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Search results for: LERAY-SCHAUDER DEGREE, HILBERT SPACE, GRADIENT, OTOPY
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Conley index in Hilbert spaces and the Leray-Schauder degree
PublicationZdefiniowane są liczby Bettiego i charakterystyka Eulera LS-indeksu dla potoków generowanych przez pole zwarte w przestrzeni Hilberta. Główna teza pracy to wzór typu Poincare-Hopfa łączący wspomnianą chatrakterystykę Eulera ze stopniem Leray-Schaudera.
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Otopy Classification of Gradient Compact Perturbations of Identity in Hilbert Space
PublicationWe prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective otopy classes of these maps, where by a local map we mean a compact perturbation of identity with a compact preimage of zero.
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Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
PublicationWe 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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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider 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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Morse cohomology in a Hilbert space via the Conley index
PublicationThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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A note on Banach space isomorphic to Hilbert space
PublicationW pracy charakteryzuje się przestrzenie Hilberta w terminach istnienia pewnych funkcji gładkich.
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Path components of the space of gradient vector fields on the two dimensional disc
PublicationWe 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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The homotopy type of the space of gradient vector fields on the two-dimensional disc
PublicationWe prove that the inclusion of the space of gradient vector fields into the space of all vector fields on D^2 non-vanishing in S^1 is a homotopy equivalence
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“Space & Satellite Technologies" intercollegiate master-degree courses of study in Tri-City (Poland)
PublicationSince summer semester of the academic year 2016/2017, two faculties of Gdansk University of Technology GUT (Faculty of Mechanical Engineering and Faculty of Electronics, Telecommunications and Informatics) together with the Gdynia Maritime University (Faculty of Electronics) and the Polish Naval Academy in Gdynia (Faculty of Command and Naval Operations) have opened intercollegiate master -...
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Engineering and Management of Space Systems (EMSS) - an international joint Master's double-degree program
PublicationDynamic development of the space sector of European, and especially of Polish and German economies results in a necessity for suitable Higher Education Institution graduates. The increasing digitization, distribution and networking of technical systems leads to the necessity of a degree programme teaching “the systems view” and “interdisciplinarity” methods and skills. Furthermore, it is necessary to consider the entire life cycle...
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Connected components of the space of proper gradient vector fields
PublicationWe show that there exist two proper gradient vector fields on Rn which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps.
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Path components of the space of gradient vector fields on the two-dimensional disc
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Adam Dąbrowski dr inż.
PeopleAdam Dabrowski has obtained a PhD in mechanical engineering from Gdańsk University of Technology and MSc. degree in mechatronics from Technische Universität Hamburg. He has an industry experience in Institute of Aviation Engineering Design Center (Warsaw, Poland) and SICK AG (Hamburg, Germany). Additionally, as an assistant at Gdansk University of Technology he teaught courses on mechanics, space mechanisms and dynamics of space...
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The Hopf type theorem for equivariant gradient local maps
PublicationWe 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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Proper gradient otopies
PublicationWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.
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Proper gradient otopies
PublicationWe prove that the inclusion of the space of proper gradient local maps into the space of proper local maps induces a bijection between the sets of the respective otopy classes of these maps.
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Bernstein-type theorem for ϕ-Laplacian
PublicationIn this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...
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The Hopf theorem for gradient local vector fields on manifolds
PublicationWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.
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E-cohomological Conley index
PublicationIn this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical...
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Particle swarm optimization algorithms for autonomous robots with deterministic leaders using space filling movements
PublicationIn this work the swarm behavior principles of Craig W. Reynolds are combined with deterministic traits. This is done by using leaders with motions based on space filling curves like Peano and Hilbert. Our goal is to evaluate how the swarm of agents works with this approach, supposing the entire swarm will better explore the entire space. Therefore, we examine different combinations of Peano and Hilbert with the already known swarm...
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Gradient versus proper gradient homotopies
PublicationWe 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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Karolina Lademann mgr
PeopleCurriculum vitae
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublicationIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...
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Quantum structure in competing lizard communities
PublicationAlmost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing...
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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The Maslov index and the spectral flow—revisited
PublicationWe give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...
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Simple sufficient condition for subspace to be completely or genuinely entangled
PublicationWe introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We...
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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Mariusz Figurski prof. dr hab. inż.
PeopleMariusz Józef Figurski (born 27 April 1964 in Łasinie, Poland) - Polish geodesist, professor of technical sciences, professor at the Gdańsk University of Technology. Early life and education He passed the matriculation examination in 1983 after he had finished Jan III Sobieski High school in Grudziądz. He graduated the Military University of Technology on an individual mode at the Faculty of Electromechanics and Civil Engineering...
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The parallel environment for endoscopic image analysis
PublicationThe jPVM-oriented environment to support high performance computing required for the Endoscopy Recommender System (ERS) is defined. SPMD model of image matching is considered and its two implementations are proposed: Lexicographical Searching Algorithm (LSA) and Gradient Serching Algorithm (GSA). Three classes of experiments are considered and the relative degree of similarity and execution time of each algorithm are analysed....
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Low-dimensional bound entanglement with one-way distillable cryptographic key
PublicationIn this paper, we provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 circle times 4, which shows that peculiar security contained in bound entangled states does not need high-dimensional systems. We show that for these states a positive key rate can be obtained by one-way Devetak-Winter (DW) protocol. Subsequently, the volume of bound entangled key-distillable...
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A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems
PublicationIn 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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Thematic Areas in the Polish Countryside and Their Role in Local Development
PublicationThe article defines the phenomenon of space thematisation with regards to rural areas in Poland. The typology of thematic spaces and criteria of their comparative description have been proposed. Thematic villages, home gardens, amusement parks and housing estates have been distinguished. They have been compared in terms of spatial availability, the degree of user participation and the commercial vs. non-commercial creation purpose....
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Hidden Tensor Structures
PublicationAny single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration...
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The potential of computational methods for the categorization of architectural objects on the example of media architecture
PublicationThe paper presents an example of the categorization of architectural objects and assessment of the characteristics of urban space, based on the analysis of specific features of architectural objects and urban landscape. The conducted analysis refers to media architecture and is presented in the complex context of the development of media solutions. The field of influence of IT on architecture is also stressed, both on the architect’s...
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Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios
PublicationThe problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes...
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Marek Czachor prof. dr hab.
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Paweł Tysiąc dr inż.
PeopleHe was born on March 25, 1992 in Gdańsk. After graduating from Junior High School No. 32, he attended the VIII Liceum Ogólnokształcące im. National Education Commission in Gdańsk, classes with a mathematical and geographical profile, obtaining a secondary school-leaving examination certificate in 2011. Then, in 2011-2016, he continued his studies at the Faculty of Civil and Environmental Engineering of the Gdańsk University of...
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Expedited antenna optimization with numerical derivatives and gradient change tracking
PublicationDesign automation has been playing an increasing role in the development of novel antenna structures for various applications. One of its aspects is electromagnetic (EM)-driven design closure, typically applied upon establishing the antenna topology, and aiming at adjustment of geometry parameters to boost the performance figures as much as possible. Parametric optimization is often realized using local methods given usually reasonable...
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Justyna Szostak dr inż.
PeopleI Gdańsk University of Technology: Chair of the Rector’s Internationalization Committee (October 2020 - Present) Erasmus + Coordinator for students and staff members, Faculty of Applied Physics and Mathematics (Mar 2017 - Present) Dean's Proxy for Internationalization, Faculty of Applied Physics and Mathematics (October 2020 - Present) Coordinator of the International Relations Office of the Faculty of Applied Physics and...
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublicationWe 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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Expedited Globalized Antenna Optimization by Principal Components and Variable-Fidelity EM Simulations: Application to Microstrip Antenna Design
PublicationParameter optimization, also referred to as design closure, is imperative in the development of modern antennas. Theoretical considerations along with rough dimension adjustment through supervised parameter sweeping can only yield initial designs that need to be further tuned to boost the antenna performance. The major challenges include handling of multi-dimensional parameter spaces while accounting for several objectives and...
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Low-fidelity model considerations for simulation-based optimisation of miniaturised wideband antennas
PublicationHere, variable-fidelity electromagnetic (EM)-based design optimisation of miniaturised antennas is discussed. The authors focus on an appropriate selection of discretisation density of the low-fidelity EM model, which results in good performance of the optimisation algorithm in terms of its computational complexity and reliability. Trust-region gradient search with low-fidelity model corrected by means of non-linear frequency scaling...
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On low-fidelity models for variable-fidelity simulation-driven design optimization of compact wideband antennas
PublicationThe paper addresses simulation-driven design optimization of compact antennas involving variable-fidelity electromagnetic (EM) simulation models. Comprehensive investigations are carried out concerning selection of the coarse model discretization density. The effects of the low-fidelity model setup on the reliability and computational complexity of the optimization process are determined using a benchmark set of three ultra-wideband...
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout 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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Wpływ zmian dopuszczalnych wartości parametrów geometrycznych i kinematycznych na podatność modernizacyjną układów torowych
PublicationPodatnością modernizacyjną nazywamy stopień przystosowania analizowanego odcinka linii kolejowej do zmiany prędkości eksploatacyjnej. Skala możliwych zmian prędkości (w sensie jej zwiększenia) jest wypadkową istniejącego układu geometrycznego linii w planie, ograniczeń lokalizacyjnych oraz dopuszczalnych wartości parametrów geometrycznych i inematycznych. Jakiekolwiek zmiany tych ostatnich wpływają bezpośrednio na obliczenie elementarnych...
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Tropospheric delays derived from GNSS observations during the derecho event in Poland of 11th August 2017
Open Research DataPropagation of global navigation satellite systems (GNSS) radio signals is disturbed by the current state of the Earth's atmosphere. For this reason, advances processing of GNSS signals can be used for investigation of the atmospheric condition. In case of troposphere, the GNSS signals allow for obtain information of tropospheric delay, which is mainly...
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Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources
PublicationElectromagnetic fields are quantized in a manifestly covariant way by means ofa class of reducible "center-of-mass N-representations" of the algebra of canonical commutationrelations (CCR). The four-potential Aa(x) transforms in these representations as aHermitian four-vector field in Minkowski four-position space (without change of gauge), butin momentum space it splits into spin-1 massless photons and two massless scalars. Whatwe...