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Stable Field Electron Emission and Plasma Illumination from Boron and Nitrogen Co‐Doped Edge‐Rich Diamond‐Enhanced Carbon Nanowalls
PublikacjaSuperior field electron emission (FEE) characteristics are achieved in edge-rich diamond-enhanced carbon nanowalls (D-ECNWs) grown in a single-step chemical vapor deposition process co-doped with boron and nitrogen. The structure consists of sharp, highly conductive graphene edges supplied by a solid, diamond-rich bottom. The Raman and transmission electron microscopy studies reveal a hybrid nature of sp3-diamond and sp2-graphene...
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Exploring novel Cd(ii) complexes with 5-methyl-4-imidazolecarboxaldehyde: synthesis, structure, computational insights, and affinity to DNA through switchSense methodology
PublikacjaA series of four Cd(II) complexes with 5-methyl-4-imidazolecarboxaldehyde (L) with different inorganic anions within or outside the coordination sphere of general formula: [CdCl2 L2 ] (1), [CdBr2 L 2] (2), [CdI2L 2] (3), and [CdL4 ](PF6 )2 ·3H2 O (4) was synthesized through one-step and two-step reactions, respectively. All complexes were obtained as colorless crystals without the need for recrystallization and exhibited solubi- lity...
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Cross-Linking, Morphology, and Physico-Mechanical Properties of GTR/SBS Blends: Dicumyl Peroxide vs. Sulfur System
PublikacjaIn this work, ground tire rubber and styrene–butadiene block copolymer (GTR/SBS) blends at the ratio of 50/50 wt%, with the application of four different SBS copolymer grades (linear and radial) and two types of cross-linking agent (a sulfur-based system and dicumyl peroxide), were prepared by melt compounding. The rheological and cross-linking behavior, physico-mechanical parameters (i.e., tensile properties, abrasion resistance,...
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Boron doped Nanocrystalline Diamond-Carbon Nanospike Hybrid Electron Emission Source
PublikacjaElectron emission signifies an important mechanism facilitating the enlargement of devices that have modernized large parts of science and technology. Today, the search for innovative electron emission devices for imaging, sensing, electronics, and high-energy physics continues. Integrating two materials with dissimilar electronic properties into a hybrid material is an extremely sought-after synergistic approach envisioning a...
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Thermal and Mechanical Behavior of Elastomers Incorporated with Thermoregulating Microcapsules
PublikacjaPolyurethane (PU) is one of the principal polymers in the global plastic market thanks to its versatility and continuous improvement. In this work, PU elastomeric materials having thermoregulating properties through the incorporation of microcapsules (mSD-(LDPE·EVA-RT27)) from low-density polyethylene and vinyl acetate containing paraffin®RT27 as PCM were produced. Elastomers were synthesized while varying the molar ratio [NCO]/[OH]...
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POM/EVA Blends with Future Utility in Fused Deposition Modeling
PublikacjaPolyoxymethylene (POM) is one of the most popular thermoplastic polymers used in the industry. Therefore, the interest in its potential applications in rapid prototyping is understandable. Nevertheless, its low dimensional stability causes the warping of 3D prints, limiting its applications. This research aimed to evaluate the effects of POM modification with ethylene-vinyl acetate (EVA) (2.5, 5.0, and 7.5 wt.%) on its processing...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Alkohol-społeczny problem XXI wieku. Zastosowanie biowskaźników spożywania alkoholu w diagnostyce medycznej.
PublikacjaAlkohol etylowy jest legalną i ogólnodostępną substancją o działaniu psychoaktywnym. Spożywany w niewielkich ilościach może pozytywnie wpływać na zdrowie, ale jego nadmierna konsumpcja powoduje silne uzależnienie. Może być to przyczyną agresywnych zachowań, przemocy w rodzinie, problemów w kontaktach z ludźmi, problemów z prawem, samobójstw, wypadków samochodowych oraz problemów finansowych. Dlatego też, szybka i jednoznaczna diagnostyka...
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INWESTYCJE A ZATRUDNIENIE W POLSCE W PERSPEKTYWIE FINANSOWE 2007-2013
PublikacjaNakłady inwestycyjne przedsiębiorstw traktowane są jako jeden z głównych czynników wzrostu gospodarczego. Ich wielkość i dynamika mogą mieć wpływ na zmiany w poziomie zatrudnienia. Światowy kryzys finansowy przyczynił się do spowolnienia dynamiki wzrostu oraz gwałtownego spadku w 2009 roku PKB w większości gospodarek świata. We wspomnianym okresie w Polsce zaobserwowano spowolnienie gospodarcze, które miało wpływ na decyzje...
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Tradycyjne i nowoczesne kanały dystrybucji wykorzystywane w procesie świadczenia usług ubezpieczeniowych dojrzałym konsumentom
PublikacjaPrzedmiotem artykułu są usługi ubezpieczeniowe świadczone z wykorzystaniem tradycyjnych i nowoczesnych kanałów dystrybucji. W artykule skoncentrowano się na osobach powyżej 50 roku życia, szczególnie narażonych na zjawisko wykluczenia cyfrowego. Na podstawie przeglądu literatury sformułowano hipotezę badawczą: cechy społeczno – demograficzne osób powyżej 50 roku życia wpływają na ich skłonność do korzystania z usług ubezpieczeniowych...
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Wartości rekomendowane wskaźników sprawności działania dla przedsiębiorstw z sektora MSP
PublikacjaNiniejszy artykuł poświęcony jest zagadnieniu sprawności działania małych i średnich przedsiębiorstw. W trakcie przeprowadzonych badań wykorzystano 34 820 sprawozdania finansowe przedsiębiorstw. Dla potwierdzenia zróżnicowania sprawności działania w zależności od przynależności sektorowej przedsiębiorstwa wykorzystano test nieparametryczny Kruskala – Wallisa. Zawarte w artykule wyniki badań dowodzą, że MSP należące do różnych działów...
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Wzmocnienie przestrzennych dźwigarów kratowych z zastosowaniem dodatkowego podparcia i sprężenia
PublikacjaPodczas obowiązkowego przeglądu technicznego obiektu budowlanego stwierdzone zostały deformacje stalowych prętów wykratowania przestrzennych dźwigarów dachowych. Opinie techniczne dotyczące stanu technicznego potwierdziły wstępnie wykryte nieprawidłowości i nakazywały podjęcie kroków zaradczych w postaci opracowania koncepcji naprawy, a w jej ślad projektu budowlanego i wykonawczego. Do czasu naprawy obiekt został dopuszczony do...
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Metoda diagnostyki łożysk na podstawie analizy przebiegów prądu i napięcia zasilającego silnik indukcyjny.
PublikacjaW niniejszej monografii przedstawiono oryginalne podejście i realizację diagnostyki łożysk silników indukcyjnych przy użyciu metody opartej na pomiarach i analizie iloczynu wartości chwilowych prądu i napięcia zasilającego maszyny. Uzyskane wyniki badań eksperymentalnych na obiektach rzeczywistych okazały się zbieżne z wynikami badań symulacyjnych i potwierdziły, że powstanie uszkodzeń łożysk w silniku skutkuje pojawieniem się...
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Konkurencyjność w handlu usługami wybranych krajów Europy Środkowo-Wschodniej
PublikacjaCelem artykułu jest ocena pozycji konkurencyjnej w handlu usługami wybranych krajów Europy Środkowo-Wschodniej – Czech, Estonii, Litwy, Łotwy, Polski, Słowacji oraz Węgier na tle gospodarki światowej. Dane wykorzystane do analizy pochodzą z bazy danych WIOD i obejmują lata 1995 – 2011. Podstawą oceny pozycji konkurencyjnej jest wskaźnik RCA obliczony na podstawie krajowej wartości dodanej oraz na podstawie eksportu brutto. Źródłem...
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Metody projektowania ułatwiającego testowanie dla układów cyfrowych
PublikacjaPrzedstawiono przegląd metod ułatwiających testowanie DFT (Design for Testability) dla układów cyfrowych. Zaprezentowano metody stosowane na poziomie układów scalonych, pakietów oraz systemów elektronicznych. Pokazano heurystyczne metody projektowania pozwalające na zwiększenie sterowalności i obserwowalności układów oraz metody strukturalne, a wśród nich układy BILBO (Built-In Logic Block Observer), BIST (Built-In Self Test),...
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Therapeutic intervention by the simultaneous inhibition of DNA repair and type I or type II DNA topoisomerases: one strategy, many outcomes
PublikacjaMany anticancer drugs reduce the integrity of DNA, forming strand breaks. This can cause mutations and cancer or cell death if the lesions are not repaired. Interestingly, DNA repair-deficient cancer cells (e.g., those with BRCA1/2 mutations) have been shown to exhibit increased sensitivity to chemotherapy. Based on this observation, a new therapeutic approach termed 'synthetic lethality' has been developed, in which radiation...
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THE ESSENCE OF THE TRANSFORMATION OF SOCIO-ECONOMIC RELATIONS IN THE NATIONAL ECONOMY: THEORETICAL AND METHODOLOGICAL ASPECT
PublikacjaThe article is devoted to a thorough study of the theoretical and methodological foundations of the essence of the transformation of socio-economic relations of the national economy. Based on the study of scientific sources, a proper definition of the concept of "transformation of socio-economic relations" was formed. It is proposed to consider transformational processes from the point of view of their direct or indirect impact...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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The use of Response Surface Methodology for reliability estimation of aluminum silo subjected to wind load
PublikacjaAn axisymmetric aluminum silo model with a single, standardized geometric imperfection of its lateral surface is considered. The silo is wind – loaded only. The paper is focused on the critical, or limit value of wind pressure, both producing a loss of stability of the silo. This value is affected by vertical coordinate (position) of the imperfection and the angular relation between the imperfection and the wind direction. Reliability...
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SHM System of the Roof Structure of Sports Arena “Olivia”
PublikacjaThe paper presents a structural health monitoring system of the Sports Arena “Olivia” in Gdansk, Poland. The system was installed because of doubts about the roof stability due to observed buckling of the steel truss members. The SHM system was based on nonlinear FEM models used for detection of type of near failure modes of the roof. The application of detailed FEM model in current state updated on data from in situ loading testes...
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Method of lines for nonlinear first order partial functional differential equations.
PublikacjaClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublikacjaInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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Meiothermus ruber cells as β-galactosidase activity biocatalyst
PublikacjaThe current study allowed to establish the possibility of using whole cells of thermophilic bacteria Meiothermus ruber as a biocatalyst with β-galactosidase activity. β-galactosidases are used for hydrolysis of lactose as well as for oligosaccharides synthesis. The advantages of using whole bacterial cells catalysis is not only elimination of tedious, expensive protein isolation and/or purification but also stabilization of enzymes...
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Selection of energy storage units by genetic algorithm for mitigating voltage deviations
PublikacjaIn recent years, energy storage units have become very popular. They are applied both for economic and technical purposes. Unfortunately, the cost of such devices is still high and selecting their proper location and rated power have to be performed precisely. In this paper, a Genetic-Algorithm-based optimization method for selecting the best configuration of energy storage units in the power network is proposed. The presented...
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Selected dynamic properties of adaptive proportional observer of induction motor state variables
PublikacjaThis paper presents problems related to the design and the stability of adaptive proportional observer which is used for estimation of magnetic flux and motor speed in sensorless control systems of induction motor. The gain matrix of the observer was chosen by genetic algorithm and alternatively by pole placement method. It has been shown that adaptive proportional observer is stable if the...
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CGO FILMS ON YSZ ELECTROLYTE FABRICATED BY SPRAY PYROLYSIS FOR SOFC
PublikacjaINTRODUCTION Solid oxide fuel cells are one of the fastest developing energy converters. The advancement introduced by research community provides steady state progress is stability and performance of the fuel cells. Significant influence on the cell’s performance and stability is related to cell design. The simplest design just consists of an anode, a solid electrolyte and a cathode. However, in order to improve the properties,...
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Fabrication of the cross-linked PVA/TiO2/C nanocomposite membrane for alkaline direct methanol fuel cells
PublikacjaA crosslinked Poly(vinyl alcohol) based composite membrane was developed through a phase inversion process for use in alkaline direct methanol fuel cells (ADMFCs). The titanium dioxide (TiO2) and carbon nanoparticles (NPs) have been incorporated into the PVA polymer matrix to improve the mechanical and thermal properties. The membrane samples were further modified with maleic acid, a carboxylic acid acting as the cross-linker,...
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Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems
PublikacjaThe problem of state estimation (reconstruction of the state vector) for a given class of biochemical systems under uncertain system dynamics has been addressed in this paper. In detail, the bioreactor at a water resource recovery facility represents the considered biochemical systems. The biochemical processes taking place in the bioreactor have been modelled using an activated sludge model. Based on this model, an appropriate...
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Thermoplastic starch nanocomposites using cellulose-rich Chrysopogon zizanioides nanofibers
PublikacjaGreen thermoplastic starch (TPS) nanocomposite films aided by cellulose nanofibers (CNFs) from Chrysopogon zizanioides roots were developed and characterized. When compared to other lignocellulosic fibers, Chrysopogon zizanioides roots revealed exceptionally high cellulose content (~48%). CNFs were separated using an environmentally friendly acid isolation technique that included three stages: (i) alkali treatment; (ii) bleaching;...
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Imidazole-Based Lithium Salt LiHDI as a Solid Electrolyte Interphase-Stabilising Additive for Lithium-Conducting Electrolytes
PublikacjaLithium salt LiHDI (lithium 4,5-dicyano-2-(n-heptafluoropropyl)imidazolide) is proposed as a solid electrolyte interphase-stabilising additive for lithium-ion batteries, which can be added in a smaller amount than fluoroethylene carbonate (FEC) and vinylene carbonate (VC) additives. Electrolytes containing either lithium 4,5-dicyano-2-(trifluoromethyl)imidazolide (LiTDI) or battery-standard LiPF6 were tested with various amounts...
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Improving the Performance of a Graphite Foil/Polyaniline Electrode Material by a Thin PEDOT:PSS Layer for Application in Flexible, High Power Supercapacitors
PublikacjaIn this study, we present a novel strategy for enhancing polyaniline stability and thus obtaining an electrode material with practical application in supercapacitors. A promising (graphite foil/polyaniline/poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) GF/PANI/PEDOT:PSS) electrode material was characterized and used in the construction of a symmetric supercapacitor that provides an outstanding high power density. For this...
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Evaluation and rationale of the performance of several elastomeric composites incorporating devulcanized EPDM
Publikacjathylene Propylene Diene rubber (EPDM), is present in many applications. However, its crosslinked structure makes difficult its recycling. The use of devulcanized EPDM, (dEPDM) as a component of elastomeric composites, is a real possibility to reuse EPDM scraps. In this study, three matrices (natural rubber (NR), styrene butadiene rubber (SBR) and EPDM rubber) have been tested including devulcanized EPDM as a recycled component....
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Thermodynamic, Anticoagulant, and Antiproliferative Properties of Thrombin Binding Aptamer Containing Novel UNA Derivative
PublikacjaThrombin is a serine protease that plays a crucial role in hemostasis, fibrinolysis, cell proliferation, and migration. Thrombin binding aptamer (TBA) is able to inhibit the activity of thrombin molecule via binding to its exosite I. This 15-nt DNA oligonucleotide forms an intramolecular, antiparallel G-quadruplex structure with a chair-like conformation. In this paper, we report on our investigations on the influence of certain...
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Chemical structures, rheological and physical properties of biopolyols prepared via solvothermal liquefaction of Enteromorpha and Zostera marina biomass
PublikacjaIn this work, liquefied biomass from the Baltic Sea was used for the preparation of rigid polyurethane (PUR) foams. The biomass contained 10 wt% of Enteromorpha macroalgae and 90 wt% of Zostera marina seagrass characterized by a high content of cellulose. The influence of time, temperature and the type of solvent on the efficiency of the liquefaction process and properties of biopolyols was determined. Obtained materials were analyzed...
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Material Design and Optimisation of Electrochemical Li-Ion Storage Properties of Ternary Silicon Oxycarbide/Graphite/Tin Nanocomposites
PublikacjaIn this work, we present the characterization and electrochemical performance of various ternary silicon oxycarbide/graphite/tin (SiOC/C/Sn) nanocomposites as anodes for lithium-ion batteries. In binary SiOC/Sn composites, tin nanoparticles may be produced in situ via carbothermal reduction of SnO2 to metallic Sn, which consumes free carbon from the SiOC ceramic phase, thereby limiting the carbon content in the final ceramic nanocomposite....
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Tuning the Laser-Induced Processing of 3D Porous Graphenic Nanostructures by Boron-Doped Diamond Particles for Flexible Microsupercapacitors
PublikacjaCarbon (sp3)-on-carbon (sp2) materials have the potential to revolutionize fields such as energy storage and microelectronics. However, the rational engineering and printing of carbon-on-carbon materials on flexible substrates remains a challenge in wearable electronics technology. This study demon-strates the scalable fabrication of flexible laser-induced graphene (LIG)-boron doped diamond nanowall (BDNW) hybrid nanostructures...
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Investigation into the Effect of Spinel Pigments on the Photostability and Combustion Properties of Ethylene-Norbornene Copolymer
PublikacjaMulticolor ethylene-norbornene (EN) composites filled with three different spinel pigments (Cobalt Green-PG50, Zinc Iron Yellow-PY 119, Praseodym Yellow-PY159) were prepared by melt mixing and characterized in terms of their stability under destructive environmental conditions. The EN films were subjected to accelerated aging by ultraviolet (UV) photooxidation for 300 h, 600 h, or 900 h. The mechanical performance of the EN composites...
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The geodetic monitoring of the engineering structure – a practical solution of the problem in 3D space
PublikacjaThe study raises the issues concerning the automatic system designed for the monitoring of movement of controlled points, located on the roof covering of the Forest Opera in Sopot. It presents the calculation algorithm proposed by authors. It takes into account the specific design and location of the test object. High forest stand makes it difficult to use distant reference points. Hence the reference points used to study the stability...
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Modelling of Different Aeration Modes Influencing Processes in SBR Bioreactor
PublikacjaCurrently, computer modelling together with the simulation tools tailored for that purpose constitute a very important element in planning technological changes within wastewater treatment plant. From the point of view of the WWTP operator every modification should be introduced in order to improve the quality of treated sewage with the lowest financial outlays. These requirements can be met by using computer programmes to effectuate...
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Knowledge Management for Managing Crisis in Tourism: Theoretical insights
PublikacjaCOVID-19 has caused an unprecedented crisis affecting the entire tourism industry. Accommodation, food, and travel sectors have been affected by the decreased number of visitors, which had a ripple effect on the financial situation of the whole industry. The purpose of this work is a better understanding of the role of knowledge management in terms of mitigating the crisis in the tourism sector, as well as a development of the...
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Gender as a Moderator of the Double Bias of Mistakes – Knowledge Culture and Knowledge Sharing Effects
PublikacjaThere is no learning without mistakes. The essence of the double bias of mistakes is the contradiction between an often-declared positive attitude towards learning from mistakes, and negative experiences when mistakes occur. Financial and personal consequences, shame, and blame force desperate employees to hide their mistakes. These adverse outcomes are doubled in organizations by the common belief that managers never make mistakes,...
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Corporate social responsibility and forward default risk under firm and industry heterogeneity
PublikacjaObjective: This study aims to evaluate the impact of corporate social responsibility on forward default risk (FDR) under the setting of firm and industry heterogeneity. Research Design & Methods: This study evaluated the impact of corporate social responsibility (CSR) on FDR using the data of 497 companies from 2007-2021 in the S&P 500 index, taking into account firm and industry heterogeneity aspects. This study utilized instrumental...
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The Response of Selected Domestic Capital Markets on the Development of COVID-19 Pandemic – a Broader View
PublikacjaObjective: The study examines how the record of the first, hundredth, thousandth, ten-thousandth, one-hundred-thousandth, and millionth cases of COVID-19 affected investor behaviour in capital markets. It also looks at whether the month in which the first case was recorded in a given market affected the direction and strength of investor reactions. Lastly, it verifies whether the two announcements made by the WHO related to COVID-19...
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Exchange-traded products in Germany: development and substitution of exchange-traded funds, exchange-traded commodities and exchange-traded notes.
PublikacjaResearch background: Exchange-traded products (ETPs) are one of the most rapidly growing categories of financial products. Their fast development has been boosted by innovative features. Three main categories of ETPs are exchange-traded funds (ETFs), exchange-traded commodities (ETCs) and exchange-traded notes (ETNs). ETCs and ETNs remain least known, even though their number on some stock exchanges is high. In Europe, Germany...
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Analysing Ways to Achieve a New Urban Agenda-Based Sustainable Metropolitan Transport
PublikacjaThe New Urban Agenda (NUA) sets a new vision of sustainable urban development to help cities deal with the challenges of changing demography. While numerous articles have addressed how the NUA can be implemented at different levels and in different areas, this article points out the potential limitations in incorporating the NUA into metropolitan transport policies. The relevance of the limitations can be seen in three main fields:...
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Rola i znaczenie zbiornika sieciowego w kształtowaniu hydrauliki i jakości wody w systemie wodociągowym
PublikacjaEksploatacja zbiornika sieciowego powinna zapewniać cykliczną wymianę wody w jego komorach. Koniecznym warunkiem prawidłowej eksploatacji zbiornika jest zgodność założeń projektowych ze stanem faktycznym. Praktyka eksploatacyjna wskazuje na szereg nieprawidłowości w tym względzie. Z powodu lokalizacji zbiornika sieciowego za nisko lub za wysoko albo wskutek błędów popełnionych w ustaleniu jego parametrów obserwuje się niestabilność...
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A PROPOSAL FOR ONE-IMAGE PHOTOGRAMMETRY SYSTEM FOR MEASURING THE CLEARANCE DISTANCE. CASE STUDY
PublikacjaMeasurement of the clearance distance (both in the context of the rail and road) is one of the current and increasingly discussed topics in the context of photogrammetric and image processing (computer vision) methods. The article presents a description of a simple and rapid method of measure the clearance distance between the obstacles by using one-image photogrammetry. The proposed method was tested for the railway, tram and...
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Cathodic activation of synthesized highly defective monoclinic hydroxyl‐functionalized ZrO2 nanoparticles for efficient electrochemical production of hydrogen in alkaline media
PublikacjaThe high electrochemical stability of Zirconia (ZrO2) at high potentials strongly suggested it as an alternative to carbon supports, which experience reduced efficiency due to some corrosion problems particularly during prolonged electrocatalysis activity. However, the use of ZrO2 was limited by its low electrical conductivity and surface area. In this work, we developed a methodology for synthesizing monoclinic ZrO2 NPs with increased...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublikacjaWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublikacjaA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...