mycophenolic acid, which we attempted to modify. The title compound forms crystals with only weak intermolecular interactions. The strongest stacking interaction is found between...
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Redox State Sensitive Spectroscopy of the Model Compound [(H-dcbpy)(2)Ru-II(NCS)(2)](2-) (dcbpy=2,2 '-Bipyridine-4,4 '-dicarboxylato)
PublikacjaThe charge transfer reaction mechanism in a ruthenium polypyridine model complex with isothiocyanato ligands, i.e., [(H-dcbpy)(2)Ru(NCS)(2)](2-) 2Bu(4)N(+) (Ru2H) (dcbpy = 2,2'-bipyridine-4,4'-dicarboxylato), has been investigated by combining UV-vis absorption, resonance Raman spectroscopy, and electrochemical methods. Understanding the photophysics of light-harvesting complexes of this class is an indispensable prerequisite to...
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Amino Acid Based Antimicrobial Agents – Synthesis and Properties
PublikacjaStructures of several dozen of known antibacterial, antifungal or antiprotozoal agents are based on the amino acid scaffold. In most of them, the amino acid skeleton is of a crucial importance for their antimicrobial activity, since very often they are structural analogs of amino acid intermediates of different microbial biosynthetic pathways. Particularly, some aminophosphonate or aminoboronate analogs of protein amino acids are...
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2-Methylphenyl 2-methoxyacridine-9-carboxylate
PublikacjaThe title compound, C22H17NO3, crystallizes in the monoclinic space group P21/c with four molecules per unit cell. The molecules are arranged in centrosymmetric pairs, joined via the C and attached H atoms in the meta position relative to the methoxy group. These pairs are bonded in the crystalline phase as a result of non-specific dispersive interactions, and through a network of C—H⋯O interactions involving the non-bonded O...
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Encapsulation of Amikacin into Microparticles Based on Low-Molecular-Weight Poly(lactic acid) and Poly(lactic acid-co-polyethylene glycol)
PublikacjaThe aim of this study was to fabricate novel microparticles (MPs) for efficient and long-term delivery of amikacin (AMI). The emulsification method proposed for encapsulating AMI employed low-molecular-weight poly(lactic acid) (PLA) and poly(lactic acid-co-polyethylene glycol) (PLA−PEG), both supplemented with poly(vinyl alcohol) (PVA). The diameters of the particles obtained were determined as less than 30 μm. Based on an in-vitro...
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Chromogenic amides of pyridine-2,6-dicarboxylic acid as anion receptors
PublikacjaThe synthesis of simple, chromogenic pyridine-2,6-dicarboxylic acid amides, derivates of isomeric nitroanilines and aminonitrophenols, and their ion binding properties are described. The ligands' response to ionic species was examined by naked eye and was studied with the use of UV-Vis spectroscopy in DMSO and its mixture with water. The effect of the localisation and the type of the substituents in aromatic rings were discussed....
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublikacjaFor a graph G = (V,E), a subset D \subseteq V(G) is a 2-dominating set if every vertex of V(G)\D$ has at least two neighbors in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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(7Z,7'Z)-7,7'-(1,2,4-trithiolane-3,5-diylidene)bis[2-methylquinolin-8(7H)-one] chloroform disolvate
PublikacjaTytułowy związek, C22H14N2O2S3*2CHCl3 został otrzymany jako produkt reakcji pomiędzy kwasem 8-hydroksy-2-metylochinolinokarboditionowym a trifluorooctanem magnezu (lub manganu). Procesy utlenienia oraz eliminacji siarki spowodowały kondensację dwóch cząsteczek kwasu z wytworzeniem pięcioczłonowego aromatycznego pierścienia heterocyklicznego S3C2 (tritiolanu). Cząsteczka wykazuje symetrię C2. Związek ko-krystalizuje z dwoma cząsteczkami...
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(Cyclopentadienyl){(N,N-dimethylaminoethyl)cyclopentadienyl} complexes of zirconium: Crystal structure of [(η5-C5H5)(η5-C5H4CH2CH2NHMe2)ZrCl2]2[ZrCl6]
Publikacja(C5H5)ZrCl3 reaguje z [C5H4-CH2CH2NMe2]Li dając polimer koordynacyjny {(C5H5)(C5H4-CH2CH2NMe2)ZrCl2}n, który z kolei w reakcji z HCl daje żółtozielone kryształy [(η5-C5H5)(η5-C5H4CH2CH2NHMe2)ZrCl2]2[ZrCl6]. Ten ostatni związek został scharakteryzowany za pomocą widm NMR oraz przy użyciu rentgenowskiej analizy strukturalnej. Utworzenie w/w związku wskazuje na oderwanie grup C5H5 oraz C5H4-CH2CH2NMe2 od centrum metalicznego Zr(IV).
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Dissociative electron attachment to benzoic acid (C7H6O2)
PublikacjaThe dissociative electron attachment (DEA) to benzoic acid (C6H5COOH) has been studied using an experimental crossed beam setup of a quadrupole mass spectrometer and a trochoidal electron monochromator. Relative partial cross sections for the DEA to produce negative ion fragments show the main channels for dissociation. The comparison of the present results with the ultraviolet photoelectron spectrum of benzoic acid [J. Meeks,...
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2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublikacjaSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid, a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, it exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Synthesis and antiproliferative activity of new mycophenolic acid conjugates with adenosine derivatives
PublikacjaNew conjugates of mycophenolic acid (MPA) and adenosine derivatives were synthesized and assessed as potential immunosuppressants on Jurkat cell line and peripheral blood mononuclear cells (PBMC) from healthy donors. As compared to MPA, all compounds were found to be more active against Jurkat cell line. The antiproliferative activities were compared with MPA and adenosine, in both 2′,3′-O-isopropylidene protected and free hydroxyl...
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Investigations on the immunosuppressive activity of derivatives of mycophenolic acid in immature dendritic cell
PublikacjaThe main activity of mycophenolic acid (MPA) and its analogs is the inhibition of proliferation of T cells. Here, we hypothesized that MPA and its conjugates inhibits also the activity of antigen-presenting cells (APC) including dendritic cells (DCs). We tested the effect of novel amino acid derivatives of MPA and conjugates of MPA with acridines/acridones on DCs by flow cytometry, ELISA and MLR assay. Both acridines/acridone derivatives...
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Reactions of R<sub>2</sub>P-P(SiMe<sub>3</sub>)Li with [(R'<sub>3</sub>P)<sub>2</sub>PtCl<sub>2</sub>]. A General and Efficient Entrance to Phosphanylphosphinidene Complexes of Platinum. Syntheses and Structures of [(η<sub>2</sub>-P=P<sup>i</sup>Pr<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [(η<sub>2</sub>-P=P<sup>t</sup>Bu<sub>2</sub>)Pt(p-Tol<sub>3</sub>P)<sub>2</sub>], [{η<sub>2</sub>-P=P(N<sup>i</sup>Pr<sub>2</sub>)2}Pt(p-Tol<sub>3</sub>P)<sub>2</sub>] and [{(Et<sub>2</sub>PhP)<sub>2</sub>Pt}<sub>2</sub>P<sub>2</sub>].
PublikacjaReakcje pochodnych litowych difosfanów R2P-P(SiMe3)Li z (R'3P)2PtCl2 zachodzą łatwo i prowadzą do wytworzenia bocznie (side-on) związanych fosfanofosfinidenowych kompleksów platyny [(η2-P=PR2)Pt(PR'3)2] (dla R=tBu, iPr, Et2N, iPr2N). Reakcja Ph2P-P(SiMe3)Li...
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Amino Acid and Peptide‐Based Antiviral Agents
PublikacjaA significant number of antiviral agents used in clinical practice are amino acids, short peptides, or peptidomimetics. Among them, several HIV protease inhibitors (e. g. lopinavir, atazanavir), HCV protease inhibitors (e. g. grazoprevir, glecaprevir), and HCV NS5A protein inhibitors have contributed to a significant decrease in mortality from AIDS and hepatitis. However, there is an ongoing need for the discovery of new antiviral...
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N-alkyl derivatives of 2-amino-2-deoxy-D-glucose
PublikacjaMono- i di-N-alkilowe pochodne 1,3,4,6-tetra-O-acetylo-2-amino-2-deoksy-beta-D-glukozy (alkil = metyl, etyl, propyl, butyl, pentyl, heksyl, benzyl) otrzymano w wyniku redukcyjnej alkilacji per-O-acetylo-D-glukozaminy. (N-etylo, N-propylo, N-butylo, N-pentylo, N-heksylo)-1,3,4,6-tetra-O-acetylo-2-amino-2-deoksy-beta-D-glukozy deacetylowano w celu podjęcia prób enzymatycznej fosforylacji. Wszystkie produkty scharakteryzowano za pomocą...
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Modeling of effect of plastic deformation on Barkhausen noise and magnetoacoustic emission in iron with 2% silicon
PublikacjaW modelowaniu zaadaptowano model Alessandro-Beatrice-Bertotti-Montorsi dla opisu ruchu granic nie-180 stopniowych oraz model Jiles-Atherton dla opisu wpływu plastycznej deformacji na natężenie efektu Barkhausena oraz emisji magnetoakustcznej.
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Electron collisions with methyl-substituted ethylenes: Cross section measurements and calculations for 2-methyl–2-butene and 2,3-dimethyl–2-butene
PublikacjaWe report electron-scattering cross sections determined for 2-methyl–2-butene [(H3C)HC==C(CH3)2] and 2,3-dimethyl–2-butene [(H3C)2C=C(CH3)2] molecules. Absolute grand-total cross sections (TCSs) were measured for incident electron energies in the 0.5–300 eV range, using a linear electron-transmission technique. The experimental TCS energy dependences for the both targets appear to be very similar with respect to the shape. In each...
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Microwave-assisted preparation of potato starch silicated with silicic acid
PublikacjaApplication of microwave irradiation for the silication of granular potato starch with silicic acid, and the properties of silicated starch were investigated. Potato starch was esterified on 20 min microwave irradiation of starch with silicic acid, applying the power of 450 or 800Wand, for comparison, on 120 min convectional heating of the reagent blend at 100 ◦C. The degree of esterification and the reaction efficiency did not...
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Beeswax And Palmitic Acid Utilization With Heat Pipes For Electronics Cooling
PublikacjaThis paper presents an experimental study of heat pipes supported by phase change materials (PCMs) coated at their adiabatic sections in application for electronics cooling. The PCMs investigated in this research were palmitic acid and beeswax, the latter being considered as a more cost-effective alternative. The study focused on three powers: 20W, 25W, and 30W. The experimental results revealed that the incorporation of palmitic...
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New conjugates of mycophenolic acid and their antiproliferative activity
PublikacjaThe new conjugates of mycophenolic acid (MPA) were obtained in the reaction of N6-(ω-aminoalkyl)adenosines with MPA in the presence of EDCI as a coupling reagent. New compounds 4a–h were evaluated on leukemia cell line (Jurkat) and PBMC from healthy donors. Length of the linker influenced observed activity. The compound 4b possessing 1,3-diamine spacer exhibited the most promising results and can be considered to further investigations.
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublikacjaSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid (RA), a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, RA exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Crystal Structure of N-(2-Benzoyl-4,5-dimethoxyphenethyl)-2-phenylacetamide
PublikacjaThe crystal structure of N-(2-benzoyl-4,5-dimethoxyphenethyl)-2-phenylacetamide indicates that the compound crystallizes in the monoclinic C2/c space group with eight molecules in the unit cell. The heteroatoms from the amide group form a chain of intermolecular N-H ··· O hydrogen bonds propagating along the b axis. The carbonyl group from the benzoyl substituent participates in short contacts with two H-atoms from the ethyl or...
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Hydroperoxyl radical and formic acid formation from common DNA stabilizers upon low energy electron attachment
Publikacja2-Amino-2-(hydroxymethyl)-1,3-propanediol (TRIS) and ethylenediaminetetraacetic acid (EDTA) are key components of biological buffers and are frequently used as DNA stabilizers in irradiation studies. Such surface or liquid phase studies are done with the aim to understand the fundamental mechanisms of DNA radiation damage and to improve cancer radiotherapy. When ionizing radiation is used, abundant secondary electrons are formed...
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Physical crosslinking of hyaluronic acid in the presence of phospholipids in an aqueous nano-environment
PublikacjaHyaluronic acid and phospholipids are two components in the synovial joint cavity that contribute to joint lubrication synergistically. Molecular dynamics simulations were performed and hydrogen bonds in hyaluronic acid were analyzed to identify specific sites that are responsible for its physical cross-linking. Two molecular masses of hyaluronic acid, 10 kDa and 160 kDa, were considered. We use molecular dynamics simulations and...
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Cytotoxic and Antioxidant Activities of Benzohydroxamic Acid Analogues
Publikacja20 benzohydroxamic acid analogues were synthesized and evaluated for their in vitro cytotoxicities against mouse mammary tumor cells as well as antioxidant activities against DPPH radical and superoxide anion. It was found that benzothiohydroxamic acids exhibit greater cytotoxicities than benzohydroxamic acids and N-isopropyl derivatives are more active than N-methyl ones. On the other hand, benzothiohydroxamic acids show more...
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Maternal smoking Modulates Fatty Acid Profile of Breast Milk
PublikacjaAIM: We hypothesized that the fatty acid composition of breast milk can be affected by a smoking habit in the mother. Consequently, this study verified whether maternal smoking modulates, and if so to what extent, the breast milk fatty acid profile. METHODS: The study included 20 postpartum women who declared smoking more than five cigarettes daily throughout a period of pregnancy and lactation, and 136 non-smoking postpartum women....
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An Improved Synthesis of Trisodium (R)-Homocitrate from Citric Acid
PublikacjaA method of synthesis of trisodium (R)-homocitrate starting from citric acid is reported. The procedure affords the final product of high optical purity with satisfactory yield.
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Molecular targets for antifungals in amino acid and protein biosynthetic pathways
PublikacjaFungi cause death of over 1.5 million people every year, while cutaneous mycoses are among the most common infections in the world. Mycoses vary greatly in severity, there are long-term skin (ringworm), nail or hair infections (tinea capitis), recurrent like vaginal candidiasis or severe, life-threatening systemic, multiorgan infections. In the last few years, increasing importance is attached to the health and economic problems...
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Acyl Meldrum's acid derivatives: application in organic synthesis
PublikacjaThis review is focused on one of the most important classes of Meldrum's acid derivatives commonly known as acyl Meldrum's acids. The preparation methods of these compounds are considered including the recently proposed and rather rarely used ones. The chemical properties of acyl Meldrum's acids are described in detail, including thermal stability and reactions with various nucleiophiles. The possible mechanisms of these transformations...
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Acid-aided epoxy-amine curing reaction as reflected in epoxy/Fe3O4 nanocomposites: Chemistry, mechanism, and fracture behavior
PublikacjaThis work seeks to answer the question whether or not the presence of acid functional groups accelerate epoxyamine curing reaction. Epoxy/Fe3O4 nanocomposite was considered as a case, where discussions are based on chemistry, mechanism behind curing reactions and fracture behavior influenced by acid assistance to crosslinking. Fe3O4 magnetic nanoparticles (MNPs) with nanosilica decorative layer (B-MNP) were synthesized and subsequently...
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Electron attachment and electron iozization of acetic acid clusters embedded in helium nanodroplets
PublikacjaThe effect of incident electrons on acetic acid clusters is explored for the first time. The acetic acid clusters are formed inside liquid helium nanodroplets and both cationic and anionic productsejected in to the gas phase aredetected by mass spectrometry.
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ASCORBIC ACID IN POLYURETHANE SYSTEMS FOR TISSUE ENGINEERING
PublikacjaThe introduction of the paper was devoted to the main items of tissue engineering (TE) and the way of porous structure obtaining as scaffolds. Furthermore, the significant role of the scaffold design in TE was described. It was shown, that properly designed polyurethanes (PURs) find application in TE due to the proper physicochemical, mechanical and biological properties. Then the use of L-ascorbic acid (L-AA) in PUR systems for...
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2-Coloring number revisited
Publikacja2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Weighted 2-sections and hypergraph reconstruction
PublikacjaIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
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N-Alkylation of D-glucosamine and 2-amino-2-deoxy-D-glucitol-6-phosphate
PublikacjaTematem pracy była synteza N-alkilowych pochodnych D-glukosaminy i 2-amino-2-deoxy-D-glukitolo-6-fosforanu
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Deep Eutectic Solvents or Eutectic Mixtures? Characterization of Tetrabutylammonium Bromide and Nonanoic Acid Mixtures
PublikacjaDeep eutectic solvents have quickly attracted the attention of researchers because they better meet the requirements of green chemistry and thus have the potential to replace conventional hazardous organic solvents in some areas. To better understand the nature of these mixtures, as well as expand the possibilities of their use in different industries, a detailed examination of their physical properties, such as density, viscosity,...
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Interaction of low energy electrons with formic acid monomer, dimer and trimer
PublikacjaConfigurations of the formic acid monomer, dimer and trimer are presented. We have calculated the total energies for these structures. We have considered also the negatively charged clusters and discussed the possible pathways of interaction of low energy electrons with monomers and clusters. Calculations have been executed using 6-311G** and 6-311++G** basis sets. The electron affinities of monomer and clusters are presented....
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Synthesis and biological activity of mycophenolic acid-amino acid derivatives
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CROSS SECTIONS CALCULATIONS FOR ELECTRON SCATTERING FROM RHODANINE AND CYANOACETIC ACID
PublikacjaCross sections for electron-impact ionization and for elastic electron scattering for rhodanine (C3H3NOS2) and cyanoacetic acid (C3H3NO2) have been calculated in wide impinging electron energy range.
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2-outer-independent domination in graphs
PublikacjaWe initiate the study of 2-outer-independent domination in graphs. A 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 at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...