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Search results for: N,O‐ ANDN,N‐DONORS
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2-hydroxypropanammonium benzenethiolate
PublicationZwiązek o wzorze C3H10ON+ x C6H5S- został otrzymany poprzez reakcję tiofenolu z 2-hydroksypropyloaminą. Oba fragmenty jonowe powiązane są wiązaniami wodorowymi N-H...S, O-H...S i N-H...O. Strukturę cząsteczkową i krystaliczną wyznaczono posługując się rentgenowską analizą strukturalną.
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Nanorurki węglowe domieszkowane azotem. Synteza i zastosowania
PublicationPrzedstawiono rodzaje i właściwości nanorurek węglowych. Szczególną uwagę poświęcono nanorurkom węglowym domieszkowanym azotem (N-CNT). Zaprezentowano sposoby syntezy oraz modyfikacji N-CNT. Omówiono także możliwości wykorzystania nanorurek jako elektrod w urządzeniach do magazynowania i konwersji energii elektrycznej oraz w elektrokatalizie.
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Convenient and Efficient Synthesis of Functionalized 2-Sulfenylindoles
PublicationA simple, efficient, and practical sulfenylation at the C2 position of N-tosylindoles under mild conditions was developed. The designed transformation is based on the reaction of N-tosylindoles with BuLi and S-alkyl, and S-aryl phosphorodithioates or thiotosylates to produce 2-sulfenylindoles in moderate to high yields. The presence of additional hydroxy, carboxy, or amino functionalities did not disturb the formation of products
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Modeling nitrous oxide production by a denitrifying-enhancedbiologically phosphorus removing (EBPR) activated sludge in thepresence of different carbon sources and electron acceptors
PublicationIn this study, the IWA Activated Sludge Model No. 2d (ASM2d) was expanded to identify the most important mechanisms leading to the anoxic nitrous oxide (N2O) production in the combined nitrogen (N) and phosphorus (P) removal activated sludge systems. The new model adopted a three-stage denitrification concept and was evaluated against the measured data from one/two-phase batch experiments carried out with activated sludge withdrawn...
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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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The searchlight problem for road networks
PublicationWe consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines, or two or more line segments, in the plane. Some of the intersections of the road network are occupied by stationary guards equipped with a number of searchlights, each of which can emit a single ray of light in any direction along the lines (or line segments) it is on. The goal is to detect the intruder,...
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Application of surface active amino acid ionic liquids as phase-transfer catalyst
PublicationFive structurally related morpholinium derived ionic liquids containing N-acetyl-glycinate anion were synthesized and their thermal stability, surface properties and activity as phase transfer catalysts investigated. The thermal properties were studied by differential scanning calorimetry, while the adsorption at the air/water interface and micellization behavior was analyzed by surface tension measurements, conductometry and isothermal...
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On the relationship between the structural and volumetric properties of solvated metal ions in O-donor solvents using new structural data in amide solvents
PublicationThe structures of the N,N-dimethylformamide (dmf), N,N-dimethylacetamide (dma), and N,N-dimethylpropionamide (dmp) solvated strontium and barium ions have been determined in solution using large angle X-ray scattering and EXAFS spectroscopy. The strontium ion has a mean coordination number (CN) between 6.2 and 6.8, and the barium ion has a mean CN between 7.1 and 7.8 in these amide solvents. The non-integer numbers indicates that...
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Antibiotic resistance in Staphylococcus aureus strains isolated from cows with mastitis in the eastern Poland and analysis of susceptibility of resistant strains to alternative non-antibiotic agents: lysostaphin, nisin and polymyxin B.
PublicationThe aim of the studies was analysis of resistance of Staphylococcus aureus isolates from bovine mastitis in eastern part of Poland to a set of 20 antibiotics and three alternative agents: lysostaphin, nisin and polymyxin B. Eighty-six out of 123 examined isolates were susceptible to all of 20 tested antibiotics (70 %). The highest percentage of resistance was observed in the case of β-lactam antibiotics: amoxicillin (n=22, 17.9...
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Nitrogen-incorporated boron-doped diamond films for enhanced electrochemical supercapacitor performance
PublicationThe electrochemical (EC) supercapacitor, known for its rapid charging, reliability, and versatile applications, demands optimized electrode characteristics and an understanding of their electrochemical behaviour. Although boron-doped diamond (BDD) holds promise as a supercapacitor electrode, a crucial gap exists in comprehending its material behaviour under specific growth conditions. Here, nitrogen-incorporated BDD (N-BDD) films...
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Crystallographic study of self-organization in the solid state including quasi-aromatic pseudo-ring stacking interactions in 1-benzoyl-3-(3,4-dimethoxyphenyl)thiourea and 1-benzoyl-3-(2-hydroxypropyl)thiourea
Publication1-Benzoylthioureas contain both carbonyl and thiocarbonyl functional groups and are of interest for their biological activity, metal coordination ability and involvement in hydrogen-bond formation. Two novel 1-benzoylthiourea derivatives, namely 1-benzoyl-3-(3,4-dimethoxyphenyl)thiourea, C₁₆H₁₆N₂O₃S, (I), and 1-benzoyl-3-(2-hydroxypropyl)thiourea, C₁₁H₁₄N₂O₂S, (II), have been synthesized and characterized. Compound (I) crystallizes...
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Rheology of potato starch chemically modified with microwave-assisted reactions
PublicationNative potato starch was sulfated, selenated, borated, silicated and zincatated by means of microwave-assisted reactions with varying doses of relevant reagents. Resulting products were characterized involving rheological behavior of pastes, their weight-average molecular weight (Mw), and radius of gyration (Rg). Most of the pastes showed shear-thinning behavior, with the flow behavior index (n) below unity. The pastes of starch...
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Analytical calculations of scattering lengths for a class of long-range potentials of interest for atomic physics
PublicationWe derive two equivalent analytical expressions for an $l$th partial-wave scattering length $a_{l}$ for central potentials with long-range tails of the form % \begin{math} \displaystyle V(r)=-\frac{\hbar^{2}}{2m}\frac{Br^{n-4}}{(r^{n-2}+R^{n-2})^{2}} -\frac{\hbar^{2}}{2m}\frac{C}{r^{2}(r^{n-2}+R^{n-2})}, \end{math} % ($r\geqslant r_{s}$, $R>0$). % For $C=0$, this family of potentials reduces to the Lenz potentials discussed in...
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Application of the Anammox Process for Treatment of Liquid Phase Digestate
PublicationThe liquid phase of the digestate (LPD) contains a relatively high concentration of nitrogen, with total ammonium nitrogen being the dominant form of nitrogen, as well as other essential nutrients such as phosphorus and potassium. Consequently, it must be treated before it is released into the environment. However, there are no reports of co-purification of LPD in the anammox process in sequencing batch reactor with granular sludge,...
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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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Elimination and migration of hydrogen in the vacuum-ultraviolet photodissociation of pyridine molecules
PublicationElimination of the excited hydrogen atoms H(n), n = 4–7, and hydrogen migration in formation of the excited NH(A 3Π) free radicals in the photodissociation of pyridine, C5H5N, molecules have been studied over the 17.5–70 eV photon energy range. In the measurements the photon-induced fluorescence spectroscopy technique has been applied. Both fragments are produced through excitation of pyridine molecules into higher-lying superexcited...
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Scheduling with precedence constraints: mixed graph coloring in series-parallel graphs.
PublicationW pracy rozważono problem kolorowania grafów mieszanych, opisujący zagadnienie szeregowania zadań, w którym zależności czasowe zadań mają charakter częściowego porządku lub wzajemnego wykluczania. Dla przypadku, w którym graf zależności jest szeregowo-równoległy, podano algorytm rozwiązujący problem optymalnie w czasie $O(n^3.376 * log n)$.
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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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Planar chiral dianthranilide and dithiodianthranilide molecules: optical resolution, chiroptical spectra, and molecular self-assembly.
PublicationChiralny planarnie diantranilid został rozdzielony na enancjomery przy użyciu chlorku (-)-(1S,4R)-kamfanoilu. Konfigurację absolutną (S)-enancjomeru ustalono na podstawie analizy rentgenograficznej monokryształu jego N,N'-dikamfoilopochodnej. Natomiast rozdział ditiodiantranilidu na enancjomery przeprowadzono poprzez tworzenie związków inkluzyjnych z (R,R)-1,2-diaminocykloheksanem. Otrzymanemu w ten sposób enancjomerowi przypisano...
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ZASTOSOWANIE PROCESU ANAMMOX W OCZYSZCZANIU WÓD POOSADOWYCH
PublicationNiniejszy artykuł przedstawia możliwości biologicznego usuwania azotu z wód poosadowych pochodzących z procesów przeróbki osadów. Otrzymane w połączonym procesie nitrytacja-anammox szybkości usuwania azotu, porównano z osiąganymi w konwencjonalnym procesie nitryfikacjadenitryfikacja. Obserwowana objętościowa szybkość procesu anammox mieści się w zakresie 0,245–0,262 kg N m-3d-1i jest bardzo zbliżona do wartości prezentowanych w...
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A Novel Coupling Matrix Synthesis Technique for Generalized Chebyshev Filters With Resonant Source–Load Connection
PublicationThis paper reports a novel synthesis method for microwave bandpass filters with resonant source–load connection. In effect, a network realizing N+1 transmission zeros (where N is the number of reflection zeros) is obtained. The method is based on a prototype transversal coupling matrix (N+2, N+2) with source and load connected by a resonant circuit formed by a capacitor in parallel with a frequency-invariant susceptance. To complement...
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Distributed largest-first algorithm for graph coloring.
PublicationW artykule zaprezentowano rozproszony, probabilistyczny algorytm kolorowania grafów. Kolorowanie uzyskane jest optymalne lub prawie optymalne dla takich klas grafów jak koła dwudzielne, gąsienice czy korony. Udowodniono, że algorytm ten działa w czasie O(D^2 log n) rund dla dowolnego grafu n wierzchołkowegoo stopniu maksymalnym D.
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Synthesis and antimicrobial activity of 6-sulfo-6-deoxy-D-glucosamine and its derivatives
Publication6-Sulfo-6-deoxy-D-glucosamine (GlcN6S), 6-sulfo-6-deoxy-D-glucosaminitol (ADGS) and their N-acetyl and methyl ester derivatives have been synthesized and tested as inhibitors of enzymes catalyzing reactions of the UDP-GlcNAc pathway in bacteria and yeasts. GlcN6S and ADGS at micromolar concentrations inhibited glucosamine-6-phosphate (GlcN6P) synthase of microbial origin. The former was also inhibitory towards fungal GlcN6P N-acetyl...
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The role of the combined nitrogen-sulfur-carbon cycles for efficient performance of anammox-based systems
PublicationThe combined anammox/mixotrophic denitrification process was conducted in two granular sequencing batch reactors (SBRs) during a 200-day operation. Both reactors were fed with synthetic medium, but SBR2 was enriched with additional sulfate (SO4 2 ) which influenced sulfate reduction ammonium oxidation (SRAO) and heterotrophic reduction of SO4 2 by sulfate reducing bacteria. It was hypothesized that the addition of SO4 2 could...
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Łączenie danych pomiarowych z dodatkową wiedzą metrologiczną w celu oceny niepewności pomiaru
PublicationPrzedstawiono modus operandi w ocenie niepewności pomiaru dla krótkich serii pomiarowych. Metoda wykorzystuje dodatkową wiedzę metrologiczną do zwiększenia liczby stopni swobody rozkładu t-Studenta, uzyskiwanego w wyniku bayesowskiej analizy wyników pomiarów. W rezultacie możliwe jest oszacowanie niepewności standardowych dla najkrótszych serii pomiarowych, o długości n=2 i n=3.
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Green's function for the wavized Maxwell fish-eye problem
PublicationRozpatrzono niezależne od czasu skalarne równanie falowe dla ośrodka typu ''rybie oko'' Maxwella w przestrzeni R^N (N >=2). Pokazano, że równanie to posiada unikalne własności transformacyjne względem inwersji w pewnej klasie hipersfer. Wykorzystano ten fakt do znalezienia zamkniętej postaci funkcji Greena, oraz uogólnionej funkcji Greena, dla wyjściowego równania.
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Efficient Method for the Synthesis of Functionalized Basic Maleimides
PublicationA three-step procedure involving Diels-Alder condensation of maleic anhydride with furane, formation of N-substituted imide upon reaction with appropriate diamine and a final retro Diels-Alder regeneration of the maleic carbon-carbon double bond is proposed for an unequivocal synthesis of N-substituted basic maleimides. The novel method is characterized by mild reaction conditions, easy work-up, high yields and no need for additional...
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Gradient versus proper gradient homotopies
PublicationWe compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classi cations are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from R^n to R^n and proper gradient maps from R^2 to R^2 with the Brouwer degree greater or equal to zero.
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Cobalt(II) tri-tert-butoxysilanethiolates with bidentate spacer ligands
PublicationOtrzymano szereg nowych tri-tert-butoksysilanotiolanów Co(II) z dwudonorowymi N,N'-ligandami takimi jak pirazyna, chinoksalina i 4,4'-bipy. W przypadku pirazyny i chinoksaliny otrzymane kompleksy są bimetaliczne, w których atomy metali połączone są odpowiednią aminą. Użyty do syntezy 4,4'-bipy pozwolił na otrzymanie dwóch odmian polimorficznych kompleksu {[Co{SSi(tBuO)3}2]2(μ-4,4'bipy)}, a także polimeru koordynacyjnego o wzorze...
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Algorithms for testing security in graphs
PublicationIn this paper we propose new algorithmic methods giving with the high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] \cap S| >= |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based...
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Wykorzystanie języka VHDL do modelowania układów pracujących w logice wielowartościowej i arytmetyce resztkowej
PublicationW pracy przedstawiono bibliotekę zbudowaną w oparciu o język VHDL, przeznaczoną do symulacji elementów pracujących w logice wielowartościowej i w arytmetyce resztowej. Zaprezentowano również bramki prądowe - nowe elementy logiczne cechujące się znacznie mniejszym poziomem szumu cyfrowego. Pokazano przykłady sumatorów działających w logice wielowartościowej z podstawą N, lub w arytmetyce resztowej modulo N. Wyróżniającą cechą sumatorów...
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Soil and groundwater contamination as a result of sewage sludge land application
PublicationThe leaching of chemical compounds (N-NO3, N-NH4, Norg, P-PO4, Ptot) and trace elements (Cd, Cu, Cr, Ni, Zn, and Pb) from sewage sludge and their migration through the soil profile was the subject of the study. The column experiments were carried out under atmospheric conditions corresponding to naturally occurring storm events - sewage sludge amended soil was irrigated with high rates of water. The column filter media used in...
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Seasonal changes of the concentrations of mineral forms of nitrogen and phosphorus in watercourses in the agricultural catchment area (Bay of Puck, Baltic Sea, Poland)
PublicationThe Baltic Region countries are obliged to meet the stringent limits of N and P discharge set by HELCOM for 2021. Area sources of pollution, including agriculture, are considered the main contributors of biogenic compounds. The Bay of Puck as an inner part of the Baltic Sea is particularly sensitive to eutrophication caused by nutrient in flow from agricultural lands. Rivers and streams inflowing to the Bay of Puck transport nitrogen...
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Modeling organic nitrogen conversions in activated sludge bioreactors
PublicationFor biological nutrient removal (BNR) systems designed to maximize nitrogen removal, the effluent total nitrogen (TN) concentration may range from 2.0 to 4.0 g N/m3 with about 25-50% in the form of organic nitrogen (ON). In this study, current approaches to modeling organic N conversions (separate processes vs. constant contents of organic fractions) were compared. A new conceptual model of ON conversions was developed and combined...
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Bee Pollen and Bee Bread as a Source of Bacteria Producing Antimicrobials
PublicationThe principal objective of the study was the isolation and identification of bacteria that are present in mature bee bread (BB) and dried (ready for selling and consumption) bee pollen (BP). Obtained isolates were screened for their potential to inhibit select human pathogenic bacteria and their ability to produce enzymes of particular industrial importance. Four and five samples of BP and BB, respectively, were used for the study....
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Process control of air stream deodorization from vapors of VOCs using a gas sensor matrix conducted in the biotrickling filter (BTF)
PublicationThis article presents the validity, advisability and purposefulness of using a gas sensor matrix to monitor air deodorization processes carried out in a peat-perlite-polyurethane foam-packed biotrickling filter. The aim of the conducted research was to control the effectiveness of air stream purification from vapors of hydrophobic compounds, i.e., n-hexane and cyclohexane. The effectiveness of hydrophobic n-hexane and cyclohexane...
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Application of a hybrid mechanistic/machine learning model for prediction of nitrous oxide (N2O) production in a nitrifying sequencing batch reactor
PublicationNitrous oxide (N2O) is a key parameter for evaluating the greenhouse gas emissions from wastewater treatment plants. In this study, a new method for predicting liquid N2O production during nitrification was developed based on a mechanistic model and machine learning (ML) algorithm. The mechanistic model was first used for simulation of two 15-day experimental trials in a nitrifying sequencing batch reactor. Then, model predictions...
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Magazynowanie energii elektrycznej i gospodarka wodorowa
PublicationW artykule dokonano przegl ą du aktualnych technologii magazynowania energii elektrycznej oraz zestawiono uzyskiwane parametry w aspekcie zastosowa ń w zasobnikach systemowych. Przedstawiono studium mo ż liwo ś ci magazynowania energii z odnawialnych ź róde ł energii (O Ź E) w zasobnikach akumulatorowych i elektrowniach szczytowo-pompowych w Polsce. Omówiono tak ż e mo ż liwo ś ci wykorzystania...
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Definicje kognitywne osoby niepełnosprawnej intelektualnie – na wybranych przykładach
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Complex multiplier based on the polynomial residue number system
PublicationPrzedstawiono próbę zaprojektowania mnożnika zespolonego 4x4 opartego na algorytmie Skavantzosa i Stouraitisa. W algorytmie stosuje siękodowanie liczb n-bitowych jako wielomianów stopnia 7 w pierścieniu wielomianów modulo (x^8-1) z n/4-bitowymi współczynnikami. Mnożenie zespolone jest wykonywane jako 8-punktowy splot cykliczny. Podanoopóżnienie i złożoność sprzętową jak również porównanie ze standardowym.rozwiązaniem.
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Formation, crystal and molecular structures of heteroleptic zinc(II) tri-tert-butoxysilanethiolates with ZnNO2S2 and ZnN2S2 coordination pattern.
PublicationZsyntetyzowano pięć tri-tert-butoksysilanotiolanów cynku zawierających jako dodatkowe ligandy heterocykliczne, zasady azotowe. Wzór ogólny tych kompleksów to Zn(SSi(OBut)3)2L, gdzie L=alfa-pikolina, 2,4-lutydyna, N-metyloimidazol lub Zn(SSiOBut)3)2L2, gdzie L=N-metyloimidazol lub pirydyna. Określono strukturę krystaliczną otrzymanych związków oraz zmierzono widma IR i NMR.
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Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines
PublicationWe consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s1, s2, and s3 to minimize the schedule length. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We how that if the graph is 2-chromatic then the problem can be solved in O(n^2) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1>s2=s3.
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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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New coordination polymers based on a V-shaped ligand and lanthanides: Structural description and symmetry-luminescence correlation using europium as a probe
PublicationWe have synthesized new luminescent coordination polymers using 4,4'-sulfonyldibenzoic acid (H2SDA) and several lanthanide ions by open crystallization in DMF. Three different 1-D structures were obtained, as determined by single-crystal X-ray diffraction: [La(η2-NO3)(μ-SDA)(DMF)3]n (1), [Sm(η2-NO3)(μ-SDA)(DMF)2 2DMF]n (3), [Ln(η2-NO3)(μ-SDA)(DMF)2 DMF]n (Ln ¼ Eu (4), Dy (5), Ho (6), Er (7), Tm (8) and Lu(9)). A 2-D structure,...
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Generating fractal tiles using Voronoi diagrams
PublicationPraca opisuje szczególną klasę podziałów powierzchni n-wymiarowego torusa na komórki o fraktalnym brzegu. Zbiór komórek przejawia nietypowe własności samopodobieństwa, może zostać użyty do wypełnienia przestrzeni R^n w sposób periodyczny lub aperiodyczny ze zmienną gęstością podziałów. Zaproponowany został algorytm do generowania takich podziałów używając diagramów Woronoja. Opisana metoda może mieć zastosowania w grafice komputerowej.
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Electron-scattering total cross sections for complex molecules: group additivity rule
PublicationZaprezentowano całkowite przekroje czynne na rozpraszanie elektronów na dwóch rodzinach drobin: pierwszej - zawierającej azot jako atom centralny [N(CH3)3, NH2CH3, NH3]oraz drugiej - rodzinę eterów cyklicznych [c-(CH2)nO, gdzie n=2-5]. Zostało pokazane, że TCS dla niektórych drobin wieloatomowych można wyznaczyć na podstawie wyników TCS dla drobin o prostszej budowie lub ich fragmentów.
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Podstawy określania współczynników równoważności obciążenia osi do projektowania nawierzchni drogowych
PublicationPraca przedstawia rys historyczny rozwoju charakterystyki obciążenia dróg przez ruch. Omówiono wpływ przyjęcia wielkości obciążenia standardowego osi równoważnej na wyniki analizy ruchu. Przedstawiono metodę doświadczalną AASHTO i współczynniki obliczone według tej metody w przypadku polskich warunków. Podano wzory do obliczeń współczynników dla osi podwójnych i potrójnych. Przedstawiono metodę francuską i jej porównanie z metodą...
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On-line Search in Two-Dimensional Environment
PublicationWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids:...
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Collision-free network exploration
PublicationMobile agents start at different nodes of an n-node network. The agents synchronously move along the network edges in a collision-free way, i.e., in no round two agents may occupy the same node. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest time required to reach a configuration in which each agent has visited all nodes and returned to its starting location. In...
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On the Limiting Distribution of Lempel-Ziv’78 Redundancy for Memoryless Sources
PublicationWe study the Lempel-Ziv'78 algorithm and show that its (normalized) redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper, in particular, by presenting a new simplified proof of the central limit theorem (CLT) for the number of phrases in the LZ'78 algorithm. We first analyze the asymptotic behavior of the total path length in the associated digital search...