Wyniki wyszukiwania dla: PERIODIC POINTS, TOPOLOGICAL DEGREE, SMOOTH MAPS.
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Indices of interations and periodic points of simplical maps of smooth type
PublikacjaW 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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On the growth of the number of periodic points for smooth self maps of a compact manifold
PublikacjaDla 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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Minimal number of periodic points for smooth self-maps of S^3
PublikacjaW 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
PublikacjaNiech 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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Minimizing the number of periodic points for smooth maps. Non-simply connected case
PublikacjaNiech 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 simply-connected manifolds with periodic sequence of Lefschetz numbers
PublikacjaLet 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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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet 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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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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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublikacjaLet 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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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet $r$ 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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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
PublikacjaFor 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
PublikacjaLet 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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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
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Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball
PublikacjaDla 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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Minimal number of periodic points for smooth self-maps of simply-connected manifolds
Dane BadawczeThe problem of finding the minimal number of periodic points in a given class of self-maps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant D_r[f] is equal to the minimal number of r-periodic points...
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Estimates for minimal number of periodic points for smooth self-maps of simply-connected manifolds
Dane BadawczeWe consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant Dr[f] is equal to the minimal number of r-periodic points in the smooth homotopy class of f. We assume that r is odd and all coefficients b(k) of so-called periodic expansion of Lefschetz numbers of iterations are...
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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
PublikacjaLet 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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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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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 4 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 4 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 6 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 6 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 5 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 5 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 8 and homology groups with the sum of ranks less or equal to 10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 8 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 7 and homology groups with the sum of ranks less or equal to10
Dane BadawczeAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 7 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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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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Seiberg-Witten invariants the topological degree and wall crossing formula
PublikacjaFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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Shub’s conjecture for smooth longitudinal maps of S^m
PublikacjaLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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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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Maps with bounded sequence of indices of interations and finitaly many periodic points
PublikacjaW 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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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165-2169].
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublikacjaConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Minimal number of periodic points for C^1 self-maps of compact simply-connected manifolds
PublikacjaNiech 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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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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Degree of T-equivariant maps in R^n
PublikacjaW pracy przedstawiona jest konstrukcja niezmienniczego stopnia topologicznego dla odwzorowań z symetriami działających na przestrzeni euklidesowej z inwolucją. Udowodnione jest twierdzenie, że dwa dopuszczalne i gradientowe odwzorowania niezmiennicze są niezmienniczo homotopijne wtedy i tylko wtedy, gdy są one homotopijne niezmienniczo i gradientowo.
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublikacjaWe give a complete description of possible sequences ofindices of iterations of f at an isolated fixed point, answering inaffirmative the Chow, Mallet-Paret and Yorke conjecture posed in[S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index whichis a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983,pp. 109-131].
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublikacjaWe present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectrum in Hilbert space. Two possible applications are discussed.
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Equivariant degree of convex-valued maps applied to set-valued BVP
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On delay differential equations with almost periodic boundary conditions started from different points
PublikacjaDyskutowany 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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Justyna Signerska-Rynkowska dr inż.
OsobySince 2021 visiting assistant professor in Dioscuri Centre in Topological Data Analysis (Institute of Mathematics of the Polish Academy of Sciences, IMPAN) Since 2016 assistant professor at Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, Department of Differential Equations and Mathematics Applications 2020 - 2023 Principal Investigator in "SONATA" grant “Challenges of low-dimensional...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn 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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The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori
Dane BadawczeThe dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasi-unipotent self-maps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz...
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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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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of...
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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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Dynamics of S-unimodal maps used in population modeling.
Dane BadawczeS-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence...
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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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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublikacjaThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...
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Topological model of aptitude of the measurement circuits of main subassemblies of an internal combustion engine crankshaft-piston assembly
PublikacjaThe paper presents a topological model allowing to determine the probability of aptitude of the diagnosing system (SDG) individual measuring circuits and also to determine to what degree they influence the assessment of the technical condition of an arbitrary main subassembly of crankshaft-piston assemblies as a diagnosed system (SDN).
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Integrate-and-fire models with an almost periodic input function
PublikacjaWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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Path components of the space of gradient vector fields on the two dimensional disc
PublikacjaWe present a short proof that if two gradient maps on the twodimensional disc have the same degree, then they are gradient homotopic.
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Degree product formula in the case of a finite group action
PublikacjaLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Effects of the Origin and Deacetylation Degree of Chitosan on Properties of Its Coatings on Titanium
PublikacjaThe properties of chitosan coatings on titanium surfaces may be influenced by a variety of factors, including their chemical characteristics and the deposition method. The aim of this research was to determine the influence of a chitosan’s origin (a type of shrimp) and deacetylation degree (DD), when deposited on a very smooth titanium surface, on adhesion and biological behavior. The tests were performed using chitosan of a degree...
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublikacjaWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems
PublikacjaIn this work we will be concerned with the existence of an almost homoclinic solution for a perturbed Newtonian system in a finite dimensional space. It is assumed that a potential is C^1 smooth and its gradient is bounded with respect to a time variable. Moreover, a forcing term is continuous, bounded and squere integrable. We will show that the appproximative scheme due to J. Janczewska for a time periodic potential extends to...
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A remark on singular sets of vector bundle morphisms
PublikacjaIf characteristic classes for two vector bundles over the same base space do not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in the base over which a morphism between such bundles is not bijective. Moreover, we show that this set is topologically non-trivial.
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Gradient versus proper gradient homotopies
PublikacjaWe compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classi cations are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from R^n to R^n and proper gradient maps from R^2 to R^2 with the Brouwer degree greater or equal to zero.
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Guided wave propagation signals measured on corroded stiffened panels
Dane BadawczeThe fundamental antisymmetric Lamb mode was excited by piezoelectric transducers attached at the pre-selected points on stiffened panels, representing typical structural ship components. The specimens were exposed to accelerated marine corrosion degradation, so the signals were collected to analyze the influence of the degree of degradation on the wave...
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Magnetic field maps of an astable multivibrator in frequency range from 30 MHz to 3 GHz – spatial detection
Dane BadawczeThe data presents a result of near field measurements of electromagnetic emissions radiated from the PCB of a small electronic device. An efficient method of modelling the magnetic and electric field emissions is the measurements in the near field using electric and magnetic probes. The attached files contain magnetic field maps created on based measurements...
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Magnetic field maps of an astable multivibrator in frequency range from 100 kHz to 50 MHz
Dane BadawczeThe data presents a result of near field measurements of electromagnetic emissions radiated from the PCB of a small electronic device. An efficient method of modelling the magnetic and electric field emissions is the measurements in the near field using electric and magnetic probes. The attached files contain magnetic field maps created on based measurements...
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Electric field maps of an astable multivibrator in frequency range from 30 MHz to 3 GHz
Dane BadawczeThe data presents a result of near field measurements of electromagnetic emissions radiated from the PCB of a small electronic device. An efficient method of modelling the magnetic and electric field emissions is the measurements in the near field using electric and magnetic probes. The attached files contain electric field maps created on based measurements...
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Magnetic field maps of an astable multivibrator in frequency range from 30 MHz to 3 GHz – selective detection
Dane BadawczeThe data presents a result of near field measurements of electromagnetic emissions radiated from the PCB of a small electronic device. An efficient method of modelling the magnetic and electric field emissions is the measurements in the near field using electric and magnetic probes. The attached files contain magnetic field maps created on based measurements...
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Electronics for Mechanical Engineering (2023)
Kursy OnlineName of the course: Electronics (M:32011W0)Specialization: Design and Production Engineering (WM), 1st degree - bachelor/eng., stationary, 2018/2019 - winter semester (currently sem. 4) Number of hours: 30hECTS points: 2 Teacher (lecture/laboratories): Piotr Kurgan
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Stochastic intervals for the family of quadratic maps
Dane BadawczeNumerical analysis of chaotic dynamics is a challenging task. The one-parameter families of logistic maps and closely related quadratic maps f_a(x)=a-x^2 are well-known examples of such dynamical systems. Determining parameter values that yield stochastic-like dynamics is especially difficult, because although this set has positive Lebesgue measure,...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Dane BadawczeMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered...
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The Hopf type theorem for equivariant gradient local maps
PublikacjaWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Spike patterns and chaos in a map-based neuron model
PublikacjaThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
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DETERMINATION OF VERTICAL DISPLACEMENTS IN RELATIVE MONITORING NETWORKS
PublikacjaThe 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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Galerkin formulations with Greville quadrature rules for isogeometric shell analysis: Higher order elements and locking
PublikacjaWe propose new Greville quadrature schemes that asymptotically require only four in-plane points for Reissner-Mindlin (RM) shell elements and nine in-plane points for Kirchhoff-Love (KL) shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree of the elements. For polynomial degrees 5 and 6, the approach delivers high accuracy, low computational cost, and alleviates membrane and...
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Unsupervised Learning for Biomechanical Data Using Self-organising Maps, an Approach for Temporomandibular Joint Analysis
PublikacjaWe proposed to apply a specific machine learning technique called Self-Organising Maps (SOM) to identify similarities in the performance of muscles around human temporomandibular joint (TMJ). The performance was assessed by measuring muscle activation with the use of surface electromyography (sEMG). SOM algorithm used in the study was able to find clusters of data in sEMG test results. The SOM analysis was based on processed sEMG...
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New transition curve adapted to railway operational requirements
PublikacjaThe paper points to the limited possibilities of improving the existing situation in the area of transition curves used in geometrical layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this...
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Database of the estimations of the numbers of simplices of triangulation of some classical Lie groups
Dane BadawczeIt is know that any smooth manifold can be triangulated. The number of simplices of triangulation of a given manifold depends on its topological and combinatorial structure. The data consists of the lower bounds for the numbers of simplices of each dimension of any triangulation of classical Lie groups U(n), SU(n), Sp(n), and SO(n) for n up to 25. Each...
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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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Homoclinics for singular strong force Lagrangian systems in R^N
PublikacjaWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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Diagnostics of historic columns using wave propagation
PublikacjaThis paper presents a numerical analysis of elastic wave propagation in columns of historical buildings for diagnostics purposes. Numerical calculations were performed using the finite element method in the Abaqus software package. The analysis was carried out for three types of brick columns: a full column, a column filled with debris, and a column empty inside. The excitation was in the form of a wave packet and signals of propagating...
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Smooth Particle Hydrodynamics (SPH) approach in simulating large penetration into soil
PublikacjaA study of Smooth Particle Hydrodynamics (SPH) approach for predicting large soil deformation is presented. Theoretical basics of SPH method, including the equations governing, discussion of the importance of smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocodes simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into soil caused...
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Anna Sobieraj-Żłobińska dr inż.
OsobyAnna Sobieraj-Żłobińska (ur. 1977 w Przasnyszu) ukończyła Liceum Ogólnokształcące im. Komisji Edukacji Narodowej w Przasnyszu. Od 1996 kontynuowała naukę na Wydziale Geodezji i Gospodarki Przestrzennej na Akademii Rolniczo-Technicznej im. Michała Oczapowskiego w Olsztynie. W 2001 zdobyła tytuł magistra inżyniera na Uniwersytecie Warmińsko-Mazurskim w Olsztynie (temat pracy dyplomowej „Określenie modelu regresji wielokrotnej do...
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Assessment of the Current Potential of Hydropower for Water Damming in Poland in the Context of Energy Transformation
PublikacjaThe present paper indicates that hydropower, including small hydropower plants (SHPs), may play a very important role in Poland’s energy transformation in the near future. The development of SHPs may also increase water resources in the steppe Poland. Additionally, the aim of the present research is to conduct the PEST analysis of SHPs in Poland, taking into account the SHP potential. For the first time, maps showing the power...
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Atomic force microscopy images of copper electrical contacts wear under the influence of friction
Dane BadawczeMeasurement of wear of copper electrical contacts under the influence of friction. Imaging in contact mode in the variant of scanning spreading resistance microscopy. Additionally, there are spectroscopic current-voltage curves showing local changes in electrical conductivity. NTEGRA Prima (NT-MDT) device. Probe NSG 01Pt.
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Piotr Bartłomiejczyk dr hab.
OsobyW roku 2014 zostałem zatrudniony w Katedrze Równań Różniczkowych i Zastosowań Matematyki na Wydziale Fizyki Technicznej i Matematyki Stosowanej Politechniki Gdańskiej. Zajmuję się badaniem niezmienników występujących w analizie nieliniowej. W roku 2000 uzyskałem stopień naukowy doktora w zakresie nauk matematycznych w Instytucie Matematycznym Polskiej Akademii Nauk w Warszawie. Uchwałą Rady Wydziału Matematyki, Fizyki i Informatyki...
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Seabed Topography Changes in the Sopot Pier Zone in 2010–2018 Influenced by Tombolo Phenomenon
PublikacjaBathymetric surveys of the same body of water, performed at regular intervals, apart from updating the geospatial information used to create paper and electronic maps, allow for several additional analyses, including an evaluation of geomorphological changes occurring in the coastal zone. This research is particularly important in places where the shape of the coastal zone has been violently disturbed, including by human activity....
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The Education of Analytical Chemists in Polish Universities
PublikacjaAnalytical Chemistry plays a very important role in the modern world. The main reasons are; the need of environmental monitoring, quality of food and water control, human health, quality of industrial production control, nanotechnologies and material science. Together with Inorganic Chemistry, Organic Chemistry and Physical Chemistry, Analytical Chemistry is a fundamental chemical course. The education of Analytical Chemists is...
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Face Profile View Retrieval Using Time of Flight Camera Image Analysis
PublikacjaMethod for profile view retrieving of the human face is presented. The depth data from the 3D camera is taken as an input. The preprocessing is, besides of standard filtration, extended by the process of filling of the holes which are present in depth data. The keypoints, defined as the nose tip and the chin are detected in user’s face and tracked. The Kalman filtering is applied to smooth the coordinates of those points which...
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Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements
PublikacjaWe propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific...
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Influence of image transformations and quality degradations on SURF detector efficiency
PublikacjaA method for task-oriented examination of SURF keypoint detector accuracy is presented in the paper. It consists of generating test images, based on a given exemplar, processed by affine transformations: random rotation and scaling, and varying degree of degradations: darkening, blurring, noising, and compression. Details of applied degradation procedure are presented, followed by essentials of SURF-based images matching. A distance...
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Novel sorptive extraction techniques in bioanalysis evaluated by Blue Applicability Grade Index: The paradigm of fabric phase sorptive extraction and capsule phase microextraction
PublikacjaFabric phase sorptive extraction (FPSE) and capsule phase microextraction (CPME) are two sol-gel derived microextraction techniques that emerged in the last decade towards the minimization of the environmental impact of conventional sample preparation approaches. Complementary to the well-established green metric tools, Blue Applicability Grade Index (BAGI) was recently proposed for the evaluation of method’s practicability. In...
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Time travel without paradoxes: Ring resonator as a universal paradigm for looped quantum evolutions
PublikacjaA ring resonator involves a scattering process where a part of the output is fed again into the input. The same formal structure is encountered in the problem of time travel in a neighborhood of a closed timelike curve (CTC). We know how to describe quantum optics of ring resonators, and the resulting description agrees with experiment. We can apply the same formal strategy to any looped quantum evolution, in particular to the...
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Influence of water salinity on corrosion risk - the case of the southern Baltic Sea coast.
PublikacjaWater corrosivity in Gdansk Bay, Poland, the southern part of the Baltic Sea, was investigated. The analysed region is heavily industrialized, and the coastline is very diverse. Twenty-seven test points along the coastline were selected. Water parameters such as salinity, total dissolved solids content, resistivity, conductivity, oxygenation, pH and corrosion rate were determined. The results of the investigation are presented....
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Education at the Faculty of Mechanical Engineering of the Gdańsk University of Technology
PublikacjaFaculty of Mechanical Engineering is one of the largest departments of the Gdańsk University of Technology (GUT), currently educating about 3 000 student. Lectures are conducted in five Chairs, which include 18 Divisions. In 2000 GUT introduced the European Credit Transfer and Accumulation System (ECTS). Each student should get during one academic year 60 ECTS points. Obtaining a diploma of BEng requires the acquisition of no less...
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Education at the Faculty of Mechanical Engineering of the Gdańsk University of Technology
PublikacjaFaculty of Mechanical Engineering is one of the largest departments of the Gdańsk University of Technology (GUT), currently educating about 3 000 student. Lectures are conducted in five Chairs, which include 18 Divisions. In 2000 GUT introduced the European Credit Transfer and Accumulation System (ECTS). Each student should get during one academic year 60 ECTS points. Obtaining a diploma of BEng requires the acquisition of no less...
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3D point cloud as a representation of buildings: the Nanotechnology Center and the Auditorium Novum
Dane BadawczeThe product presents the point cloud in the collection of a three-dimensional database in spatial order as the representations of the Nanotechnology Center and the Auditorium Novum buildings (located on the campus of the Gdańsk University of Technology) acquired in the laser scanning technology. According to its high accuracy and precision of data acquisition...
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Multiaxial Fatigue Behaviour of SLM 18Ni300 Steel
PublikacjaFatigue behaviour of SLM 18Ni300 steel under proportional bending-torsion loading is studied. The fatigue tests are conducted under pulsating loading conditions using tubular specimens with a transversal circular hole. Three ratios of the normal stress to shear stress are considered, namely σ/τ=4,σ/τ=2 and σ/τ = 4/3. Crack initiation sites were found for two diametrically opposite points around the hole, whose locations are governed...
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The OptD-multi method in LiDAR processing
PublikacjaNew and constantly developing technology for acquiring spatial data, such as LiDAR (light detection and ranging), is a source for large volume of data. However, such amount of data is not always needed for developing the most popular LiDAR products: digital terrain model (DTM) or digital surface model. Therefore, in many cases, the number of contained points are reduced in the pre-processing stage. The degree of reduction is determined...
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Joanna Janczewska prof. dr hab.
OsobyJoanna Janczewska odbyła studia wyższe magisterskie na kierunku Matematyka w latach 1994–1999 z wynikiem bardzo dobrym i uzyskała w 1999 roku tytuł magistra. W 2002 roku na Uniwersytecie Gdańskim uzyskała stopień naukowy doktora nauk matematycznych w zakresie matematyki. Promotorem w przewodzie doktorskim był dr hab. Andrzej Borysowicz, prof. UG. W październiku 2004 roku podjęła pracę na stanowisku adiunkta w Katedrze Algebry...
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Highly Integrable Planar-structured Printed Circularly Polarized Antenna for Emerging Wideband Internet of Things Applications in the Millimeter-Wave Band
PublikacjaThis paper proposes a numerically and experimentally validated printed wideband antenna with a planar geometry for Internet of Things (IoT) applications. This design tackles the challenges associated with deploying IoT sensors in remote areas or across extensive geographical regions. The proposed design exploits a coplanar-waveguide-fed modified microstrip line monopole for excitation of circularly polarized waves radiating in...
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Virtual reality technology in architectural education
PublikacjaContemporary virtual reality (VR) technology allows the recreation of non-existent architectural objects of which there may be no trace remaining. Virtual reality applications allow access to digital models, which visualise the lost architecture. The popularity of VR has resulted in it being applied not only to computer games, but also in visualising the past. Maps allow movement through historical trails and 3D models of architecture...
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Detection of debonding in adhesive joints using Lamb wave propagation
PublikacjaAdhesively bonded joints are widely used in many branches of industry. Mechanical degradation of this type of connections does not have significant symptoms that can be noticed during visual assessment, so non-destructive testing becomes a very important issue. The paper deals with experimental investigations of adhesively bonded steel plates with different defects. Five samples (an intact one and four with damages in the form...
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Paweł Wysocki dr inż.
OsobyW roku 1995 zdał maturę i ukończył Technikum Elektroniczne w Zespole Szkół Technicznych w Suwałkach. Następnie studiował na kierunku Geodezja i Kartografia w zakresie geodezji i systemów informacji przestrzennej na Uniwersytecie Warmińsko-Mazurskim w Olsztynie, gdzie w 2001 roku obronił dyplom magisterski. Tam też ukończył studia podyplomowe w zakresie szacowania nieruchomości. Od 2001 roku był uczestnikiem dziennych studiów doktoranckich...
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MPPT and GMPPT Implementation for Buck-Boost Mode Control of quasi-Z-Source Inverter
PublikacjaThe focus is on the maximum power point tracking implementation for the buck-boost voltage mode control of a single-phase multilevel inverter based on a three-level neutral point clamped quasi-Z-source topology. To utilize shoot-through states only when boost function is needed and avoid it in the buck mode, two different control approaches are required. This work proposes merged control system which provides switching between...
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Reduction of measurement data before Digital Terrain Model generation vs. DTM generalisation
PublikacjaModern data acquisition technologies provide large datasets that are not always necessary in its entirety to properly accomplish the goal of the study. In addition, such datasets are often cumbersome for rational processing, and their processing is time and labour consuming. Therefore, methods that enable to reduce the size of the measurement dataset, such as the generalization of the Digital Terrain Model (DTM) or the reduction...
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THE 3D MODEL OF WATER SUPPLY NETWORK WITH APPLICATION OF THE ELEVATION DATA
Publikacja3D visualization is a key element of research and analysis and as the source used by experts in various fields e.g.: experts from water and sewage systems. The aim of this study was to visualize in three-dimensional space model of water supply network with relief. The path of technological development of GESUT data (Geodezyjna Ewidencja Sieci Uzbrojenia Terenu – geodetic records of public utilities) for water supply and measurement...