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Search results for: NONLINEAR STATIC ANALYSES
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Investigation of Transmit and Receive Characteristics of Laboratory Model for the Parametric Echosounder
PublicationInvestigation and operation of devices based on nonlinear interaction of high-intensity waves have been carried out for several decades. However, it is still a new tool to study the properties of the water environment and especially the upper layers of the seabed. This paper describes the results of tests of the new device that is intended to be applied for sounding underwater areas. The device has been designed and built in collaboration with...
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Design of modified PID controllers for 3D crane control
PublicationFrom the control viewpoint, 3D crane is a dynamic, nonlinear and multidimensional electromechanical system. In this paper, five control systems using a set-point weighted PID controllers (modified controllers) are designed. These structures and properties are presented. Optimization process of controllers settings based on integral performance indices is made. Simulation tests of control systems are presented. Comparison of integral...
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Wykorzystanie metody Neldera-Meada do identyfikacji wartości parametrów niequasi-statycznego modelu małosygnałowego tranzystora MOS
PublicationW artykule zaprezentowano wyniki zastosowania metody sympleksu Neldera-Meada do ekstrakcji wartości parametrów niequasi-stycznego modelu małosygnałowego tranzystora MOS. Przedstawiono równoważny elektryczny schemat zastępczy i model matematyczny nowego modelu małosygnałowego MOSFETa dla częstotliwości mikrofalowych. Opisano zaimplementowany algorytm i otrzymane rezultaty badań.
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Fourier transform symmetry and invariance for neurocontrol of NARMA models
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Boundary value problems with causal operators
PublicationPraca dotyczy istnienia rozwiązań dla równań różniczkowych z nieliniowymi dwu-punktowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie rozwiązań takich zagadnień stosując metodę iteracji monotonicznych. Dyskutowano też nierówności różniczkowe rzędu pierwszego z dodatnimi operatorami liniowymi oraz problem rozwiązań ekstremalnych.
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Fixed orbit index for equivariant maps
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Existence of solutions for second order impulsive differential equations with deviating arguments
PublicationPraca dotyczy równań różniczkowych z impulsami i odchylonymi argumentami. Badano problem istnienia rozwiązań stosując metodę iteracji monotonicznych opartą na dolnych i górnych rozwiązaniach. Praca uogólnia szereg znanych wyników.
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Comparision principles for parabolic differential - functional initial - value problems.
PublicationBadamy paraboliczne równania z zależnością funkcyjną i podajemy kryteria jednoznaczności przy warunkach porównawczych typu Perrona i Lipschitza dla nieliniowej prawej strony. W przypadku gdy zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej, to stosujemy nierówności typu Henry'ego.
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Equivariant Conley index in Hilbert spaces and applications to strongly indefinite problems
PublicationW pracy zdefiniowano teorię indeksu Conley`a w przestrzeni Hilberta z działaniem zwartej grupy Liego. Została ona wykorzystana do szacowania z dołu ilości rozwiązań periodycznych w teorii nieliniowych autonomicznych układów Hamiltona.
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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An absorbing set for the Chialvo map
PublicationThe 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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A note on the Morse homology for a class of functionals in Banach spaces involving the 2p-area functional
PublicationIn 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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Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions
PublicationBadane są problemy brzegowe dla równań różniczkowych rzędu czwartego z odchylonymi argumentami i z warunkami brzegowymi typu całkowego. Sformułowano twierdzenie dotyczące istnienia dodatnich rozwiązań takich problemów. W dowodzie korzystano z tw. Avery-Petersona o punktach stałych dla stożków. Podano przykład ilustrujący otrzymane wyniki.
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Nonnegative solutions to nonlocal boundary value problems for systems of second-order differential equations dependent on the first-order derivatives
PublicationStosując tw. Avery-Petersona o punkcie stałym, podano warunki dostateczne na istnienie nieujemnych rozwiązań dla układów równań różniczkowych rzędu drugiego z argumentami opóźnionymi i wyprzedzonymi oraz warunkami brzegowymi zawierającymi całki Stieltjesa. Praca zawiera wiele przykładów.
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Description of the solution set of the von Karman equations for a circular plate in a small neighbourhood of a simple bifurcation point
PublicationW niniejszej pracy badamy równania von Karmana dla cienkiej, sprężystej, kołowej płyty na sprężystym podłożu, poddawanej działaniu sił ściskających wzdłuż brzegu. Są to równania różniczkowe cząstkowe IV rzędu. Stosując metody analizy nieliniowej, opisujemy zbiór rozwiązań równań von Karmana w małym otoczeniu jednokrotnego punktu bifurkacji.Badania były finansowane przez grant nr 1 P03A 042 29.
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions
PublicationPraca dotyczy warunków dostatecznych na istnienie dodatnich rozwiązań dla równań różniczkowych z wyprzedzonymi argumentami i warunkami brzegowymi zawierającymi całki Stieltjesa.
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Stability of delay induced oscillations in gene expression of Hes1 protein model
PublicationW pracy prezentowana jest matematyczna analiza modelu ekspresji genu białka Hes1. Rozważamy układ równań z dwoma opóźnieniami - w produkcji białka Hes1 oraz jego mRNA. Dowodzimy istnienia i jednoznaczności oraz nieujemności rozwiązań. Pokazujemy istnienie dokładnie jednego dodatniego stanu stacjonarnego. Wykazujemy, że stabilność stanu stacjonarnego zależy od sumy opóźnień. Podajemy warunek dostateczny na wystąpienie bifurkacji...
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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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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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The smoothness test for a density function
PublicationThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublicationStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublicationWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublicationWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Clarke duality for Hamiltonian systems with nonstandard growth
PublicationWe consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.
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Bifurcation of equilibrium forms of a gas column rotating with constant speed around its axis of symmetry
PublicationWe will be concerned with the problem of deformation of the lateral surface of a column that rotates with constant speed around its axis of symmetry. The column is filled by a gas and our goal is to investigate the deformation of the lateral surface depending on the pressure of the gas.
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
PublicationWe analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...
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Boundary value problems for first order differential equations of mixed type
PublicationPraca dotyczy równań różniczkowo-całkowych z nieliniowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie jedynego rozwiązania oraz rozwiązań ekstremalnych takich problemów. Dyskutowane są nierówności różniczkowo-całkowe. Podano przykłady ilustrujące otrzymane wyniki teoretyczne.
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On the Possibility of Increasing Ship Energy Efficiency Through Improved Propulsion Control System
PublicationThis paper summarizes the analyses conducted to assess the impact of the ship's propulsion control system on energy efficiency in calm, manoeuvre, and sea wave conditions, where the goal of the investigation is to develop new strategies for controlling the ship's motion while considering the interactions between the hull, engine, and propeller.
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Factors determining selection of production planning and control system
PublicationThe article contains a comparative characteristics of selected systems of production planning and control, such as: MRP, kanban/JiT, DBR/TOC. The results of the performed analyses served as a basis for determining key market factors related to production planning and control functions, which determine the choice of an appropriate system.
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Pre-feasibility study for treatment wetland application for wastewater treatment in dispersed development
PublicationThe aim of the paper is to present the conducted analyses of pre-feasibility study of different approaches for wastewater management in a settlement of 180 persons. In the assessment both technical and economic aspects were analyzed. The costs were calculated for three different and, at the same time, most popular as well as possible technical solutions like: (i) construction of local wastewater treatment plant with gravitational...
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Material for Automatic Phonetic Transcription of Speech Recorded in Various Conditions
PublicationAutomatic speech recognition (ASR) is under constant development, especially in cases when speech is casually produced or it is acquired in various environment conditions, or in the presence of background noise. Phonetic transcription is an important step in the process of full speech recognition and is discussed in the presented work as the main focus in this process. ASR is widely implemented in mobile devices technology, but...
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Application of the fluid–structure interaction technique for the analysis of hydrodynamic lubrication problems.
PublicationFluid–structure interaction technique seems to be one of the most promising possibilities for theoretical analysis of lubrication problems. It allows coupling of different physical fields in one computational task, taking into account the interaction between them. In this article, two sets of fluid–structure interaction analyses focusing on the bearing performance evaluation are presented. One analysis was applied to a water-lubricated...
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Correlation between natural frequencies and buckling load in a stiffened shell
PublicationThe paper deals with correlation between natural frequencies and buckling load of a stiffened shell composed of corrugated sheets and vertical stiffeners (columns). The simplified shell segment represents the buckling behaviour of a whole silo with sparsely distributed columns. The paper covers variants of linear buckling anal-yses, dynamic eigenvalue analyses and geometrically non-linear analyses of a segment modelled with shell...
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A spatio-temporal approach to intersectoral labour and wage mobility
PublicationThe article presents the spatio-temporal approach for intersectoral labor and wage mobility. Analyses of interindustry mobility were performed with the use of general entropy mobility indices (GEMM). Spatio- temporal approach was obtained thanks to the separate measurement of spatial autocorrelation and regression for each set of sectoral wage and employment structure and was conducted in each year of the research period separately....
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A Spatio-temporal Approach to Intersectoral Labour and Wage Mobility
PublicationThe article presents the spatio-temporal approach for intersectoral labor and wage mobility. Analyses of interindustry mobility were performed with the use of general entropy mobility indices (GEMM). Spatio-temporal approach was obtained thanks to the separate measurement of spatial autocorrelation and regression for each set of sectoral wage and employment structure and was conducted in each year of the research period separately....
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Two-dimensional simulations of concrete fracture at aggregate level with cohesive elements based on X-ray lCT images
PublicationThe paper presents results of two-dimensional meso-scale simulations of fracture in notched concrete beams subjected to three-point bending test. Concrete was assumed as a 4-phase material composed of aggregate grains placed in the cement matrix, interfacial transitional zones (ITZs) and macro-voids. The particle distribution was taken from real concrete beams on the basis of X-ray lCT images. Comprehensive numerical analyses were carried...
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Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility
PublicationThe accurate analysis of the seismic response of isolated structures requires the incorporation of the flexibility of supporting soil. However, it is often customary to idealize the soil as rigid during the analysis of such structures. In the present paper, seismic response time history analyses of base-isolated buildings modelled as single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) systems with linear and nonlinear...
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On Accelerated Metaheuristic-Based Electromagnetic-Driven Design Optimization of Antenna Structures Using Response Features
PublicationDevelopment of present-day antenna systems is an intricate and multi-step process requiring, among others, meticulous tuning of designable (mainly geometry) parameters. Concerning the latter, the most reliable approach is rigorous numerical optimization, which tends to be re-source-intensive in terms of computing due to involving full-wave electromagnetic (EM) simu-lations. The cost-related issues are particularly pronounced whenever...
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The risk of corporate bankruptcy - the conceptual model
PublicationThis article concerns the assessment of different types of risks influencing the corporate bankruptcy risk. The author has developed conceptual model that explains the causes and the trajectories of the collapse of enterprises. In the analyses such factors as demographic, financial, market, political and operational factors influencing the risk of failure were taken into account.
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Laminated plates and shells - first ply failure analysis within 6-parameter shell theory
PublicationThis work describes Tsai-Wu and Hashin criteria modifications, dictated by nonlinear 6-parameter shell theory with asymmetric strain measures and drilling rotation. The material law is based on standard orthotropic elastic constants for a non-polar continuum, under plane state of stress. First ply failure loads of cylindrical panel subjected to pressure and flat compressed plate are estimated by means of Finite Element Analysis....
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublicationIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublicationThe paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations. We investigate weighted difference methods for these problems. A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems...
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Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...