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Search results for: MINIMAL NUMBER OF PERIODIC POINTS
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Minimal number of periodic points for smooth self-maps of S^3
PublicationW pracy wyznaczona została najmniejsza liczba punktów periodycznych w gładkiej klasie homotopii odwzorowania sfery trójwymiarowej w siebie.
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Minimal number of periodic points for smooth self-maps of RP^3
PublicationNiech f będzie gładkim odwzorowaniem 3-wymiarowej rzeczywistej przestrzeni rzutowej w siebie, r będzie ustaloną liczbą naturalną. W artykule wyznaczona została minimalna liczba punktów r-periodycznych w gładkiej klasie homotopii odwzorowania f.
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Minimal number of periodic points for C^1 self-maps of compact simply-connected manifolds
PublicationNiech f będzie odwzorowaniem gładkiej zwartej i jednospójnej rozmaitości o wymiarze większym lub równym 3. W pracy zdefiniowany został topologiczny niezmiennik będący najlepszym dolnym oszacowaniem liczby punktów periodycznych w klasie gładkich odwzorowań homotopijnych z f.
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublicationLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublicationFor a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m 4, we provide an algorithm for estimating the values of the topological invariant D^m_r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing D^m_r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013),...
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublicationLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball
PublicationDla ciągłego odwzorowania f przestrzeni określonej w tytule w siebie, które posiada rzeczywiste wartości własne na drugiej grupie homologii, wyznaczona została minimalna liczba punktów r-periodycznych w klasie wszystkich gładkich odwzorowań homotopijnych z f.
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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Algebraic periods and minimal number of periodic points for smooth self-maps of 1-connected 4-manifolds with definite intersection forms
PublicationLet M be a closed 1-connected smooth 4-manifolds, and let r be a non-negative integer. We study the problem of finding minimal number of r-periodic points in the smooth homotopy class of a given map f: M-->M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...
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On the growth of the number of periodic points for smooth self maps of a compact manifold
PublicationDla ciągłego przekształcenia jednospójnej rozmaitości wymiaru co najmniej 3 w siebie, wykazujemy, że wzrost liczby punktów r-periodycznych w klasie homotopii może być nie szybszy niż liniowy, dla dowolnego, ustalonego r.
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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Minimizing the number of periodic points for smooth maps. Non-simply connected case
PublicationNiech f będzie gładkim odwzorowaniem zamkniętej rozmaitości o wymiarze wiekszym niż 2, a r ustaloną liczbą naturalną. W artykule zdefiniowany został niezmiennik topologiczny równy minimalnej liczbie punktów r-periodycznych w gładkiej klasie homotopii f.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet 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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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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Weak forms of shadowing in topological dynamics
PublicationWe 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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Generalized Dold sequences on partially-ordered sets
PublicationDold 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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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublicationIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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One-dimensional chaos in a system with dry friction: analytical approach
PublicationWe 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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DETERMINATION OF VERTICAL DISPLACEMENTS IN RELATIVE MONITORING NETWORKS
PublicationThe problem of determining displacements of objects is an important and current issue, in particular in terms of operational safety. This is a requirement that covers geodetic, periodic control measurements in order to determine horizontal and vertical displacements. The paper is focused on the analysis of vertical displacements. Geodetic measurements and their interpretation allow to reduce the risk of possible structural catastrophes....
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet 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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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublicationLet 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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Non-Destructive Testing of the Longest Span Soil-Steel Bridge in Europe—Field Measurements and FEM Calculations
PublicationThe article describes interdisciplinary and comprehensive non-destructive diagnostic tests of final bridge inspection and acceptance proposed for a soil-steel bridge made of corrugated sheets, being the European span length record holder (25.74 m). As an effect of an original concept a detailed and precise information about the structure short-term response was collected. Periodic diagnostics of bridge deformations was done one...
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Dold sequences, periodic points, and dynamics
PublicationIn 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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Bridge Non-Destructive Measurements Using a Laser Scanning during Acceptance Testing: Case Study
PublicationOwing to the recent proliferation of inventory works on roads and railways, bridge acceptance tests have increased exponentially. These tests’ results are often misinterpreted owing to the use of various measuring equipment types, rendering integrated interpretation problematic. It is also problematic that adjusting the measurement method is difficult when the structure’s response to load is uncertain. Therefore, it is important...
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Application of Regression Line to Obtain Specified Number of Points in Reduced Large Datasets
PublicationModern measurement techniques like scanning technology or sonar measurements, provide large datasets, which are a reliable source of information about measured object, however such datasets are sometimes difficult to develop. Therefore, the algorithms for reducing the number of such sets are incorporated into their processing. In the reduction algorithms based on the...
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Indices of interations and periodic points of simplical maps of smooth type
PublicationW pracy dowodzi się symplicjalnego odpowiednika twierdzenia Chowa, Mallet-Paret i Yorke´a. Otrzymany wynik służy do badania punktów periodycznych odwzorowań symplicjalnych gładkiego typu.
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Maps with bounded sequence of indices of interations and finitaly many periodic points
PublicationW pracy badane są związki pomiędzy globalną topologiczną strukturą przestrzeni wyrażoną w terminach charakterystyki Eulera-Poincar odwzorowań na niej określonych, a spełniających założenia z tytułu, a lokalnymi własnościami przestrzeni zdeterminowanymi przez zachowanie się tych odwzorowań w punkatach periodycznych.
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On delay differential equations with almost periodic boundary conditions started from different points
PublicationDyskutowany jest problem istnienia ekstremalnych rozwiązań dla równań różniczkowych typu opóźnionego przy odpowiednich warunkach brzegowych. Sformułowano odpowiednie twierdzenia porównawcze. W pracy zawarte są również wyniki dotyczące takich równań przy większej ilości argumentów opóźnionych.
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ELECTRICAL CONDUCTIVITY AND pH IN SURFACE WATER AS TOOL FOR IDENTIFICATION OF CHEMICAL DIVERSITY
PublicationIn the present study, the creeks and lakes located at the western shore of Admiralty Bay were analysed. The impact of various sources of water supply was considered, based on the parameters of temperature, pH and specific electrolytic conductivity (SEC25). All measurements were conducted during a field campaign in January-February 2017. A multivariate dataset was also created and a biplot of SEC25 and pH of the investigated waters...
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Preserving Trees in Automata
PublicationWe present a method to store additional information in a minimal automaton so that it is possible to compute a corresponding tree node number for a state. The number can then be used to retrieve additional information. The method works for minimal (and any other) deterministic acyclic finite state automata (DFAs). We also show how to compute the inverse mapping.
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Trees having many minimal dominating sets
PublicationWe provide an algorithm for listing all minimal dominating sets of a tree of order n in time O(1.4656^n). This leads to that every tree has at most 1.4656^n minimal dominating sets. We also give an infinite family of trees of odd and even order for which the number of minimal dominating sets exceeds 1.4167^n, thus exceeding 2^{n/2}. This establishes a lower bound on the running time of an algorithm for listing all minimal dominating...
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Sailing Vessel Routing Considering Safety Zone and Penalty Time for Altering Course
PublicationIn this paper we introduce new model for simulation sea vessel routing. Besides a vessel types (polar diagram) and weather forecast, travel security and the number of maneuvers are considered. Based on these data both the minimal travelling costs and the minimal processing time are found for different vessels and different routes. To test our model the applications SailingAssistance wad improved. The obtained results shows that...
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A Simulative Comparison of Ship Domains and Their Polygonal Approximations
PublicationThe paper investigates the impact of a precise ship domain shape on the size of collision avoidance manoeuvres. The considered collision avoidance manoeuvres include both course and speed alterations. Various ship domains are compared with their polygonal approximations, which vary in the number of points of a domain contour and placement of these points. The best of all considered approximations is determined in the course of...
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Towards a classification of networks with asymmetric inputs
PublicationCoupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms of Stewart et al (2003 SIAM J. Appl. Dyn. Syst. 2, 609–646), Golubitsky et al (2005 SIAM J. Appl. Dyn. Syst. 4, 78–100) and Field (2004 Dyn. Syst. 19, 217–243). It is known that two non-isomorphic n-cell coupled networks can determine the same sets of...
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Graphs with equal domination and certified domination numbers
PublicationA setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...
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Złote monety bulionowe – testowanie pasywnego charakteru inwestycji
PublicationCel – Wyznaczenie składu optymalnego portfela inwestycyjnego o minimalnym ryzyku, zawierającego inwestycję w polskie monety bulionowe (Orzeł Bielik) oraz inwestycję na polskiej giełdzie papierów wartościowych. Testowanie pasywnego charakteru inwestycji w monety. Metodologia badania – Konstrukcja portfeli inwestycyjnych o minimalnym ryzyku według teorii H.M. Markowitza. Autorska metoda badania pasywnego charakteru inwestycji...
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Reduced-cost surrogate modeling of input characteristics and design optimization of dual-band antennas using response features
PublicationIn this article, a procedure for low-cost surrogate modeling of input characteristics of dual-band antennas has been discussed. The number of training data required for construction of an accurate model has been reduced by representing the antenna reflection response to the level of suitably defined feature points. The points are allocated to capture the critical features of the reflection characteristic, such as the frequencies...
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Novel structure and design of enhanced-bandwidth hybrid quadrature patch coupler
PublicationA novel structure and design optimization procedure of an enhanced-bandwidth hybrid quadrature patch coupler is proposed. Improved performance of the circuit has been obtained by parameterizing the coupler sections using splines, which introduces additional degrees of freedom. Due to computational complexity of the parameter adjustment problem, a sequential design procedure is applied. In each iteration, a selected number of spline...
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An Enhanced Reduced Basis Method for Wideband Finite Element Method Simulations
PublicationIn this paper, we present a novel strategy for selecting expansion points in the reduced basis method. A single computation of the error estimator is used to select a few expansion points in the multi-parameter space simultaneously. The number of selected points is determined adaptively, based on the accuracy of the current reduced model. The reliability and efficiency of this proposed approach are illustrated by numerical tests...
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Point cloud unification with optimization algorithm
PublicationTerrestrial laser scanning is a technology that enables to obtain three-dimensional data – an accurate representation of reality. During scanning not only desired objects are measured, but also a lot of additional elements. Therefore, unnecessary data is being removed, what has an impact on efficiency of point cloud processing. It can happen while single point clouds are displayed – user decides what he wants...
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Accuracy analysis of 3D model obtained by photogrammetric method on the example of historic room from Wisłoujście Fortress
PublicationThe article presents a comparison of obtained models of a test object. Close range photogrammetry was used to obtain 3D models. As test object was used one of the rooms located in Wisłoujście Fortress in Gdańsk, Poland. Different models were obtained by using different distribution and number of reference points. Article contains analysis of differences between coordinates of control points obtained from total station measurements...
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Fast multi-criterial statistical analysis and design optimization of compact microwave couplers
Publication—A rapid statistical analysis and yield estimation of compact microwave couplers involving multiple performance parameters has been presented. The analysis is realized using a fast surrogate model representing appropriate characteristic points of the coupler response. Because of less nonlinear dependence of the characteristic points on the structure geometry (compared to the original response, i.e., S-parameters vs. frequency),...
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Thermal Self-Action of Acoustic Beams Containing Several Shock Fronts
PublicationThermal self-action of an acoustic beam with one discontinuity or several shock fronts is studied in a Newtonian fluid. The stationary self-action of a single sawtooth wave with discontinuity (or some integer number of these waves), symmetric or asymmetric, is considered in the cases of self-focusing and self- defocusing media. The results are compared with the non-stationary thermal self-action of the periodic sound. Thermal self-action...
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VIBRATION PARAMETERS FOR DAMAGE DETECTION IN STRUCTURES
PublicationThe aim of this paper is to examine how damage indicators are sensitive to changing number of frequencies and mode shapes and also to number and location of measurement points. The influence of measurement errors was also analyzed for all cases. For the analysis, those damage indicators are chosen which use changes in such modal parameters as natural frequencies and mode shapes and also differences between the curvatures of the damaged...
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Total Domination Versus Domination in Cubic Graphs
PublicationA dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...
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Zero-Pole Space Mapping for CAD of Filters
PublicationIn this paper, we propose a new space-mapping technique tailored to the CAD of microwave filters. The goal of space mapping is to achieve a satisfactory design with the minimal number of fine model evaluations. In our approach, the filter is represented by a rational function. To quickly align the coarse and fine models, and to speed up the direct optimization of the coarse model, we propose matching the zeros and poles of a rational...
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Broadcast copies reveal the quantumness of correlations
PublicationWe study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations-mutual information-with the notion of broadcast copies-i.e., generally nonfactorized copies-of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization...