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Search results for: M-INTEGRAL, J-INTEGRAL, ANTI-PLANE SHEAR, MOONEY–RIVLIN MATERIAL, RIGID INCLUSION
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M-integral for finite anti-plane shear of a nonlinear elastic matrix with rigid inclusions
PublicationThe path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem...
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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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Anti-plane waves in an elastic thin strip with surface energy
PublicationWe consider anti-plane motions of an elastic plate taking into account surface energy within the linear Gurtin–Murdoch surface elasticity. Two boundary-value problems are considered that describe complete shear dynamics of a plate with free faces or with free and clamped faces, respectively. These problems correspond to anti-plane dynamics of an elastic film perfectly or non-perfectly attached to a rigid substrate. Detailed analysis...
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Monotone method to Volterra and Fredholm integral equations with deviating arguments
PublicationPraca dotyczy problemów istnienia rozwiązań równań całkowych typu Volterry i Fredholma z odchylonymi argumentami. Podano warunki dostateczne na istnienie rozwiązań w odpowiedniej klasie. Pewne nierówności całkowe typu opóźnionego są również przedmiotem badań.
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Pediatria Integral
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Solution of coupled integral equations for quantum scattering in the presence of complex potentials
PublicationIn this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublicationThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
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Równania całkowe (Integral equations) 2022/2023
e-Learning CoursesWFTIMS, studia II stopnia, kierunek: Matematyka, specjalność: Geometria i grafika komputerowa, sem. 3
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Some integral transforms and their applications
PublicationMotywacją napisania pracy były równania różniczkowe cząstkowe z odchyleniem przy pochodnych. Ponieważ w tym przypadku nie funkcjonuje teoria charakterystyk, więc badamy nowe przekształcenia całkowe w celu znalezienia odpowiedniej aproksymacji jednostajnej lub średniokwadratowej dla zagadnienia Cauchy`ego. Przedstawiamy również eksperymenty numeryczne oparte na zmodyfikowanej metodzie Galerkina.
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Green analytical chemistry as an integral part of sustainable education development
PublicationGreen chemistry is an important way of thinking in the field of chemistry and aims to conduct processes in accordance with the principles of sustainable development. It is the application of a wide range of principles that minimize the impact of both chemical processes and products on the environment. And what about analytical chemistry? Without a doubt, analytical chemistry plays an important role in the sustainable development...
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Surface finite viscoelasticity and surface anti-plane waves
PublicationWe introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are...
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Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations
PublicationVarious numerical methods were proposed for analysis of the light scattering phenomenon. Important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation (DDA). DDA uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo (MC)...
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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Minimization of integral functionals in Sobolev spaces
PublicationPraca ma charakter przeglądowy i jest skierowana do młodych matematyków i doktorantów. Dotyczy problematyki omawianej przeze mnie na Zimowej Szkole Centrum Badań Nieliniowych im. J.P. Schaudera w Toruniu w roku 2009. Zawarłam w niej wybrane, znane wyniki dotyczące problemu minimalizacji funkcjonałów całkowych w przestrzeniach Sobolewa funkcji jednej zmiennej.
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Differential equations with integral boundary conditions
PublicationStosuje się metodę iteracji monotonicznych opartą na dolnym i górnym rozwiązaniu. Przy jednostronnym warunku Lipschitza uzyskano pewne wyniki dotyczące rozwiązań zwyczajnych równań różniczkowych z całkowym warunkiem brzegowym. Sformułowano warunki dostateczne na istnienie jedynego rozwiązania (lub rozwiązań ekstremalnych) w pewnym segmencie. Podano przykłady ilustrujące przyjęte założenia.
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The Influence of Shear Deformation in analysis of plane frames
PublicationThe focus of the paper is to investigate the influence of shear deformation effect on the distribution of internal forces and frame deformation. To estimate shear deformation effect, the Timoshenko beam theory and the concept of shear deformation coefficients are used. Analysis of example frames gives the possibility to evaluate what have the most impact on size of shear deformation and in which type of frames the shear deformation...
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Study of Aliphatic Polyurethanes by the Low-Field 1H NMR Relaxometry Method with the Inversion of the Integral Transformation
PublicationIn this paper, the distributions of the 1H nuclear magnetic resonance (NMR) spin–lattice and spin–spin relaxation times are used to characterize the mobility of different sections of macromolecules of aliphatic polyurethanes and the cross-linking density of polymer chains. The NMR relaxometry method with inversion of integral transformation is applied to study the effect of poly (ethylene glycol) and glycerol phosphate calcium...
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Anti-plane surface waves in media with surface structure: Discrete vs. continuum model
PublicationWe present a comparison of the dispersion relations derived for anti-plane surface waves using the two distinct approaches of the surface elasticity vis-a-vis the lattice dynamics. We consider an elastic half-space with surface stresses described within the Gurtin–Murdoch model, and present a formulation of its discrete counterpart that is a square lattice half-plane with surface row of particles having mass and elastic bonds different...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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Robustly feasible integral LQ-MPC controller for output tracking in constrained linear systems
PublicationW pracy rozważany jest regulator predykcyjny typu dual-mode MPC z liniowo kwadratowym wskaźnikiem jakości w aplikacji do krzepkiego śledzenia wyjść liniowego obiektu dyskretnego w obecności addytywnych zakłóceń. W celu zapewnienia dopuszczalności sterowań regulatora wykorzystano teorię zbiorów niezmienniczych. W celu polepszenia śledzenia wyjść i odrzucenia zakłóceń w regulatorze wykorzystano działanie całkujące (integral control)....
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Inspirations Of Pope Francis’ Concept Of Integral Ecology
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
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On Anti-Plane Surface Waves Considering Highly Anisotropic Surface Elasticity Constitutive Relations
PublicationWithin the framework of highly anisotropic surface elasticity model we discuss the propagation of new type of surface waves that are anti-plane surface waves. By the highly anisotropic surface elasticity model we mean the model with a surface strain energy density which depends on incomplete set of second derivatives of displacements. From the physical point of view this model corresponds to a coating made of a family of parallel...
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On the peculiarities of anti-plane surface waves propagation for media with microstructured coating
PublicationWe discuss new type of surface waves which exist in elastic media with surface energy. Here we present the model of a coating made of polymeric brush. From the physical point of view the considered model of surface elasticity describes a highly anisotropic surface coating. Here the surface energy model could be treated as 2D reduced strain gradient continuum as surface strain energy depends on few second spatial derivatives of...
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Simulating propagation of coherent light in random media using the Fredholm type integral equation
PublicationStudying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g....
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Observation Value Analysis – Integral Part of Bayesian Diagnostics
PublicationThe decision making process, in general, is understood as a process of selecting one of the available solutions to the problem. One of possible approaches supporting the process is Bayesian statistical decision theory providing a mathematical model to make decisions of a technical nature in conditions of uncertainty. Regarding above, a detailed subject of the research is to analyze the value of the observation, which is a part...
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Observation value analysis - integral part of Bayesian diagnostics
PublicationDetailed subject of the research is to analyse the value of the observation, which is a part of preposterior analysis. For the presented network, the main objective was to determine, conducting of which of three tests is the most valuable from the perspective of determining possible need or possibility to omission expensive technical expertise. The main advantage of preposterior analysis is answering the question which of the considered...
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Effects of interfacial sliding on anti-plane waves in an elastic plate imperfectly attached to an elastic half-space
PublicationWe study the anti-plane shear waves in a domain consisting of an elastic layer (plate) with a coating attached to an elastic half-space (substrate). We assume an imperfect contact between the layer and the half-space, allowing some sliding. We also assume some elastic bonds between the layer and the substrate. On the free top surface we apply the compatibility conditions within the Gurtin–Murdoch surface elasticity. We found two...
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Synthesis, structure and physical properties of Ru ferrites: BaMRu5O11 (M= Li and Cu) and BaM'2Ru4O11 (M'=Mn, Fe and Co)
PublicationW pracy opisano syntezę, strukturę i właściwości fizyczne pięciu nowych związków z rodziny ferrytów na bazie Ru, których wzór chemiczny jest BaMRu5O11 (M = Li, Cu) i BaM'2Ru4O11 (M' = Mn, Fe, Co).
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Application and evaluation of M-EPDG for performance analysis of Polish typical flexible and rigid pavements
PublicationThe main goal of the paper is to implement and evaluate the M-EPDG and the software AASHTOware to analyse the performance of new flexible and rigid pavements designed according to the Polish catalogues, which are comparable with analogous catalogues used in other European countries. For this purpose the site-specific inputs for Poland were determined and described in the paper as well as compared to the default input data used...
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In-plane shear nonlinearity in failure behavior of angle-ply laminated shells
PublicationThe paper concerns the progressive failure analysis of laminates with the in-plane shear nonlinearity accounted for.The nonlinear shear response of the layer is described by the constitutive relation treating the stresses as a function of strains. Thus it can be easily incorporated into the displacement-based FEM codes. The brittle failure mechanisms of the fibers and the matrix of the layer are recognized with the use of the Hashin...
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Sylwester Kaczmarek dr hab. inż.
PeopleSylwester Kaczmarek received his M.Sc in electronics engineering, Ph.D. and D.Sc. in switching and teletraffic science from the Gdansk University of Technology, Gdansk, Poland, in 1972, 1981 and 1994, respectively. His research interests include: IP QoS and GMPLS and SDN networks, switching, QoS routing, teletraffic, multimedia services and quality of services. Currently, his research is focused on developing and applicability...
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Journal of Integral Equations and Applications
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INTEGRAL EQUATIONS AND OPERATOR THEORY
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Extensions of Quasilinearization Method for Differential Equations with Integral Boundary Conditions
PublicationPraca dotyczy równań różniczkowych z warunkami brzegowymi typu całkowego. Podano warunki dostateczne na istnienie jedynego rozwiązania takiego zagadnienia i pokazano, że odpowiednio konstruowane ciągi monotoniczne są zbieżne do tego rozwiązania i jest to zbieżność kwadratowa. Te monotoniczne ciągi są przybliżonymi rozwiązaniami problemu wyjściowego i obustronnie szacują szukane rozwiązanie.
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Analysis of Selected Approaches to the Integral Pedagogy in Polish Pedagogical Thought
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A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF NONLINEAR FRACTIONAL INTEGRAL EQUATIONS
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Implementation of non-local integral models into commercial FE methods
PublicationArtykuł omawia implementacje nielokalnych modeli typu całkowego do komercyjnych programów MES. Implementacje pokazano na przykładzie programu Abaqus.
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DEM investigations of two-dimensional granular vortex- and anti-vortex- structures during plane strain compression.
PublicationDEM investigations of two-dimensional granular vortex- and anti-vortex- structures during plane strain compression.
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Evaluation of possibilities in identification and susceptibility testing for Candida glabrata clinical isolates with the Integral System Yeast Plus (ISYP)
PublicationThe aim of this study was to evaluate possibilities of correct identification and susceptibility testing of C. glabrata clinical isolates with Integral System Yeast Plus (ISYP). For species identification, as the reference method, API Candida test and species-specific PCR reactions were used. The potential of antifungal susceptibility testing by the ISYP test was compared with the Sensititre Yeast One. Whilst the reference methods...
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Samoilenko`s method to differential algebraic systems with integral boundary conditions.
PublicationProblemy różniczkowo-algebraiczne z warunkami brzegowymi (typu całkowego) są przedmiotem badań. Zastosowano metodę Samoilenki w powiązaniu z metodą porównawczą. O prawych stronach zagadnienia zakładano, że spełniają warunek Lipschitza oraz promień spektralny odpowiedniej macierzy jest mniejszy od 1.Podane zostały warunki dostateczne na istnienie rozwiązania omawianego zagadnienia.
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On Nonlinear Volterra Integral Equations With State Dependent Delays in Several Variables
PublicationW pracy badane jest istnienie i jednoznaczność rozwiązań nieliniowego równania całkowego typu Volterry z opóźnionym argumentem zależnym od funkcji niewiadomej wielu zmiennych. Poszukiwane są ciągłe rozwiązania lipschitzowskie. Rozwiązania są poszukiwane metodą porównawczą z zastosowaniem twierdzenia Banacha o punkcie stałym.
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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An integral-differential method for impedance determination of the hydrogen oxidation process in the presence of carbon monoxide in the proton exchange membrane fuel cell
PublicationThe impedance of a proton exchange membrane fuel cell powered by hydrogen contaminated with carbon monoxide, ranging from 150 to 300 ppb, is measured and discussed. The tested range of CO concentration complied with the fuel standard specified in the ISO standards. Studies of influence of CO contamination on operation of PEMFC are crucial for further development and commercialization of fuel cells for automotive applications. Based...
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Jacek Tejchman prof. dr hab. inż.
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Load introduction to composite columns revisited—Significance of force allocation and shear connection stiffness
PublicationThe AISC 360-16 Specification recommends that the design shear force between parts of a composite column in the load introduction area shall be calculated based on the force allocation at ultimate limit state. Applicability of this straightforward method to the load levels that usually arise in slender composite columns is questionable, as this capacity-based force allocation is only true when the axial force is equal to the plastic...
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Wiktoria Wojnicz dr hab. inż.
PeopleDSc in Mechanics (in the field of Biomechanics) - Lodz Univeristy of Technology, 2019 PhD in Mechanics (in the field of Biomechanics) - Lodz Univeristy of Technology, 2009 (with distinction) List of papers (2009 - ) Wojnicz W., Wittbrodt E., Analysis of muscles' behaviour. Part I. The computational model of muscle. Acta of Bioengineering and Biomechanics, Vol. 11, No.4, 2009, p. 15-21 Wojnicz W., Wittbrodt E., Analysis of...
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Modelling of shear zones during quasi-static granular silo flow using material point method (MPM)
PublicationThe paper focuses on confined silo flow of cohesionless sand. The problem considered is a quasi-static flow in a plane strain model silo with parallel walls simulated with the material point method (MPM). The simulation used a non-local hypoplastic constitutive model. Initially, the paper validated the implemented numerical approach with basic element tests and a plane strain compression test. The subsequent MPM calculations for...