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Relationship between the betalain composition in Opuntia ficus indica and Beta vulgaris varieties and biological activity of their extracts
PublicationBetalains are a class of pigments that are much less com- monly found in nature than anthocyanins or carotenoids. They occur only in a few edible plants such as red beetroot (Beta vulgaris), prickly pears (Opuntia ficus indica), amaranth (Amaranthus sp.) and some mushrooms. This group of pig- ments can be divided into two major groups: yellow vulgax- anthins and red betanins. Despite their structural similarity to compounds from...
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Sequential treatment of landfill leachate by electrocoagulation/aeration, PMS/ZVI/UV and electro-Fenton: Performance, biodegradability and toxicity studies
PublicationThis study presents a systematic study on sequential treatment of highly resistant landfill leachate by electrocoagulation (EC)/aeration, sulfate radical advanced oxidation process (SR-AOP) and electro-Fenton (EF). In case of SR-AOP, peroxymonosulfate (PMS) catalyzed by zero valent iron (ZVI) and ultraviolet irradiation (UV) system was developed. Treatment process was optimized in respect to COD removal. Analysis of results revealed...
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Wykorzystanie bezrozpuszczalnikowych technik przygotowania próbek w procedurach oznaczania lotnych związków chlorowcoorganicznych w próbkach płynów biologicznych
PublicationDążność do oznaczania możliwie szerokiego spektrum analitów w próbkach charakteryzujących się złożonym, a często i zmiennym składem matrycy, stanowi siłę napędową do działań analityków w zakresie poszukiwania zarówno nowych rozwiązań metodycznych jak i aparaturowych. Szczególnie w przypadku ciekłych próbek środowiskowych i biologicznych konieczne są specjalne operacje i czynności (na etapie ich przygotowania) przed etapem oznaczeń...
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Conserved motifs of MutL proteins
PublicationtThe MutL protein is best known for its function in DNA mismatch repair (MMR). However, there isevidence to suggest that MutL is not only the linker connecting the functions of MutS and MutH in MMR,but that it also participates in other repair systems, such as Very Short Patch (VSP), Base Excision (BER)and Nucleotide Excision Repair (NER). This study set out to identify the most highly conserved aminoacid sequence motifs in MutL...
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An Overview of Treatment Approaches for Octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) Explosive in Soil, Groundwater, and Wastewater
PublicationOctahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX) is extensively exploited in the manufacturing of explosives; therefore, a significant level of HMX contamination can be encountered near explosive production plants. For instance, up to 12 ppm HMX concentrations have been observed in the wastewater effluent of a munitions manufacturing facility, while up to 45,000 mg/kg of HMX has been found in a soil sample taken from...
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Superhydrophobic sponges based on green deep eutectic solvents for spill oil removal from water
PublicationThe paper described a new method for crude oil-water separation by means of superhydrophobic melamine sponges impregnated by deep eutectic solvents (MS-DES). Due to the numerous potential of two-component DES formation, simple and quick screening of 156 non-ionic deep eutectic solvents using COSMO-RS (Conductor-like Screening Model for Real Solvents) computational model was used. DES which were characterized by high solubility...
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Improved degradation of etodolac in the presence of core-shell ZnFe2O4/SiO2/TiO2 magnetic photocatalyst
PublicationIn the present study, susceptibility to photocatalytic degradation of etodolac, 1,8-diethyl-1,3,4,9 – tetrahydro pyran - [3,4-b] indole-1-acetic acid, which is a non-steroidal anti-inflammatory drug frequently detected in an aqueous environment, was for the first time investigated. The obtained p-type TiO2-based photocatalyst coupled with zinc ferrite nanoparticles in a core-shell structure improves the separation and recovery...
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Coupling transformation of carbon, nitrogen and sulfur in a long-term operated full-scale constructed wetland
PublicationThe coupling transformation of carbon, nitrogen and sulfur compounds has been studied in lab-scale and pilot-scale constructed wetlands (CWs), but few studies investigated full-scale CW. In this study, we used batch experiments to investigate the potentials of carbon, nitrogen and sulfur transformation in a long-term operated, full-scale horizontal subsurface flow wetland. The sediments collected from the HSFW were incubated for...
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Dimethyl ether (DME) as potential environmental friendly fuel
PublicationIn recent years, there has been a growing interest in replacing petroleum fuels with so-called second generation environmental friendly fuels. Compared to traditional petroleum fuels dimethyl ether (DME) could be used as a clean high-efficiency compression ignition fuel with reduced particulate matter (PM), sulfur oxides (SOx), hydrocarbons (HC), carbon monoxide (CO) as well as combustion noise. Compared to some of the other leading...
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The Ellenbogen’s “Matter as Software” Concept for Quantum Computer Implementation: IV. The X@C60 Molecular Building Blocks (MBBs) and Computing System Lifetime Estimation
PublicationThe problem of approximate lifetimes of individual X@C60 MBBs and tip-based nanofabricated quantum computing device systems is discussed under the conservative assumption of single-point failure. A single chemical transformation of the C60 cage into high-energy opened o-C60 isomer which forms the communication canal for the low energy transfer of an X atom from X@C60 MBB to the outside environment was studied. According to the...
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The experience of movement in the built form and space: A framework for movement evaluation in architecture
Publication“Movement in architecture” is an organized system of various types of movements stimulated by specific architectural elements. This research was conducted through a qualitative-analytical method and empirical and bibliographical research methods with the aim to categorize different types of movements based on the explorer and observer relationships with the built space and form. So far, most of the related studies have focused...
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In vitro and in silico assessment of anti-inflammatory activity of cocoa powders
PublicationPlants are considered the major sources of biologically active compounds, which provide unlimited opportunities for their use either as medical treatments or as novel drug formulations. Cocoa powder is frequently used in nutrition and is known to have many benefits thanks to its wide range of biological activities. The presented study was focused on th evaluation of the anti-inflammatory potential of extracts obtained from cocoa...
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Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space
PublicationWe consider the anti-plane shear waves in a domain consisting of an infinite layer with a thin coating lying on an elastic half-space. The elastic properties of the coating, layer, and half-space are assumed to be different. On the free upper surface we assume the compatibility condition within the Gurtin–Murdoch surface elasticity, whereas at the plane interface we consider perfect contact. For this problem there exist two possible...
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Termodynamika oddziaływań substancji tetrafenylowych z wodą w świetle teorii funkcjonału gęstości
PublicationW termodynamice roztworów elektrolitów istotne jest zagadnienie podziału eksperymentalnie wyznaczanych wielkości termodynamicznych na udziały jonowe. Z uwagi na niemożność niezależnego wyznaczenia jonowych wielkości cząstkowych, podział wielkości charakteryzujących elektrolit musi być z konieczności dokonany w oparciu o założenie pozatermodynamiczne. Obecnie przyjmuje się, że najbardziej uzasadnionym teoretycznie i eksperymentalnie...
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Active Linear Tunable Resistance Element and Application to Feedforward Linearization of CMOS Transconductance Amplifier
PublicationW pracy przedstawiono koncepcję układową przestrajalnego rezystora liniowego MOS wykorzystującego tranzystory pracujące w zakresie triodowym. Opracowana struktura, jak wykazały symulacje komputerowe, charakteryzuje się dobrymi właściwościami zarówno jeżeli chodzi o zakres przestrajania jak i liniowość charakterystyk przejściowych. Pozwoliło to efektywnie wykorzystać prezentowany element do linearyzacji operacyjnego wzmacniacza...
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Metodyka i rezultaty oznaczania mgły oraz lotnych składników organicznych podczas nalewu asfaltów
PublicationW pracy przedstawiono i porównano metodyki analityczne opracowane w celu kontroli stężenia składników występujących w powietrzu wypływającym do systemu utylizacji oparów, z cystern w czasie nalewu asfaltu drogowego. Badania dotyczyły, oddzielnie, lotnych składników organicznych oraz mgły, zatrzymywanej przez filtr z włókniny. Identyfikację i oznaczanie lotnych związków organicznych wykonywano techniką kapilarnej chromatografii...
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A Multi Rig Screening Test for Thin Ceramic Coatings in Bio - Tribological Applications
PublicationA method is presented for the comparative testing of wear resistance of ceramic coatings made from materials potentially feasible in tribo - medical applications, mainly orthopaedic implants made from ceramics coated metals for low cost, long life and low wear particle emission into the body. The method was devised as the main tool for use in research and is comprised of flat on flat and ball on flat surface (sliding) tests. Seven...
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Fabrication of polyurethane and polyurethane based composite fibers by the electrospinning technique for soft tissue engineering of cardiovascular system
PublicationElectrospinning is the unique technique, which provides forming of polymeric scaffolds for soft tissue engineering, which include tissue scaffolds for soft tissues of cardiovascular system. Such artificial soft tissues of cardiovascular system may possess mechanical properties comparable to native vascular tissues. Electrospinning technique gives the opportu nity to form fibres with nm- to μm-scale in diameter. The arrangement...
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Non-toxic fluorine-doped TiO2 nanocrystals from TiOF2 for facet-dependent naproxen degradation
PublicationIn the present study, the photocatalytic degradation of naproxen (NPX), which is a nonsteroidal anti-inflammatory drug (NSAID), frequently detected in drinking water, was investigated. The F-doped TiO2 with defined morphology was successfully obtained from TiOF2 and applied for photocatalytic degradation under UV-vis and visible light. All samples were characterised by X-ray diffraction, scanning electron microscopy, X-ray photoelectron...
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Fluorine ions in photocatalysts’ synthesis: an obstacle or an ally? The investigation of photocatalysts in Ti-O-F system
PublicationTitanium(IV) oxide (TiO2) is one of the most promising photocatalysts, which is expected to be applied in the photocatalytic degradation of xenobiotics. For sustainable development and green chemistry approach recently, much effort has been paid to enhance TiO2 photocatalytic activity in UV-vis light by modifying its structure. The photocatalytic process’s complexity cannot be simply described as electron-hole pairs generations...
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Mono- and bimetallic (Pt/Cu) titanium(IV) oxide core–shell photocatalysts with UV/Vis light activity and magnetic separability
PublicationTitanium(IV) oxide is one of the most widely investigated photocatalysts. However, separation of nano-sized particulate titania might result in profitless technologies for commercial applications. Additionally, bare titania is almost inactive under the Vis range of solar spectrum due to its wide bandgap. Therefore, the present study aims to prepare novel coreinterlayer- shell TiO2 magnetic photocatalysts modified with metal nanoparticles...
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Experimental and theoretical investigation of the reactivity of [(BDI*)Ti(Cl){η2-P(SiMe3)-PiPr2}] towards selected ketones
PublicationIn this work, we report a new type of reactivity of [(BDI*)Ti(Cl){η2-P(SiMe3)-PiPr2}] (1) towards ketones (BDI* = 2,6-diisopropylphenyl-β-methyldiketiminate ligand). In the reaction of 1 with acetone, cyclopentanone or cyclohexanone, a ketone moiety is inserted into Ti–Pphosphanyl or Ti–Pphosphido bonds to form complexes with a new C–P–P moiety, providing [(BDI*)Ti(Cl){η2-P(SiMe3)-PiPr2-C(Me)2O}] (2a), [(BDI*)Ti(Cl){η2-OC(Me)2P(SiMe3)-PiPr2}]...
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Comparison of nitrogen and VFA removal pathways in autotrophic and organotrophic anammox reactors
PublicationOrganotrophic anammox is a promising process for treating both nitrogen and organic containing wastewater than that of the traditional autotrophic anammox for sole nitrogen removal. However pathways of nitrogen removal particularly at metagenomic level in both processes are still unknown. Here we report, metabolic pathways of nitrogen removal in two lab-scale sequencing batch reactors (SBR), one autotrophic and another organotrophic...
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Physical properties and electronic structure of La3Co and La3Ni intermetallic superconductors
PublicationLa3Co and La3Ni are reported superconductors with transition temperatures of 4.5 and 6 K, respectively. Here, we reinvestigate the physical properties of these two intermetallic compounds with magnetic susceptibility χ, specific heat Cp and electrical resistivity ρ measurements down to 1.9 K. Although bulk superconductivity is confirmed in La3Co, as observed previously, only a trace of it is found in La3Ni, indicating that the...
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Interlaboratory Test to Characterize the Cyclic Behavior of Bituminous Interlayers: An Overview of Testing Equipment and Protocols
PublicationThe performance assessment of multi-layered pavements strongly depends on the mechanical behavior of the interface between bituminous layers. So far, comprehensive studies have been carried out mainly using quasi-static laboratory tests focusing on the interlayer shear strength at failure. However, it is generally recognized that cyclic shear testing will lead to the determination of parameters which are more closely linked to...
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Flexible Knowledge–Vision–Integration Platform for Personal Protective Equipment Detection and Classification Using Hierarchical Convolutional Neural Networks and Active Leaning
PublicationThis work is part of an effort to develop of a Knowledge-Vision Integration Platform for Hazard Control (KVIP-HC) in industrial workplaces, adaptable to a wide range of industrial environments. The paper focuses on hazards resulted from the non-use of personal protective equipment (PPE). The objective is to test the capability of the platform to adapt to different industrial environments by simulating the process of randomly selecting...
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Interlaboratory Test to Characterize the Cyclic Behavior of Bituminous Interlayers: An Overview of Testing Equipment and Protocols
PublicationThe performance assessment of multi-layered pavements strongly depends on the mechanical behavior of the interface between bituminous layers. So far, comprehensive studies have been carried out mainly using quasi-static laboratory tests focusing on the interlayer shear strength at failure. However, it is generally recognized that cyclic shear testing will lead to the determination of parameters which are more closely linked to...
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ROSANNE Project: New Procedure for Noise Characterisation of Road Surfaces in Europe
PublicationROSANNE is a collaborative project in the 7th EU Framework Programme which aims at harmonising measurement methods for skid resistance, noise emission and rolling resistance of road pavements as a preparation for standardization. The project started in November 2013 and is developing and improving standards in the field of working group CEN/TC 227/WG 5. Regarding the influence of the pavement on the road traffic noise emission,...
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Techno‐economic evaluation of a natural deep eutectic solvent‐based biorefinery: Exploring different design scenarios
PublicationThis paper presents a comprehensive techno‐economic evaluation of an integrated natural deep eutectic solvent (NADES)‐based biorefinery – a 1 ton day−1 capacity design plant. The key parameters include payback period, net present value (NPV), and internal rate of return (IRR). These were compared with the parameters of conventional biorefineries. The ‘n th plant’ results clearly revealed that the single product‐based biorefinery...
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A strong preference for the TA/TA dinucleotide step discovered for an acridine-based, potent antitumor dsDNA intercalator, C-1305: NMR-driven structural and sequence-specificity studies
PublicationTriazoloacridinone C-1305, a potent antitumor agent recommended for Phase I clinical trials, exhibits high activity towards a wide range of experimental colon carcinomas, in many cases associated with complete tumor regression. C-1305 is a well-established dsDNA intercalator, yet no information on its mode of binding into DNA is available to date. Herein, we present the NMR-driven and MD-refined reconstruction of the 3D structures...
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Synteza kompleksów β-diketiminowych oraz PNP tytanu(III) i tytanu(IV) z ligandem fosfanylofosfidowym i fosfanylofosfinidenowym. Badanie reaktywności β-diketiminowych kompleksów tytanu(III) z ligandem fosfanylofosfidowym
PublicationPierwszym głównym tematem prezentowanej pracy była synteza kompleksów β-diketiminowych (MeNacNac-; [ArNC(Me)CHC(Me)NAr]-) oraz PNP (bis[2-(diizopropylofosfino)-4-metylofenyloamina]) tytanu z ligandem fosfanylo-fosfidowym i fosfanylofosfinidenowym. Układy te otrzymuje się w reakcjach chlorkowych kompleksów β-diketiminowych oraz PNP z solami litowymi difosfanów (RR’P-P(SiMe3)Li) (R = tBu, iPr; R’ = tBu, iPr, Ph). Optymalizacja warunków...
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Tracking of the broadband source of the underwater noise in the very shallow water conditions
PublicationThe paper contains the result s, both theoretical and experimental , connected with the tracking of the underwater noise source as small ships, pontoon , diver and so on. The pro blem of security in the shallow water area is the challenge for underwater acousticians. In this paper there is take n into account the detection of the sources that move on the surface of the sea or underwater in shallow...
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Desirability-based optimization of dual-fuel diesel engine using acetylene as an alternative fuel
Publicationhe study examined the dual-fuel engine performance employing acetylene gas as primary fuel and diesel as pilot fuel. The engine's operational parameters were adjusted using the Box-Behnken design, and the results were recorded. The best operating settings were yielded as 81.25 % engine load, 4.48 lpm acetylene gas flow rate and the compression ratio were 18. At this optimized setting the BTE was 27.1 % and the engine emitted 360...
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Pressure effects on the superconductivity of the HfPd2Al Heusler compound: Experimental and theoretical study
PublicationPolycrystalline HfPd2Al has been synthesized using the arc-melting method and studied under ambient-pressure conditions by x-ray diffraction from room temperature up to 450 °C. High-pressure x-ray diffraction up to 23 GPa was also performed using Diacell-type membrane diamond anvil cells. The estimated linear thermal expansion coefficient was found to be α=1.40(3)×10−5K−1, and the bulk modulus derived from the fit to the third-order...
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Supply current signal and artificial neural networks in the induction motor bearings diagnostics
PublicationThis paper contains research results of the diagnostics of induction motor bearings based on measurement of the supply current with usage of artificial neural networks. Bearing failure amount is greater than 40% of all engine failures, which makes their damage-free operation crucial. Tests were performed on motors with intentionally made bearings defects. Chapter 2 introduces the concept of artificial neural networks. It presents...
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Application of Artificial Neural Networks to Predict Insulation Properties of Lightweight Concrete
PublicationPredicting the properties of concrete before its design and application process allows for refining and optimizing its composition. However, the properties of lightweight concrete are much harder to predict than those of normal weight concrete, especially if the forecast concerns the insulating properties of concrete with artificial lightweight aggregate (LWA). It is possible to use porous aggregates and precisely modify the composition...
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Superconductivity in LiGa2Ir Heusler type compound with VEC = 16
PublicationPolycrystalline LiGa2Ir has been prepared by a solid state reaction method. A Rietveld refnement of powder x-ray difraction data confrms a previously reported Heusler-type crystal structure (space group Fm-3m, No. 225) with lattice parameter a= 6.0322(1) Å. The normal and superconducting state properties were studied by magnetic susceptibility, heat capacity, and electrical resistivity techniques. A bulk superconductivity with...
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Superconductivity in Metal-Rich Chalcogenide Ta2Se
PublicationThe metal–metal bond in metal-rich chalcogenide is known to exhibit various structures and interesting physical properties. Ta2Se can be obtained by both arc-melting and solid-state pellet methods. Ta2Se crystallizes a layered tetragonal structure with space group P4/nmm (No. 129; Pearson symbol tP6). Each unit cell consists of four layers of body-centered close-packing Ta atoms sandwiched between two square nets of Se atoms, forming...
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Study on polymer modified road asphalt mixture
PublicationThe formulation of ternary asphalt-additives blend composed of crumb rubber : low-density polyethylene (CR : LDPE) and crumb rubber : textile fiber (CR : TF) couples, and quaternary asphalt additives-blend composed of (CR : LDPE : TF) triplets on the virgin asphalt to optimize the asphalt basic and rheological properties and to use the extrusion process of two or three additives to obtain composite materials of them, as well as...
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Golden artefacts, resin figurines, body adhesives and tomb sediments from the pre-Columbian burial site El Caño (Gran Coclé, Panamá): tracing organic contents using molecular archaeometry
PublicationThis research aimed to determine the origin of organic residues from funerary contexts in the El Ca~no settlement (Gran Cocl�e area, Panam�a, Central America) by means of multiple molecular probing techniques (GC-MS of organic solvent extracts and pyrolysis-GC-MS, THM-GC-MS and FTIR of solid samples). The samples include particles of precious resin figurines, fillings of golden objects, tomb sediments, plant exudates from extant...
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Study of microstress state of P91 steel using complementary mechanical Barkhausen, magnetoacoustic emission, and X-ray diffraction techniques
PublicationThe paper deals with assessment of microstress state of martensite P91 steel using three complementary techniques: mechanical Barkhausen emission, magnetoacoustic emission (MAE), and X-ray diffraction (XRD) profile analysis. Magnetic coercivity Hc and microstructure were investigated with inductive magnetometry and magnetic force microscopy (MFM), respectively. Internal stress level of P91 steel was modified by heat treatment....
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Visual content representation and retrieval for Cognitive Cyber Physical Systems
PublicationCognitive Cyber Physical Systems have gained significant attention from academia and industry during the past few decade. One of the main reasons behind this interest is the potential of such technologies to revolutionize human life since they intend to work robustly under complex visual scenes, which environmental conditions may vary, adapting to a comprehensive range of unforeseen changes, and exhibiting prospective behavior...
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Superconductivity in a breathing kagome metals ROs2 (R = Sc, Y, Lu)
PublicationWe have successfully synthesized three osmium-based hexagonal Laves compounds ROs2 (R = Sc, Y, Lu), and discussed their physical properties. LeBail refinement of pXRD data confirms that all compounds crystallize in the hexagonal centrosymmetric MgZn2- type structure (P63/mmc, No. 194). The refined lattice parameters are a = b = 5.1791(1) Å and c = 8.4841(2) Å for ScOs2, a = b = 5.2571(3) Å and c = 8.6613(2) Å for LuOs2 and a =...
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Effect of composition on the thermal properties and structure of M-Al-Si-O-N glasses, M = Na, Mg, Ca
PublicationThe primary objective of this study is to explore the relationship between the composition, structure, and thermal characteristics of M-Al-Si-O-N glasses, with M representing sodium (Na), magnesium (Mg), or calcium (Ca). The glasses were prepared by melting in a quartz crucible at 1650 °C and AlN precursor (powder) was utilized as a nitrogen source. The measured thermal properties studied were glass transition temperature (Tg),...
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Comprehensive Comparison of a Few Variants of Cluster Analysis as Data Mining Tool in Supporting Environmental Management
PublicationA few variants of hierarchical cluster analysis (CA) as tool of assessment of multidimensional similarity in environmental dataset are compared. The dataset consisted of analytical results of determination of metals (Na, K, Ca, Sc, Fe, Co, Zn, As, Br, Rb, Mo, Sb, Cs, Ba, La, Ce, Sm, Hf and Th) in ambient air dried and kept alive, by the means of hydroponics, moss baskets collected in 12 locations on the area of Tricity (Poland)....
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Superconducting SrSnP with Strong Sn–P Antibonding Interaction: Is the Sn Atom Single or Mixed Valent?
PublicationThe large single crystals of SrSnP were prepared using Sn self-flux method. The superconductivity in the tetragonal SrSnP is observed with the critical temperature of ∼2.3 K. The results of a crystallographic analysis, superconducting characterization, and theoretical assessment of tetragonal SrSnP are presented. The SrSnP crystallizes in the CaGaN structure type with space group P4/nmm (S.G. 129, Pearson symbol tP6) according...
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Radioactivity of drilling cuttings from shale resources of the Lower Paleozoic Baltic Basin, Poland
PublicationFractionated drilling wastes originating from shale gas exploration in the Baltic Basin in Pomerania were subjected to the measurements of mean activity concentrations of naturally occurring radioactive materials (NORMs).To better understand rock structure and texture, the X-ray diffraction analysis (XRD) and scanning electron microscopy(SEM) observation were used. To compare activity concentration of radionuclides in bulk wastes...
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A LUMPED-CIRCUIT MODEL OF CIRCULAR PISTON TRANSDUCER FOR MODELING ITS PERFORMANCE IN DUAL FREQUENCY OPERATING MODES
PublicationThe paper presents novel network equivalent circuit of piezoceramic circular disc transducer that takes into account thickness and ra dial mode of vibrations. The starting point of the analysis is 4-port description of circular disc element representing the solution of wave equation set in radial and thickness directions. Th e approximate solution for harmonic case is represented in the form of 4x4 matrix, which is syn thesized...
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The Effectiveness of Rubber Bumpers in Reducing the Effects of Earthquake-Induced Pounding between Base-Isolated Buildings
PublicationTh e methods for preventing earthquake-induced structural pounding between two adjacent buildings include ensuring a sufficient separation distance between them or decreasing their relative displacement during seismic excitation. Some equations or even specific values of such gap sizes between two buildings have been introduced so as to avoid collisions. Increasing the stiffness of buildings, using tuned mass dampers, applying...
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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...