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Search results for: asymptotic series expansion
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Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models
PublicationTernary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).
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A multirate approach to DDS algorithm versus Taylor-series expansion technique.
PublicationPokazano, że cyfrowy generator syntezy bezpośredniej (DDS) można traktować jako algorytm wieloszybkościowy. Rozważono i porównano dwa sposoby wykorzystania pamięci. W pierwszym z nich zastosowano filtr ułamkowo-opóźniający o strukturze Farrowa. Drugie podejście oparto na rotacji fazy na podstawie rozwinięcia w szereg Taylora. Eksperymenty pokazują, że za pomocą obu tych sposobów, dla sinusoidy zespolonej generowanej w kwadraturowym...
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Surface effects of network materials based on strain gradient homogenized media
PublicationThe asymptotic homogenization of periodic network materials modeled as beam networks is pursued in this contribution, accounting for surface effects arising from the presence of a thin coating on the surface of the structural beam elements of the network. Cauchy and second gradient effective continua are considered and enhanced by the consideration of surface effects. The asymptotic homogenization technique is here extended to...
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Wavepacket of the Universe and its Spreading
PublicationWavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is obtained if one regards time evolution as a dynamical process...
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Technologia medyczna w obiektach świadczących usługi lecznicze- Medical technology in healthcare facilities
PublicationArchitektura budynków szpitalnych kreowana jest pod silnym wpływem wymagań sanitarno-higienicznych oraz wytycznych wynikających z charakteru świadczonych usług medycznych. Naczelną rolę odgrywa tu technologia medyczna, która jest zasobem wiedzy, procesów organizacyjnych i środków fizycznych uczestniczących w realizacji zdefiniowanych świadczeń zdrowotnych. Istotnym elementem takiej kreacji architektonicznej jest szereg procesów...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic 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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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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Structure and thermal expansion of liquid bismuth
PublicationExperimental structural data for liquid Bi were used for estimation of the main structure parameters as well as the thermal expansion coefficient both in supercooled and superheated temperature ranges. It was shown that the equilibrium melt had a positive thermal expansion coefficient within a temperature range upon melting and a negative one at higher temperatures. The former was related to structure changes upon melting, whereas...
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Asymptotic error expansions for Schoenberg type operators.
PublicationW pracy wyprowadzono rozwinięcie asymptotyczne dla błędu w L2 operatorówSchoenberga.
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Static Series and Shunt-series PE Voltage-quality Controllers
PublicationAs presented in the Chap. 7 static shunt power electronics (PE) voltage-quality controllers protect the utility electrical system from the unfavorable impact of customer loads. Shunt controllers, as shown in Chap. 6, are recommended mainly for mitigation of the causes of disturbances, and not their effects in distanced nodes of a power-electronics system. In the case when reduction of disturbances effects is required, which leads...
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Thermal and Chemical Expansion in Proton Ceramic Electrolytes and Compatible Electrodes
PublicationThis review paper focuses on the phenomenon of thermochemical expansion of two specific categories of conducting ceramics: Proton Conducting Ceramics (PCC) and Mixed Ionic-Electronic Conductors (MIEC). The theory of thermal expansion of ceramics is underlined from microscopic to macroscopic points of view while the chemical expansion is explained based on crystallography and defect chemistry. Modelling methods are used to predict...
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Asymptotic formulas for the error in linear interpolation
PublicationWyznaczono asymptotyczny wzór dla błędu w liniowej interpolacji z dowolnymi węzłami.
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The asymptotic formula for the error in orthogonal projection
PublicationW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Cavity-expansion approximation for projectile impact and penetration into sand
PublicationA one-dimensional problem of a spherical cavity expanding at a constant velocity from zero initial radius in an infinite granular medium, which has the first-kind self-similar solution, is considered. We are solving this dynamic spherical cavity-expansion problem to model rigid spheres penetrating into a granular media. Elastic–plastic deformation of the granular media is described in a barotropic approximation, using the high-pressure...
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Subcritical Thermodynamic Cycles with Organic Medium and Isothermal Expansion
PublicationThe efffciencies of the Organic Rankine Cycle (ORC) are not very high and only very seldom do they exceed 20%. The increase and optimization of initial parameters and certain modifications of the thermodynamic cycle make it possible to overcome these drawbacks. A new modified cycle has been described and analyzed in detail in the paper. Similarly to the Ericsson cycle for gas turbines, isothermal expansion in the turbine is suggested...
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Asymptotic error expansions for Schoenberg type operators
PublicationPrzedstawiono L^p błąd dla rozwinięć dla operatorów Schoenberga
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On asymptotic periodicity of kernel double Markovian operators
PublicationIt is proved that a kernel, doubly Markovian operator T is asymptotically periodic if and only if its deterministic σ-field Σd(T)(equivalently Σd(T∗)) is finite. It follows that kernel doubly Markovian operator T is asymptotically periodic if and only if T∗ is asymptotically periodic.
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A Formal Approach to Model the Expansion of Natural Events: The Case of Infectious Diseases
PublicationA formal approach to modeling the expansion of natural events is presented in this paper. Since the mathematical, statistical or computational methods used are not relevant for development, a modular framework is carried out that guides from the external observation down to the innermost level of the variables that have to appear in the future mathematical-computational formalization. As an example we analyze the expansion of Covid-19....
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Experiences from operation of various expansion devices in small scale ORC
PublicationThe main aim of this paper was to present various expansion devices for an application in the small scale ORC system. The investigations were carried out in two parallel directions. One direction was to design and construct a device dedicated to the analyzed ORC system. The second direction was to adapt existing expansion devices for the needs of the analyzed ORC system. Four various devices were described and presented together...
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Interactive Query Expansion with the Use of Clustering by Directions Algorithm
PublicationThis paper concerns Clustering by Directions algorithm. The algorithm introduces a novel approach to interactive query expansion. It is designed to support users of search engines in forming web search queries. When a user executes a query, the algorithm shows potential directions in which the search can be continued. This paper describes the algorithm and it presents an enhancement which reduces the computational complexity of...
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3D POINT-CLOUD SPATIAL EXPANSION BY TOTAL LEAST-SQUARES LINE FITTING
PublicationPoint-cloud spatial expansion (PCSE) allows the creation of a new pointcloud form that presents an alternative geometry of an entire object in a single spatial view. Spatial expansion facilitates the analysis process and introduces an additional spatial parameter describing the point cloud. An important element of the PCSE method is determining the position of the axis of symmetry of a symmetrical object: the procedure for determining...
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Polynomial Chaos Expansion in Bio-and Structural Mechanics
PublicationThis monograph presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the...
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Polynomial Chaos Expansion in Bio- and Structural Mechanics
PublicationThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair...
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Investigation of noises in the EPN weekly time series
PublicationThe constantly growing needs of permanent stati ons’ velocities users cause their stability level to increase. To this research we included more than 150 stations located across Europe operating within the EUREF Permanent Network (EPN) w ith weekly changes in the ITRF2005 reference frame. The obvious long-range dependencies in the stochastic part of GPS time series were p roven by Ljung-Box...
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Application of Illuminating Modes concept in modal expansion of elliptical resonator
PublicationIn the paper an IlluminatingModes (IM) approach as an extension of Spectral Domain Approach (SDA) is presented. IM concept is applied to the case of open microstrip planar elliptical resonator. A modal expansion of currents induced in the structures during illuminating them by a single plane wave is the novelty of the method. As an example of application of the method, we present the results obtained by an examination of two resonators...
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Transcriptional activity of epigenetic remodeling genes declines in keratinocytes after in vitro expansion
PublicationPURPOSE: In vitro expansion is an invaluable method to obtain keratinocytes in amounts necessary for effective transplantation therapies. In vitro cell culturing provokes questions concerning potential epigenetic alterations occurring in expanded cells in the context of usefulness for transplantation and safety. The purpose of this study was to investigate as to whether keratinocyte expansion is associated with changes in the activity...
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Container port expansion towards the sea in the context of maritime spatial planning
PublicationThe growth of ships causes a significant increase in demand for new port surfaces and demands for the depths of water bodies in the ports. Due to technological changes in the transshipment and development pressure ports lacks space and they move towards the sea with their activities. The paper discusses the reasons for the phenomenon of expansion of ports towards the sea and its effects on maritime spatial planning.
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Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems
PublicationThe 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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Hybrid analysis of microwave components in cylindrical coordinates with function expansion in subdomains.
PublicationW artykule zaproponowano wydajną metodę przyspieszenia analizy FDTD, poprzez podział dziedziny obliczeniowej i zastosowanie różnych algorytmów w różnych elementach dziedziny. Zaproponowano uniwersalną metodę łączenia techniki PEE (Partial Eigenfunction Expansion)i niezmodyfikowanej FDTD w jednej analizie. Uzyskano redukcję liczby zmiennych oraz wydłużenie kroku czasowego.
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Experimental and Numerical Study on Pounding of Structures in Series
PublicationPounding between structures in series during earthquakes may cause serious damage in the structural elements. The aim of this paper is to show the results of an experimental and numerical study that is focused on pounding between more than two structures which may be described as “structures in series”. In this study, the shaking table experiments, as well as the numerical analyses, were performed using three tower models including...
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TESTING CONTRACTION AND THERMAL EXPANSION COEFFICIENT OF CONSTRUCTION AND MOULDING POLYMER COMPOSITES
PublicationThe paper presents results of systematic tests of contraction and thermal expansion coefficients of materials based on polymer composites. The information on the above material properties is essential both at the design stage and during the use of finished products. Components for the samples were selected in such a way as to represent typical materials used for production of construction and moulding elements. The performed tests...
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Photoelectron spectroscopy of a series of acetate and propionate esters
PublicationThe electronic state and photoionization spectroscopy of a series of acetate esters: methyl acetate, isopropyl acetate, butyl acetate and pentyl acetate as well as two propionates: methyl propionate and ethyl propionate, have been determined using vacuum-ultraviolet photoelectron spectroscopy. These experimental investigations are complemented by ab initio calculations. The measured first adiabatic and vertical ionization energies...
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Employees’ self-expansion as a mediator between perceived work conditions and work engagement and productive behaviors
PublicationThere has been increasing scientific interest in the relationships between self-perception and group identity development processes as well as the behavioural implications of these processes in organizational contexts. Recently, the concept of workplace self-expansion has been introduced to work and organizational psychology. That is, the self-expanding characteristics of work and the workplace have been related to job satisfaction...
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A new multi-process collaborative architecture for time series classification
PublicationTime series classification (TSC) is the problem of categorizing time series data by using machine learning techniques. Its applications vary from cybersecurity and health care to remote sensing and human activity recognition. In this paper, we propose a novel multi-process collaborative architecture for TSC. The propositioned method amalgamates multi-head convolutional neural networks and capsule mechanism. In addition to the discovery...
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The work of Professor Andrzej Lasota on asymptotic stability and recent progress
PublicationPraca poświęcona jest wkładowi Profesora Andrzeja Lasoty w teorię asymptotycznej stabilności iteracji operatorów stochastycznych na przestrzeni ostatnich 36 lat. Podkreślono aplikacyjny charakter wyników, pokazując stosowne przykłady z modelowania rozwoju komórki, optymalizacji wierceń geologicznych i ewolucji modeli kwantowych.
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
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Video of LEGO Bricks on Conveyor Belt Dataset Series
PublicationThe dataset series titled Video of LEGO bricks on conveyor belt is composed of 14 datasets containing video recordings of a moving white conveyor belt. The recordings were created using a smartphone camera in Full HD resolution. The dataset allows for the preparation of data for neural network training, and building of a LEGO sorting machine that can help builders to organise their collections.
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Single and Series of Multi-valued Decision Diagrams in Representation of Structure Function
PublicationStructure function, which defines dependency of performance of the system on performance of its components, is a key part of system description in reliability analysis. In this paper, we compare two approaches for representation of the structure function. The first one is based on use of a single Multi-valued Decision Diagram (MDD) and the second on use of a series of MDDs. The obtained results indicate that the series of MDDs...
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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TIME SERIES DATA FOR 3D FLOOD MAPPING
PublicationThanks to the ability to collect information about large areas and with high frequency in time areas threatened by floods can be closely monitored. The effects of flooding are socio-economic losses. In order to reduce those losses, actions related to the determination of building zones are taken. Moreover, the conditions to be met by facilities approved for implementation in such areas are determined. Therefore, satellite data...
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Comparison of EHD devices with parallel and in series spiked electrodes
PublicationIn this paper two electrohydrodynamic (EHD) devices for gas pumping and cleaning are presented. In both cases to induce an airflow in these EHD devices corona discharge was used. The discharge was generated between the spiked electrodes set parallel (the first case) or in series (the second case) and the plate electrodes. An asymmetric electric field and generated discharge result in unidirectional gas flow through the EHD device....
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Asymptotic modelling and design of some microlayered functionally graded heat conductors
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Regression points in non-intrusive polynomial chaos expansion method and D-optimal design
PublicationThe paper addresses selected issues of uncertainty quantification in the modelling of a system containing surgical mesh used in ventral hernia repair. Uncertainties in the models occur e.g. due to variability of abdominal wall properties among others. In order to include them, a non-intrusive regression-based polynomial chaos expansion method is employed. Its accuracy depends on the choice of regression points. In the study a relation...
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A Conformal Circularly Polarized Series-Fed Microstrip Antenna Array Design
PublicationA conformal circularly polarized series-fed microstrip array design for broadside radiation is presented. The array aperture under design is conformal to a cylindrical surface of a given radius. The approach we present primarily addresses focusing of the circularly polarized major lobe of the conformal array by proper dimensioning of the aperture spacings. The proposed analytical models yield the values of the element spacings...
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Dynamic polarizability of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the Dirac-Coulomb Green function
PublicationWe utilize the Sturmian expansion of the Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997)] to obtain components of the dynamic dipole polarizability tensor of the relativistic hydrogenlike atom in the ground state. It is found that the tensor may be expressed in terms of two independent quantities: a scalar polarizability and a vector polarizability, the latter being of the relativistic origin. In the static...
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Assessing historical church tower asymmetry using point cloud spatial expansion
PublicationChurch towers are key cultural heritage. In theory, towers are vertical, while facade elements are symmetrically positioned around the tower axis. However, during service of a structure, building and lifetime conditions cause deviations, with associated risks. Laser scanning point clouds can be used to assess the structural state but a universal approach was missing. The proposed algorithm first estimates the tower inclination,...
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Times Series Analysis Of Road Safety Trends At The Regional Level In Poland
PublicationThe paper presents possibility of applying a structural times series modeling with explanatory and intervention variables as a tool capable for explaining the changes in the monthly number of fatalities and seriously injured in traffic accidents. The analysis covers regional level and takes into consideration traffic accidents data of two regions: Pomorskie and Warmia-Mazury. In addition short-term forecasts for the two regions...
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Earthquake–induced pounding on response of adjacent structures in series: experimental and numerical study
PublicationPounding between structures in series during earthquakes may cause serious damage in the structur-al elements. The aim of this paper is to show the results of an experimental and numerical study that is focused on pounding between more than two structures which may be called "structures in series". In this study, the shaking table experiments, as well as the numerical analyses, were performed using three tower models including...
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Road safety analysis in Poland using time-series modelling techniques
PublicationA number of international studies argue that there is a correlation between the number of traffic fatalities and the degree of public activity. The studies use the unemployment rate to support that argument. As unemployment grows miles travelled fall, a factor known to affect road safety. This relationship seems to be true for Poland, as well. The model presented in the paper is intended to prove it. It is a structural time-series local...