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TOPOLOGY AND ITS APPLICATIONS
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TOPOLOGY
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Characteristics of the topology of the Internet
PublicationRozdział dotyczy charakterystyki topologii Internetu. Ukazuje zagrożenia wynikające z bezskalowego charakteru sieci. Opisuje naturę ataku - destrukcyjnego działania mającego na celu wyeliminowanie ważnego elementu sieci. Przedstawia reguły doboru tras, pozwalające ustanawiać ścieżki realizacji połączeń omijające określone węzły sieci, narażone na atak.
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Scanning networks with cactus topology
PublicationThe family of Pursuit and Evasion problems is widelystudied because of its numerous practical applications,ranging from communication protocols to cybernetic andphysical security. Calculating the search number of a graphis one of most commonly analyzed members of this problemfamily. The search number is the smallest number of mobileagents required to capture an invisible and arbitrarily fastfugitive, for instance piece of malicious...
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GEOMETRY & TOPOLOGY
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Quantum Topology
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Journal of Topology
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On the topology of spaces of partial and local maps
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Topology recognition and leader election in colored networks
PublicationTopology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in networks whose nodes are equipped with...
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Analysis of blood vessel topology by cubical homology
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Topology of vibro-impact systems in the neighborhood of grazing
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A boost topology active power factor corrector.
PublicationPrzedstawiono układ analogowego aktywnego korektora zbudowanego na układzie scalonym kontrolera PWM oraz tranzystorem MOS jako okresowo przełączonym kluczem. Układ korektora zapewnia pobór prądu z sieci energetycznej w postaci przebiegu prawie sinusoidalnego o małych zniekształceniach i w fazie z sinusoidalnym napięciem sieci.
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CRVG - a new model for wireless networks topology generation
PublicationThis paper presents a new model of wireless network topology generator. Its main advantage is the possibility of relatively sparse networks generation. Because no iteration is needed, the model can be used for massive generation of networks for testing. The topological properties of produced graphs place them in the class of scale free networks, resembling real ones.
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Applied General Topology
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Journal of Topology and Analysis
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Algebraic and Geometric Topology
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Three-dimensional Weyl topology in one-dimensional photonic structures
PublicationTopological features, in particular distinct band intersections known as nodal rings, usually requiring three-dimensional structures, have now been demonstrated experimentally in an elegantly simple one-dimensional photonic crystal.
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Topology Discovery of Hierarchical Ethernet LANs without SNMP support
PublicationThis paper presents an algorithm that allows for discovery of layer-2 hierarchical Ethernet network topology using agents running on selected end nodes. No SNMP, MIB, hardware, firmware, or operating system-level software modification is required. The method is based on transmission of customized Ethernet frames among installed software agents. It can be used to discover the topology of LAN or one VLAN segment as long as no MAC...
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A Linear Phase Filter in Quadruplet Topology With Frequency-Dependent Couplings
PublicationThis letter presents a design of a linear phase microwave bandpass filter. The filter is composed of four resonators arranged in the quadruplet topology. Making the cross and one direct coupling dispersive gives additional design flexibility. The first advantage of using frequency-dependent couplings is the possibility to chose an arbitrary location of a pair of complex transmission zeros (TZs) in the s-domain. The second one is...
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Dynamics of Topology-dependent Water Purification by Siliceous Zeolite Membranes
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Impact of WDM Network Topology Characteristics on the Extent of Failure Losses
PublicationW artykule dokonano oceny wpływu charakterystyk topologicznych sieci na rozmiar strat po awarii węzła/łącza będącej następstwem ataku. W tym celu wprowadzono współczynnik ATRF. Wyniki badań pokazały, że wykorzystanie standardowej metryki odległości do wyznaczania tras podstawowych prowadzi do istotnego zwiększenia liczby połączeń uszkodzonych w wyniku ataku w porównaniu ze skutkami awarii losowej.
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The Importance of Contextual Topology in the Process of Harmonization of the Spatial Databases on Example BDOT500
PublicationIn this work, we present two detailed problems of topological errors in spatial database. Both issues are inconsistencies in the database, i.e. interior topological relationships layers of buildings and the relationship between the buildings layer and the layer of plots. That inconsistency is related to the residual polygons that arise as a result of overlapping objects, or gaps between objects. The occurrence of this type of error...
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Topology improvements in scale-free networks when assuring security and survivability
PublicationW artykule zaproponowano heurystyczny algorytm iteracyjny (NEA) kontrolowanego rozrostu sieci, zmniejszający stopień jej bezskalowości. Pokazano, że odpowiednia kontrola rozrostu sieci, prowadzi do uzyskania sieci o topologii zbliżonej do regularnej, a więc w duzym stopniu odpornej na celowe działania niszczące - ataki. Właściwości algorytmu zostały przebadane przy pomocy dedykowanego symulatora dla reprezentatywnej próby inicjalnych...
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Methods of Functional Analysis and Topology
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Journal of Applied and Computational Topology
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EM-driven topology evolution for bandwidth enhancement of hybrid quadrature patch couplers
PublicationA broad operational bandwidth is one of the key performance figures of hybrid patch couplers. Due to the lack of systematic design procedures, bandwidth enhancement is normally obtained through manual modifications of the structure geometry. In this work, an optimization-based topology evolution for EM-driven design of patch couplers with enhanced bandwidth has been proposed. The method exploits a novel spline-based EM model where...
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On topology optimization of large deformation contact-aided shape morphing compliant mechanisms
PublicationA topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal elements. Negative circular masks are employed to perform dual task, i.e., to decide material states of each element and also, to generate rigid contact surfaces. Each mask is characterized by...
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A Simple-Topology Compact Broadband Circularly Polarized Antenna With Unidirectional Radiation Pattern
PublicationIn this letter, a geometrically simple, reflector-backed single-point-fed circularly polarized (CP) antenna with unidirectional radiation pattern is presented. The structure comprises a simple coplanar waveguide (CPW) feeding circuit with an open slot etched on one side of the coplanar ground. The enhanced CP bandwidth is obtained by combining the loop mode, the slot mode, and the asymmetrical configuration of the coplanar ground...
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Novel topology of compact coplanar waveguide resonant cell low-pass filter
PublicationIn this study, a novel pseudoelliptic function low-pass filter (LPF) constituted by a compact coplanar waveguide resonant cell has been designed and manufactured. The lumped-element seven-pole prototype has been adequately realized by using complementary perturbations located both in signal line and ground plane metallization. The fabricated uniplanar LPF offers a compact size of 5.6 x 9.8 mm2, return loss better than 26 dB over...
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Reconfigurable Dual Active Bridge (DAB) Converter Topology for Aircraft Application System
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Multicoil dynamic wireless power transfer topology with shared primary side compensation system
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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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Analyzing sets of phylogenetic trees obtained from bayesian MCMC process using topology metrics
PublicationThe reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationship between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations amongorganisms and geographical areas.In the paper, we describe a general method for comparing hylogenetic trees....
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Coupled-Resonator Waveguide Filter in Quadruplet Topology With Frequency-Dependent Coupling - A Design Based on Coupling Matrix
PublicationThis letter presents an application of a recently developed coupling matrix synthesis technique to design of coupled-resonator filters with dispersive inter-resonator couplings. This technique is used to design a novel coupled-cavity bandpass filter. Measurements validate the design and confirm effectiveness of the synthesis method. The filter is a four-pole generalized Chebyshev filter with three transmission zeros. Resonators...
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A 100 kW 1.2 kV 20 kHz DC-DC converter prototype based on the Dual Active Bridge topology
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Comparative analysis of three‐phase dual active bridge converter with different transformer topology and modern universal control for DC microgrids
PublicationThe presented work discusses issues related to the use of modern multiphase topologies of Dual Active Bridge (DAB)-type converters. Converters of this type are widely used in most DC microgrid applications. The introduction emphasizes a comparative analysis between single-phase and multi-phase DAB topologies within high-power DC microgrids, delving into their respective advantages, drawbacks, design procedures, and considerations...
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TOPOLOGY PROCEEDINGS
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Computational Topology Workshop
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Topology and Dynamical Systems in Action - Summer school 2023
e-Learning CoursesThe course is designed for participants in the Spinnaker summer school in mathematics.
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Existence of periodic orbits for a perturbed vector field
PublicationPrzy nałożeniu pewnego warunku na odwzorowanie Poincarego, wyrażonego w języku indeksów iteracji, dowodzi się istnienia orbit periodycznych dla zaburzonego pola wektorowego.
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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet 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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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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Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index
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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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Bounded solutions of odd nonautonomous ODE
PublicationBorsuk-Ulam type argument is used in order to prove exstence of nontrivial bounded solutions to some nonautonomous differential euations which are odd with respect to the spatial variable. A Poincare compactification trick is also applied.
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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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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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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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Lefschetz periodic point free self-maps of compact manifolds
PublicationLet 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,