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Rok 2025
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A facile synthesis by spark plasma sintering of mobile lithium ions into oxynitride glass-ceramic matrix: Insight and perspective
PublikacjaThe quest for efficient energy storage solutions has led to the development of solid-state Li-on batteries (SSBs), which utilize solid-state electrolyte (SSE) materials instead of organic liquid electrolytes. This study investigates the effect of increasing Li content in a Ca11Al14Si16O49N10 glass-ceramic material on its structural, thermal, physical, and electrical properties. Spark Plasma Sintered (SPS) glass-ceramic samples...
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Acceleration deforms exponential decays into generalized Zipf-Mandelbrot laws
PublikacjaAn exponentially decaying system looks as if its decay was a generalized power or double-exponential law, provided one takes into account the relativistic time dilation in a detector, the delay of the emitted signal, and the accelerations of both the source and the detector. The same mathematical formula can be found in generalizations of the Zipf-Mandelbrot law in quantitative linguistics and in the dynamics of ligand binding...
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Calculations of Cross-Sections for Positron Scattering on Benzene
PublikacjaIn this work, we present a theoretical study on positron scattering by benzene molecules over a broad energy range (1–1000 eV). The aim of this work is to provide missing data from partial cross-sections for specific processes. In particular, calculations of cross-sections for direct ionization and electronic excitation were carried out for benzene molecules in the gas phase. An estimate for the cross-section for positronium formation...
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Chemical Origins of Optically Addressable Spin States in Eu2(P2S6) and Eu2(P2Se6)
PublikacjaLanthanide materials with a 4f7 electron configuration (8S7/2) offer an exciting system for realizing multiple addressable spin states for qubit design. While the 8S7/2 ground state of 4f7 free ions displays an isotropic character, breaking degeneracy of this ground state and excited states can be achieved through local symmetry of the lanthanide and the choice of ligands. This makes Eu2+ attractive as it mirrors Gd3+ in exhibiting...
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Corrosion Resistance and Structure of Cr−O−N Coatings Formed in Vacuum Arc Plasma Fluxes With PIIID
PublikacjaCr−O−N-based vacuum arc coatings are very promising for the wear and corrosion protection of various steel parts. The aim of the work was to determine the effect of frequency and amplitude of the pulsed bias voltage (UB) on the elemental and phase composition, mechanical, and corrosion properties of Cr−O−N coatings. They have an amorphous structure with embedded nanosized solid solution crystallites based on CrN with a cubic structure...
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Cross-Section Calculations for Electron-Impact Ionization of Pyrimidine Molecule and Its Halogenated Derivatives: 2-Chloropyrimidine, 5-Chloropyrimidine, 2-Bromopyrimidine and 5-Bromopyrimidine
PublikacjaThe total cross-sections for the single electron-impact ionization of pyrimidine (C4H4N2), 2-chloropyrimidine (2-C4H3ClN2), 5-chloropyrimidine (5-C4H3ClN2), 2-bromopyrimidine (2-C4H3BrN2) and 5-bromopyrimidine (5-C4H3BrN2) molecules have been calculated with the binary-encounter-Bethe model from the ionization threshold up to 5 keV. The input data for the BEB calculations concerning electronic structure of the studied targets have...
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Deep eutectic solvent enhances antibacterial activity of a modular lytic enzyme against Acinetobacter baumannii
PublikacjaIn this study, we evaluated the combined effect between MLE-15, a modular lytic enzyme composed of four building blocks, and reline, a natural deep eutectic solvent. The bioinformatic analysis allowed us to determine the spatial architecture of MLE-15, whose components were bactericidal peptide cecropin A connected via a flexible linker to the cell wall binding domain (CBD) of mesophilic 201ϕ2 − 1 endolysin and catalytic domain...
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Defective TiO2 for CO2 photoreduction: Influence of alkaline agent and reduction temperature modulation
PublikacjaThis study investigates the synthesis and characterization of Black TiO2 photocatalyst (TiO2-x) through the sol-gel method combined with NaBH4 reduction at different temperatures (350 °C, 500 °C, and 650 °C). The photocatalytic performance for CO2 reduction was evaluated, revealing that TiO2-x_500°C sample exhibited the highest efficiency. This enhanced performance is mainly attributed to a higher concentration of oxygen vacancies...
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Dynamic Electrochemical Impedance Spectroscopy in Galvanostatic Mode as a Tool for Passive Layer State Monitoring in a Chloride Solution Under a Mechanical Load
PublikacjaMechanical stress is one of the factors influencing the initiation of pitting corrosion and deterioration of the protective properties of the passive layer on stainless steel. The tests carried out on AISI 304L stainless steel showed that, in the 3.5% NaCl environment for samples loaded in the elastic and plastic range, no pitting corrosion initiation was observed. Only mechanical damage of the passive layer occurred. Galvanodynamic...
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Efficacy of modal curvature damage detection in various pre-damage data assumptions and modal identification techniques
PublikacjaThe efficacy of modal curvature approach for damage localization is discussed in the paper in the context of input data. Three modal identification methods, i.e., Eigensystem Realization Algorithm (ERA), Natural Excitation Technique with ERA (NExT-ERA) and Covariance Driven Stochastic Subspace Identification (SSI-Cov), and four methods of determining baseline data, i.e., real measurement of the undamaged state, analytical function,...
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Energy landscape and structural transformations of C38 penta-fullerene: The stabilizing role of octagons and insights into penta-octa-penta-fullerene
PublikacjaTheoretical investigations were conducted to study the stability and energy landscape of C38 penta-fullerene, a structure comprising six penta-graphene unit cells. Vibrational analysis at the B3LYP/def2SVP level revealed 18 negative frequencies, indicating the dynamic instability of penta-fullerene. Analyzing the energy profiles for these vibrational modes led to the identification of six energetically favourable isomers, featuring...
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Enhanced electrochemical performance of sulfur-doped laser-induced graphene supercapacitors: Synergistic effects of doping and plasmochemical surface modification
PublikacjaThis work introduces a novel, scalable methodology for rapidly fabricating sulfur-doped laser-induced graphene with enhanced porosity and wetting characteristics, targeting advanced supercapacitor applications. An infrared laser scribing technique was employed to create a three-dimensional porous graphene network, with in-situ sulfur doping achieved through physical evaporation using powder precursor. A second-pass laser process...
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Experimental and Theoretical Study on Electron Interactions with Acetic Acid Molecules
PublikacjaThe absolute total cross section for electron collisions with acetic acid has been measured using an electrostatic electron spectrometerand linear transmission method for collision energies ranging from 0.4 to 300eV. Elastic electron scattering from acetic acid within a low-energy range has also been studied theoretically using the Schwinger multichannel and R-matrix methods, in the static-exchange and static-exchange plus polarization...
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Investigation of structural, thermal, and electrical properties of sodium-doped oxynitride glass-ceramics
PublikacjaThis study aimed to investigate the influence of Na2O addition on the structural, thermal, and electrical characteristics of oxynitride glass-ceramics within the Na–K–Mg–Ca–Al–Si–O–N system. Oxynitride glass-ceramic samples were prepared via spark plasma sintering (SPS) with sodium oxide doping levels ranging from 0 wt% to 12 wt%. FESEM analysis revealed changes in sample morphology with increasing sodium content, indicating the...
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Mobile mutual-visibility sets in graphs
PublikacjaGiven a connected graph G, the mutual-visibility number of G is the cardinality of a largest set S such that for every pair of vertices x, y ∈ S there exists a shortest x, y-path whose interior vertices are not contained in S. Assume that a robot is assigned to each vertex of the set S. At each stage, one robot can move to a neighbouring vertex. Then S is a mobile mutual-visibility set of G if there exists a sequence of moves of...
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New insights into structural, optical, electrical and thermoelectric behavior of Na0.5Bi0.5TiO3 single crystals
PublikacjaThe single crystals of lead-free Na0.5Bi0.5TiO3 were grown using the Czochralski method. The energy gaps determined from X-ray photoelectron spectroscopy (XPS) and optical measurements were approximately 2.92 eV. The current-voltage characteristics, depolarization current, dc (σdc) and ac (σac) electrical conductivity, and Seebeck coefficient of the crystals were investigated. The frequency/temperature-dependent electrical properties...
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Optimal bandgap of a single-junction photovoltaic cell for the mobile Internet-of-Things
PublikacjaThe procedure for determining the maximum power of a single-junction photovoltaic cell operating in various types of lighting is presented. This is a key issue for photovoltaics powering the mobile Internet-of-Things (IoTs). The simulations performed are based on the detailed balance principle, without any of simplifying assumptions included in the Shockley-Queisser model. Optimal energy bandgap for diffuse solar light was found...
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Optimizing conductivity in Na-V-Te-O glass through controlled heat treatment
PublikacjaSemiconducting Na2O-V2O5-TeO2 glasses with various Na2O contents were melted and subjected to controlled heating to improve conductivity. Topography analysis were performed using confocal microscopy and scanning electron microscopy on both as-quenched and heat-treated samples. X-ray diffraction confirmed the amorphous nature of the samples post-melting, with subsequent heating resulting in the formation of nanocrystallites primarily...
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Physicochemical properties of La0.5Ba0.5Co1-xFexO3-δ (0≤x≤1) as positrode for proton ceramic electrochemical cells
PublikacjaWe report on essential properties of materials in the series La0.5Ba0.5Co1-xFexO3-δ as positrodes for proton ceramic electrochemical cells (PCECs). The unit cell and thermochemical expansion coefficient (TCEC) of these cubic perovskites decrease with iron content x, the TCEC of La0.5Ba0.5FeO3-δ going as low as 11·10-6 1/K. The materials behave as LaMO3 perovskites with small band gaps and Ba acting as acceptors compensated by electron...
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Polymer-Enhanced Active Layer Crystallization in Low-Temperature Carbon-Based Perovskite Solar Cells
PublikacjaHigh-efficiency perovskite solar cells (PSCs) are emerging as a promising next-generation, low-cost, photovoltaic technology. A key advantage of PSCs is their compatibility with diverse manufacturing techniques, enabling the pursuit of low-cost, stable PSCs. Carbon electrodes, known for their scalability, chemical inertness, and ease of processing through screen printing, have recently seen the development of low-temperature carbon...
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Restrained differential of a graph
PublikacjaGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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Self-Calibrating Stress Measurement System Based on Multidirectional Barkhausen Noise Measurements
PublikacjaThe system presented in this paper enables automatization of the two-dimensional calibration process (determination of Barkhausen noise (BN) intensity dependence on in-plane components of strain). Then, using dedicated software created by the authors in LabVIEW environment, and with the help of two dimensional calibration data one can effectively determine strain and stress distribution i.e. magnitude and orientation of main strain/stress...
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Silver and Silver/Sodium Bisphosphonate Salts: Rare Examples of Molecular Solid Solutions and Their Biological Activity as Dual-Action Compounds
PublikacjaBisphosphonates (BPs) are an important treatment for osteoporosis and bone metastases due to their low toxicity, high thermostability, and the ability to inhibit bone resorption. Notably, BPs like alendronate, which contain a primary amine group, exhibit potent antiresorptive and antiangiogenic properties. Recent studies have focused on enhancing the BP properties by incorporating bioactive metals to increase their therapeutic...
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Solvent Selection as a Key Factor in the Performance of Semitransparent Heterojunctions Composed of Hydrogenated Nanotubes and Bismuth Sulfides
PublikacjaResearch on titanium nanotubes modified with metal sulfides, particularly bismuth sulfide (Bi2S3), aims to create heterostructures that efficiently absorb sunlight and then separate photogenerated charge carriers, thereby enhancing the energy conversion efficiency. This study shows a key role of solvent used for sulfide and bismuth salt solutions used during successive ionic layer adsorption and reaction (SILAR) onto the morphology,...
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The influence of chitosan's molecular weight, concentration, and dissolution method on the properties of electrophoretically deposited coatings on the Ti13Nb13Zr alloy surface
PublikacjaIn this study, the effects of molecular weight (high, medium, and low), concentration (0.1 and 0.5 %) and dissolution method (in a rarely used hydroxyacetic acid and utilizing a novel CO2 saturation) of chitosan on the microstructure, chemical composition, wettability, surface roughness, adhesion, corrosion resistance and antibacterial activity of chitosan coatings electrophoretically deposited (10 V, 1 min) on β titanium alloy...
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Theoretical design of nanocatalysts based on (Fe2O3)n clusters for hydrogen production from ammonia
PublikacjaThe catalytic activities of high-spin small Fe(III) oxides have been investigated for efficient hydrogen production through ammonia decomposition, using the artificial force induced reaction method within the framework of density functional theory with the B3LYP hybrid exchange–correlation functional. Our results reveal that the adsorption free energy of NH3 on (Fe2O3 )n (n = 1–4) decreases with increasing cluster size up to n...
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Thermoelectric and electrical properties of triple-conducting multicomponent oxides based on substituted barium cerate-zirconate
PublikacjaMulticomponent oxides often have exceptional thermal stability and interesting electronic properties. The present work presents the thermoelectric and electrical properties of the Ba(Zr0.2Hf0.2Sn0.2Ti0.2Fe0.2)O3−δ and Ba(Zr0.1Hf0.1Sn0.1Ti0.1Co0.1Ce0.1Bi0.1Fe0.1Y0.1Zn0.1)O3−δ multicomponent perovskites. Single-phase cubic perovskites were synthesized using the solid-state reaction method. They were characterized using X-ray...
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Thermoelectric and electrical transport properties of mixed-conducting multicomponent oxides based on Ba(Zr,Ce)O3-δ
PublikacjaIn this work, the chosen physicochemical properties of single-phase multicomponent oxides BaTi1/8Fe1/8Co1/8Y1/8Zr1/8Sn1/8Ce1/8Hf1/8O3-δ and BaTi1/9Fe1/9Co1/9Y1/9Zr1/9Sn1/9Ce1/9 Hf1/9Bi1/9O3-δ were studied. The microstructure of the compounds strongly depended on the presence of bismuth in the structure. The electrical transport studies showed a level of electrical conductivity of ∼10−3 - 10−2 S/cm in the temperature range 673–1073...
Rok 2024
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A modified DC Hebb–Wagner polarization method for determining the partial protonic electrical conductivity in mixed-conducting BaGd0.3La0.7Co2O6−δ
PublikacjaIn this work, partial protonic conductivity in mixed conducting (BZCY721) and BaGd0.3La0.7Co2O6−d (BGLC137) was studied. For this purpose, a modified DC Hebb–Wagner polarization method was used. A four-wire type of galvanic cell as well as a suitable calculation model was applied. The method was validated using proton conducting electrolyte – BaZr0.7Ce0.2Y0.1O3−d – as a reference material. For the first time, protonic partial conductivity...
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A note on the Morse homology for a class of functionals in Banach spaces involving the 2p-area functional
PublikacjaIn this paper we show how to construct Morse homology for an explicit class of functionals involving the 2p-area functional. The natural domain of definition of such functionals is the Banach space W_0^{1,2p}(\Omega), where p > n/2 and \Omega \subet R^n is a bounded domain with sufficiently smooth boundary. As W_0^{1,2p}(\Omega) is not isomorphic to its dual space,critical points of such functionals cannot be non-degenerate...
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A semiempirical model for low energy electron–atom transport cross sections: The case of noble gases
PublikacjaA semiempirical approach to describe low energy electron–atom transport cross sections of easy implementation and reproduction is presented. The heart of the model is an energy independent two-parameter potential that was adjusted to reproduce the accurate total cross sections for He, Ne, Ar and Kr, measured with a threshold photoelectron source technique from meV up to 20 eV. Once the potential was conceived, the model was validated...
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Additive manufacturing of Proton-Conducting Ceramics by robocasting with integrated laser postprocessing
PublikacjaA hybrid system combining robocasting and NIR laser postprocessing has been designed to fabricate layers of mixed proton-electron conducting Ba0.5La0.5Co1-xFexO3-δ ceramic. The proposed manufacturing technique allows for the control of the geometry and microstructure and shortens the fabrication time to a range of a few minutes. Using 5 W laser power and a scanning speed of 500 mm⋅s− 1, sintering of a round-shaped layer with an...
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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublikacjaLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...
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All but one expanding Lorenz maps with slope greater than or equal to $\sqrt 2$ are leo
PublikacjaWe prove that with only one exception, all expanding Lorenz maps $f\colon[0,1]\to[0,1]$ with the derivative $f'(x)\ge\sqrt{2}$ (apart from a finite set of points) are locally eventually onto. Namely, for each such $f$ and each nonempty open interval $J\subset(0,1)$ there is $n\in\N$ such that $[0,1)\subset f^n(J)$. The mentioned exception is the map $f_0(x)=\sqrt{2}x+(2-\sqrt{2})/2 \pmod 1$. Recall that $f$ is an expanding Lorenz...
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An absorbing set for the Chialvo map
PublikacjaThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublikacjaModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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angielski
PublikacjaA subset D of V (G) is a dominating set of a graph G if every vertex of V (G) − D has at least one neighbour in D; let the domination number γ(G) be the minimum cardinality among all dominating sets in G. We say that a graph G is γ-q-critical if subdividing any q edges results in a graph with domination number greater than γ(G) and there exists a set of q − 1 edges such that subdividing these edges results in a graph with domination...
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Anisotropic magnetism of polymorphic ErAl3
PublikacjaErAl3 can form in either a trigonal () or cubic () polymorph and this paper investigates the physical properties of these polymorphs through characterizations of single crystals grown in an aluminum flux. We demonstrate that polymorph selection can be achieved based on the nominal composition of the crystal growth. Magnetic measurements confirm that both −ErAl3 and −ErAl3 order antiferromagnetically at low temperatures. −ErAl3...
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Anisotropic, multiband, and strong-coupling superconductivity of the Pb0.64Bi0.36 alloy
PublikacjaThis paper presents theoretical and experimental studies on the superconductivity of Pb0.64Bi0.36 alloy, which is a prototype of strongly coupled superconductors and exhibits one of the strongest coupling under ambient pressure among the materials studied so far. The critical temperature, the specific heat in the superconducting state, and the magnetic critical fields are experimentally determined. Deviations from the single-gap...
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Assessment of High-Temperature Oxidation Properties of 316L Stainless Steel Powder and Sintered Porous Supports for Potential Solid Oxide Cells Applications
PublikacjaIn this work, oxidation properties of austenitic 316L stainless steel powder and sintered porous support were investigated at the temperature range of ~600-750 °C for 100 hours in ambient air. Oxidation kinetics was determined by continuous thermogravimetry and analyzed employing parabolic rate law. It was observed that oxidation leads to the formation of an oxide scale, with substantial oxidation occurring at ≥ 650 °C in the powder....
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Assessment of the application of selected metal-organic frameworks as advanced sorbents in passive extraction used in the monitoring of contaminants of emerging concern in surface waters
PublikacjaWater pollution has become a critical global concern requiring effective monitoring techniques and robust protection strategies. Contaminants of emerging concern (CECs) are increasingly detected in various water sources, with their harmful effects on humans and ecosystems continually evolving. Based on literature reports highlighting the promising sorption properties of metal-organic frameworks (MOFs), the aim of this study was...
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BASECOL2023 scientific content
PublikacjaContext. The global context of making numerous data produced by researchers available requires collecting and organising the data, assigning meaningful metadata, and presenting the data in a meaningful and homogeneous way. The BASECOL database, which collects inelastic rate coefficients for application to the interstellar medium and to circumstellar and cometary atmospheres, meets those requirements. Aims. We aim to present the...
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Calculation of electron scattering lengths on Ar, Kr, Xe, Rn and Og atoms
PublikacjaFocusing on the noble gases, we calculate the scattering potential using the Dirac-Coulomb Hamiltonian supplemented with a model polarization potential. We determine the scattering lengths using two methods, namely phase shifts for very small scattering energies and the shape of the wave function for zero scattering energy. We compare our theoretical electron scattering length results on Ar, Kr and Xe atoms with existing experimental...
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Changes in evaporation patterns and their impact on Climatic Water Balance and river discharges in central Poland, 1961–2020
PublikacjaThis study investigates the changes in precipitation and evaporation patterns and their impact on Climatic Water Balance and river discharges in central Poland from 1961 to 2020. The analysis focuses on two “normal” periods, 1961–1990 and 1991–2020 (according to the World Meteorological Organization). Bartlett’s test and the Kruskal–Wallis rank sum test were used to assess the homogeneity of variances and compare distributions...
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Characterization of Corrosion-Induced Fracture in Reinforced Concrete Beams Using Electrical Potential, Ultrasound and Low-Frequency Vibration
PublikacjaThe paper deals with the non-destructive experimental testing of the reinforced concrete beams under progressive corrosion. A series of experiments using electrical potential, ultrasound and low-frequency vibrations techniques are reported. Electrical potential and natural frequencies were used to characterise and monitor the corrosion process at its initial state. The P-wave velocity measurements were proved to be effective in...
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Charge density wave, enhanced mobility, and large nonsaturating magnetoresistance across the magnetic states of HoNiC2 and ErNiC2
PublikacjaWe report on magnetotransport and thermoelectric properties of two ternary carbides HoNiC2 and ErNiC2 hosting both charge density wave and long-range magnetic order. In the charge density wave state, both compounds show relatively large magnetoresistance MR ≈ 150% in HoNiC2 and ≈ 70%in ErNiC2 at a magnetic field of 9 T and temperature as low as 2 K. This positive field-linear magnetoresistance shows no signatures of saturation....
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Charge Transport in the A6B2O17 (A = Zr, Hf; B = Nb, Ta) Superstructure Series
PublikacjaThe electrical properties of the entropy stabilized oxides: Zr6Nb2O17, Zr6Ta2O17, Hf6Nb2O17 and Hf6Ta2O17 were characterized. The results and the electrical properties of the products (i.e. ZrO2, HfO2, Nb2O5 and Ta2O5) led us to hypothesize the A6B2O17 family is a series of mixed ionic-electronic conductors. Conductivity measurements in varying oxygen partial pressure were performed on A6Nb2O17 and A6Ta2O17. The results indicate...
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Cluster-spin-glass behavior in new ternary RE2PtGe3 compounds (RE = Tb, Dy, Ho)
PublikacjaTwo new ternary germanides Tb2Pt1.2Ge2.8, Dy2Pt1.15Ge2.85 and one already known germanium Ho2Pt1.1Ge2.9.were synthesized using an arc melting technique. The obtained samples were investigated by powder X-ray diffraction, which indicated that all of them crystallized in a hexagonal structure with P6/mmm (no. 191) space group. This structure is a disordered variant of the AlB2 aristotype that favors the formation of a spin-glass-like...
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Completely entangled subspaces of entanglement depth k
PublikacjaWe introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth k (k-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least k. We present an efficient construction of k-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs)....
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Consistency of Quantum Computation and the Equivalence Principle.
PublikacjaThe equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame....