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wszystkich: 190
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Wyniki wyszukiwania dla: DYNAMICAL SYSTEM
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Connection matrix theory for discrete dynamical systems
PublikacjaIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Connection matrix theory for discrete dynamical systems
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Index filtrations and Morse decomposition for discrete dynamical systems
PublikacjaOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Stability by linear approximation for time scale dynamical systems
PublikacjaWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Index filtrations and Morse decompositions for discrete dynamical systems
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Recent development in rigorous computational methods in dynamical systems
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Stability by linear approximation for time scale dynamical systems
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Frequency response based identification of fractional order dynamical systems
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Geometric methods in dynamical systems modelling: electrical, mechanical and control systems
PublikacjaRozważono zagadnienia modelowania systemów dynamicznych z zastosowaniem metod geometrii różniczkowej. Równania dynamiczne otrzymano w postaci inkluzji różniczkowych. Przestrzenie konstytucyjne przyjęto w postaci subwiązek włóknistych. Rozważono przestrzenie konstytucyjne układów elektrycznych, układów mechanicznych i układów sterowania. Podstawowe wyniki pracy dotyczą struktury przestrzeni rozwiązań rozważanych systemów.
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Designing optimal and safe control strategies for time-varying dynamical systems
PublikacjaPublikacja opisuje metodę projektowania optymalnej trajektorii punktu pracy w czasoprzestrzeni stanów przy wykorzystaniu algorytmów optymalizacji grafowej. Zakłada się deterministyczny charakter zmian dynamiki rozpatrywanego procesu. Przestrzeń robocza, będąca ograniczonym podzbiorem czasoprzestrzeni stanów, jest dzielona na zbiór segmentów, którym przypisywane są wielkości reprezentujące właściwości dynamiki własnej w obrębie...
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Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling
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Non-regular, incomplete and singular dynamical systems: impasse points indynamical systems
PublikacjaRozważono nieregularne, niezupełne i osobliwe różniczkowe systemy dynamicznez zastosowaniem metod geometrii różniczkowej.
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Toolgraph Design of Optimal and Feasible Control Strategies for Time-Varying Dynamical Systems
PublikacjaArtykuł prezentuje nową metodę projektowania optymalnych i realizowanych strategii sterowania dla wariantnych procesów dynamicznych. Centralnym ośrodkiem i narzędziem tej metody jest struktura grafu przepływowego reprezentująca istotne właściwości autonomicznej dynamiki danego procesu w przestrzeni czasowo-stanowej, składającej się z elementarnych segmentów. Strukturę tę nazywamy grafem narzędziowym przestrzeni czasowo-stanowej....
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublikacjaWe consider the Leaky Integrate-and-Fire and Perfect Integrator models of neuron’s dynamics with the input function being periodic and almost-periodic (in the sense of Stepanov). In particular we analyze properties and dynamics of the so-called firing map, which iterations give timings of consecutive spikes of a neuron. In case of a periodic input function we provide a detailed description of the sequence of interspike-intervals,...
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Adaptive Dynamical Systems Modelling of Transformational Organizational Change: with Focus on Organizational Culture and Organizational Learning
PublikacjaTransformative Organizational Change becomes more and more significant both practically and academically, especially in the context of organizational culture and learning. However computational modeling and a formalization of organizational change and learning processes are still largely unexplored. This paper aims to provide an adaptive network model of transformative organizational change and translate a selection of organizational...
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Adaptive Dynamical Systems Modelling of Transformational Organizational Change with Focus on Organizational Culture and Organizational Learning
PublikacjaTransformative Organizational Change becomes more and more significant both practically and academically, especially in the context of organizational culture and learning. However computational modeling and a formalization of organizational change and learning processes are still largely unexplored. This paper aims to provide an adaptive network model of transformative organizational change and translate a selection of organizational...
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublikacjaThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Computational Analysis of Transformational Organisational Change with Focus on Organisational Culture and Organisational Learning: An Adaptive Dynamical Systems Modeling Approach
PublikacjaTransformative Organisational Change becomes more and more significant both practically and academically, especially in the context of organisational culture and learning. However computational modeling and formalization of organisational change and learning processes are still largely unexplored. This chapter aims to provide an adaptive network model of transformative organisational change and translate a selection of organisational...
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublikacjaA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Firing map of an almost periodic input function
PublikacjaIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Fixed point indices of iterations of C^1 maps in R^3
PublikacjaW przypadku gładkiego odwzorowania w R^3 dowiedziona została hipoteza Chowa, Malleta-Pareta i Yorka dotycząca postaci ciągów indeksow iteracji oraz podano kompletny opis możliwych ciągów indeksow.
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Partial hyperbolicity and central shadowing
PublikacjaWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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General form of fixed point indices of an iterated C^1 map andinfiniteness of minimal periods
PublikacjaDla zwartego podzbioru punktów periodycznych gładkiego odwzorowania podana zostaje formuła na indeksy iteracji. Wynik stanowi uogólnienie rezultatu Chowa, Malleta-Pareta i Yorke'a.
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Shadowing is generic---a continuous map case
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On quasi-compact Markov nets
PublikacjaAnalizuje się strukturę ergodyczną netów Markowa. W szczególności podano charakteryzację ściśle ergodycznych minimalnych (L-R) netów markowskich na zwartej przestrzeni fazowej. Uzyskano warunki równoważne quasi-zwartości (L-R) netów Markowa, rozszerzając tzw. ergodyczne twierdzenie Lotz'a.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublikacjaLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublikacjaLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Distribution of the displacement sequence of an orientation preserving circle homeomorphism
PublikacjaIn some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublikacjaLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Partial hyperbolicity and central shadowing
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Distortion in the group of circle homeomorphisms
PublikacjaLet G be the group PAff+(R/Z) of piecewise affine circle homeomorphisms or the group Diff∞(R/Z) of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.
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Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
PublikacjaExperimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons, less is known about the dynamic mechanisms shaping their responses to transient inputs, although these bear significant physiological relevance. Here, we study responses to transient...
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Rich Bifurcation Structure in a Two-Patch Vaccination Model
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A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublikacjaIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublikacjaThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
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Subharmonic solutions for a class of Lagrangian systems
PublikacjaWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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Detecting coupling directions with transcript mutual information: A comparative study
PublikacjaCausal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publikacjan this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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Two examples of Quantum Dynamical Semigroups
PublikacjaThe Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous...
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A non-adiabatic wavepacket dynamical study of the low energy chargetransfer process in the S3+ + H collision
PublikacjaThe collisional system S3+ + H?S2+ + H+ has been studied using a time-dependent wavepacket methodologyin two-dimensions. Using available potential energy surfaces and coupling matrix elementsobtained from multireference ab initio calculations, five non-adiabatically coupled electronic states of1P symmetry have been included in the dynamical simulations. The collision has been studied in thelow energy regime of 1-10 eV. The wavepacket...
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Dynamical Aspects of Knowledge Evolution
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The Dynamical Projectors Method Hydro and Electrodynamics
PublikacjaThe dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book...
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Dynamical objectivity in quantum Brownian motion
PublikacjaClassical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability...
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Numerical modeling of quantum dynamical processes
PublikacjaIn this dissertation I present a high-precision (15, 18 or 33 decimal places) C++ implementation of quantum dynamics time propagation algorithms for both time-independent and time-dependent Hamiltonian with an inhomogeneous source term. Moreover I present an extension of both algorithms for time propagation to handle arbitrary number of coupled electronic levels. I have performed a careful validation of these implementations comparing...
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A dynamical model for plasma confinement transitions
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Dynamical description of quantum computing: generic nonlocality of quantumnoise
PublikacjaWe develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the 1/t4 one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error...
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Dynamical nonlocality in quantum time via modular operators
PublikacjaWe formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our...
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Dynamical properties of ordered Fe–Pt alloys
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PI observer stability and application in an induction motor control system
PublikacjaThe paper discusses the problem of stability of a proportional-integral Luenberger observer, designated for the state variables reconstruction of a linear, time-invariant dynamical system.
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Formation of carbon monoxide by radiative association: a quantum dynamical study
PublikacjaRate coefficients for the formation of carbon monoxide (CO) by radiative association of carbon and oxygen atoms are computed using quantum dynamical simulations. At temperatures above 10 K CO radiative association is dominated by C(3P) and O(3P) approaching on the A1Π potential energy curve. The rate coefficient is estimated as k=A(T/300 K)αexp−β/T with A= 1.39 × 10−18 cm3 s−1, α=−0.016 and β= 92.2 for temperatures between 6 and...
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One-dimensional chaos in a system with dry friction: analytical approach
PublikacjaWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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Magnetically induced dynamical stability of a Fe monolayer on W(110)
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Dynamical properties of pnictide ZnSnP2 from ab initio calculations
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Nonlinear Fuzzy Control System for Dissolved Oxygen with Aeration System in Sequencing Batch Reactor
PublikacjaBiological processes at a wastewater treatment plant are complex, multivariable, time varying and nonlinear. Moreover, interactions between the components are very strong. Control of dissolved oxygen is one of most important task at the plant. The level of dissolved oxygen in aerobic tanks has significant influence on behaviour and activity of microorganisms at the plant. Air for aerated tanks is supplied by the aeration system...
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Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization
PublikacjaBeat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3)...
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Dynamical processes in a multi-motor gear drive of heavy slabbing mill
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Electronic and dynamical properties of CeRh2As2 : Role of Rh2As2 layers and expected orbital order
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The Effect of Openings’ Size and Location on Selected Dynamical Properties of Typical Wood Frame Walls
PublikacjaThe wooden frame constructions are now popular in many developed countries of the world. Many of these locations where such buildings are constructed are exposed to seismic and other shocks which are generated by human activities. This paper discusses the effect of the size and location of openings in the wooden frame walls under dynamic loadings. Natural frequencies of such frames with and without openings have been determined....
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Forty-five years of the Rigid Finite Element Method
PublikacjaIn the paper there are described developments of the method in the past 45 year years in dynamical analysis of system with constant and changing in time configuration, including also control of the systems.
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Distributed correlations and information flows within a hybrid multipartite quantum-classical system
PublikacjaUnderstanding the non-Markovian mechanisms underlying the revivals of quantum entanglement in the presence of classical environments is central in the theory of quantum information. Tentative interpretations have been given by either the role of the environment as a control device or the concept of hidden entanglement. We address this issue from an information-theoretic point of view. To this aim, we consider a paradigmatic tripartite...
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Circular saw vibrations or dynamics of the spindle
PublikacjaSawing of wood with circular saws is a typical example of cutting with multi-blade tools. In that kind of cutting, theposition accuracy of following tool blades is a crucial factor which affects the cutting process and machining final effects.Position tooth errors may cause deterioration in cutting conditions, changes in loads of individual teeth and the tool as a whole,and also a decrease in accuracy and surface quality after...
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The sensitiveness of the speed of pile displacement to speed variations of hammer in beating down process
PublikacjaIn this paper there is presented dynamical system described speed of pile displacement during beating down process. Its response is determined by using Heaviside operator. There is introduced the convergence with regulator in partially ordered space. There is given an answer to the question, whetdisplacement is sensitive to hammer's speed variations.
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Influence of the Square Wave Voltage on Dynamical Properties of a Flat Voltammetric Electrode in the Time Domain by the Electrochemical Reversible Reaction
PublikacjaIn this article there is a presentation of the analysis of the polarizing voltage shape influencing dynamic properties of voltammetric electrodes when on their surface reversible reaction takes place in the time domain. The electrode polarization with linearly increasing voltage and with a square component, was analyzed. The analysis that were conducted showed that the voltammetric electrode behaves like a first order transducer....
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Simple SIR models with Markovian control
PublikacjaWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving...
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Publisher's Note: Magnetically induced dynamical stability of a Fe monolayer on W(110) [Phys. Rev. B76, 205427 (2007)]
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Weak forms of shadowing in topological dynamics
PublikacjaWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Parameter selection of an adaptive PI state observer for an induction motor
PublikacjaThe paper discusses problems connected with the parameters selection of the proportional-integral observer, designed for recon- struction of magnetic fluxes and angular speed of an induction motor. The selection is performed in several stages that are focused on different criteria. The first stage consists in selecting observer’s gains and provides desired dynamical properties, taking into consideration immunity to disturbances and...
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Robust Model Predictive Control for Autonomous Underwater Vehicle – Manipulator System with Fuzzy Compensator
PublikacjaThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order to track desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performance can be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPC as a known proficient nonlinear control approach should be improved by the uncertainty estimator...
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MACHINE VISION DETECTION OF THE CIRCULAR SAW VIBRATIONS
PublikacjaDynamical properties of rotating circular saw blades are crucial for both production quality and personnel safety. This paper presents a novel method for monitoring circular saw vibrations and deviations. A machine vision system uses a camera and a laser line projected on the saw’s surface to estimate vibration range. Changes of the dynamic behaviour of the saw were measured as a function of the rotational speed. The critical rotational...
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Robust Model Predictive Control for Autonomous Underwater Vehicle–Manipulator System with Fuzzy Compensator
PublikacjaThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order totrack desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performancecan be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPCas a known proficient nonlinear control approach should be improved by the...
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Transport of dangerous goods by rail, and threats to the subsoil of the railway surface in the event of a disaster
PublikacjaIn Poland, in 2020, the mass of dangerous goods (loads) transported by rail was 26 151.06 thousand tone. This translated into the performance of 8 899 691.89 thousand tone - km of transport performance. In 2020, these figures accounted for 11.72% of the weight of goods transported by rail. The situation is similar in other countries around the world. With such a large volume of transport of dangerous...
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Hierarchical dissolved oxygen control for activated sludge processes
PublikacjaA hierarchical controller for tracking the dissolved oxygen reference trajectory in activated sludge processes is proposed and investigated. The removal of nitrogen and phosphorous from wastewater is considered. Typically, an aeration system itself is a complicated hybrid nonlinear dynamical system with faster dynamics compared to the internal dynamics of the dissolved oxygen in a biological reactor. It is a common approach to...
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The dynamic performance analysis of the Micro-turbine's rotor supparted on slide and roling element bearings
PublikacjaThis article presents the results of investigations of dynamic characteristics of a small-dimension rotor with slide and rolling element bearings. The object of investigations was the rotor-bearing system designed for the ORC based low-power steam micro-turbine. The investigations were performed using MESWIR series programs, as well as commercial FEA software ABAQUS and MADYN 2000. The results of modal analysis of the micro-rotor...
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Rigid polyurethane foams modified with selected layered silicate nanofillers
PublikacjaThe aim of this study was to investigate the effect of three different nanofillers on the properties of rigid polyurethane foams, which were prepared by a one-step, laboratory-scale method from a two-component system at the ratio of NCO groups to OH groups equaled to 2. The reaction mixture consisted of the proper amounts of the commercial oligoether polyol, catalysts, water, nanoclays, and polymeric diphenylmethane diisocyanate....
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Multi-mode vibronic interactions in the five lowest electronic states of the fluorobenzene radical cation
PublikacjaThe multi-mode vibronic interactions between the five lowest electronic states of the fluorobenzene radical cation are investigated theoretically, based on ab initio electronic structure data, and employing the linear vibronic coupling model. Low-energy conical intersections, and strong vibronic couplings are found to prevail within the set of X-A and B-C-D cationic states, while the interactions between these two sets of states...
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Density functional LCAO calculations of vibrational modes and phonon density of states in the strained single-layer phosphorene
PublikacjaThe paper presents an investigation of phosphorene under axial strain on the phonon density of states and vibrational modes. The studies were performed by means of density functional theory (DFT) within the linear combination of atomic orbitals (LCAO). The strained models were constructed using optimised supercell techniques. The vibrational mode spectra were estimated for strains applied for both the zigzag and armchair directions...
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Genetic Hybrid Predictive Controller for Optimized Dissolved-Oxygen Tracking at Lower Control Level
PublikacjaA hierarchical two-level controller for dissolvedoxygenreference trajectory tracking in activated sludge processeshas been recently developed and successfully validated on a realwastewater treatment plant. The upper level control unit generatestrajectories of the desired airflows to be delivered by theaeration system to the aerobic zones of the biological reactor. Anonlinear model predictive control algorithm is applied to designthis...
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Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing
PublikacjaThe precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on...
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Topological invariants for equivariant flows: Conley index and degree
PublikacjaAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Cosmic-Time Quantum Mechanics and the Passage-of-Time Problem
PublikacjaA new dynamical paradigm merging quantum dynamics with cosmology is discussed.
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Unusual dynamic properties of water near the ice-binding plane of hyperactive antifreeze protein
PublikacjaThe dynamical properties of solvation water of hyperactive antifreeze protein from Choristoneura fumiferana (CfAFP) are analyzed and discussed in context of its antifreeze activity. The protein comprises of three well-defined planes and one of them binds to the surface of ice. The dynamical properties of solvation water around each of these planes were analyzed separately; the results are compared with the dynamical properties...
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Dold sequences, periodic points, and dynamics
PublikacjaIn this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
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Effect of vehicle motion stability after impact/crash on traffic safety
PublikacjaThe article presents the application of general stability theory to the study of road traffic stability immediately after an impact (crash, collision). It turns out that when modelling a collision, vehicles can be treated as colliding masses and dynamical systems can be assigned to this phenomenon.
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
PublikacjaSince offshore wind turbine supporting structures are subjected to dynamic environments with time-varying loading conditions, it is important to model their dynamic behavior and validate these models by means of vibrational experiments. In this paper assessment of dynamical state of the structure is investigated by means of both: numerical modeling, and experimental modal analysis. In experimental modal analysis, capturing the...
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Dynamics of cutting power during sawing with circular saw blades as an effect of wood properties changes in the cross section
PublikacjaIn the paper the effect of the method calculation upon the cutting power is presented. In computations were used models in which fracture toughness was incorporated. The comparison concerned models as follows: FM-CM – classic model in which the sum of all uncut chip thicknesses of the simultaneously teeth engaged represented the mean uncut chip thickness, FM-FDM – full dynamical model in which besides variable uncut chip thickness...
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Periodic and chaotic dynamics in a map‐based neuron model
PublikacjaMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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Morse inequalities via Conley index theory
PublikacjaThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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NUMERICAL MODEL QUALITY ASSESSMENT OF OFFSHORE WIND TURBINE SUPPORTING STRUCTURE BASED ON EXPERIMENTAL DATA
PublikacjaAs a structure degrades some changes in its dynamical behavior can be observed, and inversely, observation and evaluation of these dynamical changes of the structure can provide information of structural state of the object. Testing of the real structure, besides of being costly, can cover only limited working states. It is particularly considerable in case of hardly accessible, and randomly/severely dynamically loaded offshore...
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Curlicues generated by circle homeomorphisms
PublikacjaWe investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...
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Theory of valence-band and core-level photoemission from plutonium dioxide
PublikacjaThe correlated-band theory implemented as a combination of the local-density approximation with the dynamical mean-field theory is applied to PuO2. An insulating electronic structure, consistent with the experimental valence-band photoemission spectra, is obtained. The calculations yield a nonmagnetic ground state that is characterized by a noninteger filling of the plutonium 5f shell. The noninteger filling as well as the satellites...
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The effect of circular saw blade clamping diameter on its resonant frequencies
PublikacjaIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with the...
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The Effect of Circular Saw Blade Clamping Diameter on its Resonant Frequencies
PublikacjaIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of the saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with...
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Theoretical study of thermofrictional oscillations due to negative friction-temperature characteristic
PublikacjaAnalytical study on oscillations of a body on a moving counterbody has been done by assuming imperfect frictional thermal contact and friction that decreases with contact temperature. It has been shown that stick-slip oscillation occurs due to decrease of friction coefficient when the body moves in the opposite direction to the counterbody. Dynamical characteristics, such as conditions for stable sliding and limit cycles, have...
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On Computing Curlicues Generated by Circle Homeomorphisms
PublikacjaThe dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...
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Dynamics of Field Line Mappings in Magnetic Flux Tubes
PublikacjaWe study the topological constraints on the dynamics of magnetic field lines in flux tubes. Our approach is based on the application of the topological invariant: fixed point index. We consider periodic flux tubes and find various restrictions on the field lines that come from the sequence of fixed point indices of iterations. We also analyze the case of a tube with a cylindrical obstacle, deducing some special dynamical properties...
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Multi-headed chimera states in coupled pendula
PublikacjaWe discuss the occurrence of the chimera states in the network of coupled, excited by the clock’s mechanisms pendula. We find the patterns of multi-headed chimera states in which pendula clustered in different heads behave differently (oscillate with different frequencies) and create different types of synchronous states (complete or phase synchronization). The mathematical model of the network shows that the observed chimera states...
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Generalized Dold sequences on partially-ordered sets
PublikacjaDold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...
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Billiard in a rotating half-plane
PublikacjaThe main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic...
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Security and Anonymity in Agent Systems
PublikacjaMany agent systems have been developed and suggested for commercial application. However, in spite of the significant potential offered by the agent paradigm, the lack of such important properties as security, anonymity and untracebility especially in open dynamical environment, such as the Internet, has blocked the active implementation of agent technologies. Protecting agent systems poses a more demanding challenge comparing...