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Search results for: HOMOTOPY CLASS
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublicationIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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A note on the Morse homology for a class of functionals in Banach spaces involving the 2p-area functional
PublicationIn this paper we show how to construct Morse homology for an explicit class of functionals involving the 2p-area functional. The natural domain of definition of such functionals is the Banach space W_0^{1,2p}(\Omega), where p > n/2 and \Omega \subet R^n is a bounded domain with sufficiently smooth boundary. As W_0^{1,2p}(\Omega) is not isomorphic to its dual space,critical points of such functionals cannot be non-degenerate...
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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...
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On the homotopy equivalence of the spaces of proper and local maps
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Classification of homotopy classes of equivariant gradient maps
PublicationNiech V będzie ortogonalną reprezentacją zwartej grupy Liego Gi niech S(V),D(V) oznaczają sferę jednostkową i kulę jednostkową V.Jeżeli F jest G-niezmienniczą funkcją rzeczywistą klasy C^1 na Vto mówimy, że grad F (gradient F) jest dopuszczalny, jeżeli(grad F)(x) jest różny od zera dla x należących do S(V). Pracapoświęcona jest homotopijnej klasyfikacji dopuszczalnychG-niezmienniczych odwzorowań gradientowych.
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On homotopy Conley index for multivalued flows in Hilbert spaces
PublicationPodano aproksymacyjną definicję indeksu homotopijnego, otrzymując naturalne związki z podobnymi niezmiennikami. Zbadano własności tego niezmiennika i zastosowano do badania gradientowych potoków wykazując pewne geometryczne własności zbiorów niezmienniczych
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Fault diagnosis of analog piecewise linear circuits based on homotopy
PublicationArtykuł opisuje weryfikację metodą diagnostyki analogowych układów odcinkowo-liniowych opartą na podejściu homotopijnym. Homotopia przekształca jedną funkcję f(x) w inną funkcję g(x) poprzez zmianę parametru homotopii tî[0,1]. Ścieżka homotopijna pokazuje drogę od punktu x0 z dziedziny funkcji f(x) do odpowiadającego mu punktu x* funkcji g(x). Idea metody zakłada wykorzystanie funkcji f(x) do opisu diagnozowanego układu w stanie...
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On relations between gradient and classical equivariant homotopy groups of spheres
PublicationWe investigate relations between stable equivariant homotopy groups of spheres in classical and gradient categories. To this end, the auxiliary category of orthogonal equivariant maps, a natural enlargement of the category of gradient maps, is used. Our result allows for describing stable equivariant homotopy groups of spheres in the category of orthogonal maps in terms of classical stable equivariant groups of spheres with shifted...
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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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Inducing a map on homology from a correspondence
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Homology algorithm based on acyclic subspace
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Analysis of blood vessel topology by cubical homology
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Graph Approach to the Computation of the Homology of Continuous Maps
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On mixing in the class of quadratic stochastic operators
PublicationWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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Subharmonic solutions for a class of Lagrangian systems
PublicationWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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Persistent homology as a new method of the assessment of heart rate variability
PublicationHeart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...
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Ceramics, Glass and Glass-Ceramics for Personal Radiation Detectors
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Green function diagonal for a class of heat equations
PublicationA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Study on Strategy in University Laboratory Class Teaching
PublicationLaboratory teaching is a critical way to ensure the effective input of techniques in engineering learning. Laboratory teaching not only contributes to improving course quality but also helps enrich comprehensive engineering application ability. However, there are some typical problems in current university laboratory teaching, such as rigid and isolated course design, outdated contents and materials, and not encouraging innovation...
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Double-Headed Cationic Lipopeptides: An Emerging Class of Antimicrobials
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Homoclinic solutions for a class of the second order Hamiltonian systems
PublicationW niniejszej pracy badamy istnienie orbit homoklinicznych dlaukładu Hamiltonowskiego drugiego rzędu: q^{..} + V_{q}(t,q) = f(t), gdzie V z iloczynu kartezjańskiego R x R^{n} do R jest postaciV(t,q) = -K(t,q) + W(t,q). Zakładamy, ze V jest T-okresowe ze względuna zmienną t, K spełnia tzw. ''pinching'' warunek, W jest superliniowew nieskończoności, a norma f w L^{2} jest wystarczająco mała.Orbitę homokliniczną takiego układu znajdujemy...
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Modelling method for a class of distributed-lumped parameter systems
PublicationThe paper presents an alternative approach for modelling and order reduction of continuous system. The proposed methodology combines application of two methods: the modal decomposition method and the rigid finite element method. The given continuous structure is divided into 1D continuous substructures. For each 1D substructure modal decomposition and reduction procedure is applied. Interactions between substructures are described...
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The circular chromatic index of some class 2 graphs
PublicationW artykule został wyznaczony cyrkularny indeks chromatyczny dla dwóch rodzin grafów klasy 2. Co więcej, podano nie trywialne oszacowania tego parametru dla snarków Isaacsa i Goldberga. Na koniec artykułu rozważana jest złożoność obliczeniowa problemów związanych z cyrkularnym kolorowaniem krawędzi.
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Edge coloring of graphs of signed class 1 and 2
PublicationRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Heteroclinic solutions for a class of the second order Hamiltonian systems
PublicationW pracy dowodzi się istnienia rozwiązań heteroklicznicznych dla pewnej klasy równań różniczkowych zwyczajnych drugiego rzędu typu hamiltonowskiego.
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Biodetoriation of Mater_Bi Y Class in compost with sewage sludge.
PublicationPrzedmiotem badań była mieszanina skrobi termoplastycznej z pochodną celulozy produkowana przez firmę Novamont pod nazwą handlową Mater Bi Y. Próbki o wymiarach 1,7 x 8 X 0,1 cm umieszczano w kompoście naturalnym z oczyszczalni ścieków w Gdyni. Badania po 4-ch miesiącach wykazały 96% ubytku wagi, co oznacza powolniejszą degradację w porównaniu do testów standardowych stosowanych przez firmę Novamont.
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Environmental stress cracking in e-glass and aramid/glass epoxy composites
PublicationKompozyty epoksydowe wzmocnione włóknami szklanymi są dość odporne na wpływy środowiskowe w stanie nieobciążonym, jednak po przyłożeniu obciążeń łatwo pękają w środowisku wody i rozcieńczonych kwasów. Charakterystyki propagacji pęknięć środowiskowych w laminatach szklano/epoksydowych były przedmiotem szeregu prac, jednak brak jest danych na temat zachowania laminatów o wzmocnieniu hybrydowym aramidowo-szklanym stosowanych w budowie...
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Computation of cubical homology, cohomology, and (co)homological operations via chain contraction
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Homoclinic and Heteroclinic Orbits for a Class of Singular Planar Newtonian Systems
PublicationThe study of existence and multiplicity of solutions of differential equations possessing a variational nature is a problem of great meaning since most of them derives from mechanics and physics. In particular, this relates to Hamiltonian systems including Newtonian ones. During the past thirty years there has been a great deal of progress in the use of variational methods to find periodic, homoclinic and heteroclinic solutions...
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Synthesis, Antimicrobial and Mutagenic Activity of a New Class of d-Xylopyranosides
PublicationEight N-[2-(2′,3′,4′-tri-O-acetyl-α/β-d-xylopyranosyloxy)ethyl]ammonium bromides, a new class of d-xylopyranosides containing a quaternary ammonium aglycone, were obtained. Their complete structure was confirmed using NMR spectroscopy (1H, 13C, COSY and HSQC) and high-resolution mass spectrometry (HRMS). An antimicrobial activity against fungi (Candida albicans, Candida glabrata) and bacteria (Staphylococcus aureus, Escherichia...
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Novel Class of Proton Conducting Materials—High Entropy Oxides
PublicationHere, for the first time, we present data on proton conductivity of high-entropy, single-phase perovskites. The BaZr0.2Sn0.2Ti0.2Hf0.2Ce0.2O3−δ, BaZr0.2Sn0.2Ti0.2Hf0.2Y0.2O3−δ, BaZr1/7Sn1/7Ti1/7Hf1/7Ce1/7Nb1/7Y1/7O3−δ, and BaZr0.15Sn0.15Ti0.15Hf0.15Ce0.15Nb0.15Y0.10O3−δ single-phase perovskites were synthesized. Before electrical measurements, materials were characterized using X-ray diffraction (XRD), scanning electron microscopy...
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Matching Exception Class Hierarchies between .NET, Java Environments
PublicationThe paper presents a methodology of exception classification and matching exception messages between .NET andJava environments. The methodology operates on existing exception class hierarchies and proposes two complementingapproaches: automated and manual matching. The automated matching uses the similarity measure to find associationsbetween exception messages from the two sets of classes for the considered programming languages....
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Comparison of the effectiveness of automatic EEG signal class separation algorithms
PublicationIn this paper, an algorithm for automatic brain activity class identification of EEG (electroencephalographic) signals is presented. EEG signals are gathered from seventeen subjects performing one of the three tasks: resting, watching a music video and playing a simple logic game. The methodology applied consists of several steps, namely: signal acquisition, signal processing utilizing z-score normalization, parametrization and...
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The effect of lithium fluoride on the thermal stability and thermoluminescence properties of borosilicate glass and glass-ceramics
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
PublicationWe consider a conservative second order Hamiltonian system \ddot{q}+ ∇V(q)=0 in R3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ∅ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
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An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems
PublicationW niniejszej pracy badamy istnienie rozwiązań prawie homoklinicznych (ang. almost homoclinic solutions) dla pewnej klasy układów Newtona. Rozwiązanie prawie homokliniczne otrzymujemy jako granicę ciągu rozwiązań okresowych dla pewnego ciągu równań różniczkowych.
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Traffic Type Influence on QoS Network Performance of Streaming Traffic Class
PublicationFeasibility study on QoS routing proved that the traffic type influence the network performance. The performance is defined here as a number of packets serviced by the network. In the paper additional element - buffers lengths used in service system was verified in terms of dependencies with routing performance. We present results obtained by simulation for many simulation scenarios. Analysis was done for two different network...
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Analysis and design improvement of high class roads’ arched sections in Poland
PublicationAlthough Polish road network standards, in particular higher classes of roads are improving dynamically the number of fatalities on the network is still higher that EU’s average. Ensuring road safety and high maintaining standards is a complex issue and one that poses a major challenge for all road authorities. Road accidents at high speed roads characterize specially serious material and social consequences, thus research into...
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Deep Features Class Activation Map for Thermal Face Detection and Tracking
PublicationRecently, capabilities of many computer vision tasks have significantly improved due to advances in Convolutional Neural Networks. In our research, we demonstrate that it can be also used for face detection from low resolution thermal images, acquired with a portable camera. The physical size of the camera used in our research allows for embedding it in a wearable device or indoor remote monitoring solution for elderly and disabled...
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LONG-TERM RISK CLASS MIGRATIONS OF NON-BANKRUPT AND BANKRUPT ENTERPRISES
PublicationThis paper investigates how the process of going bankrupt can be recognized much earlier by enterprises than by traditional forecasting models. The presented studies focus on the assessment of credit risk classes and on determination of the differences in risk class migrations between non-bankrupt enterprises and future insolvent firms. For this purpose, the author has developed a model of a Kohonen artificial neural network to...
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Homoclinic orbits for a class of singular second order Hamiltonian systems in R3
PublicationW niniejszym artykule rozważamy autonomiczny układ Hamiltonowski w 3-wymiarowej przestrzeni euklidesowej, z potencjałem osiągającym maksimum globalne właściwe równe zero w początku układu współrzędnych i mającym za zbiór punktów osobliwych prostą, która nie przechodzi przez początek układu. Przy założeniu, że potencjał spełnia pewien warunek zwartości w nieskończoności i warunek Gordona w otoczeniu prostej punktów osobliwych, stosując...
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New class of quaternary ammonium salts, derivatives of methyl D-glucopyranosides.
PublicationReakcja zasad azotowych z 6-O-p-tozylo-alfa-D-glukopiranozydem metylu lub 6-O-tozylo-beta-D-glukopiranozydem metylu (prowadzona w skali mikro) dając odpowiednie sole amoniowe. Jako zasady azotowe użyto pirydyny, 2-metylopirydyny i trimetyloaminy. Produkty zostały przebadane przy użyciu spektroskopii 1H, 13C NMR, spektroskopii mas oraz analizy elementarnej a budowa jednego z nich została dodatkowo potwierdzona za pomocą rentgenowskiej...
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Learning sperm cells part segmentation with class-specific data augmentation
PublicationInfertility affects around 15% of couples worldwide. Male fertility problems include poor sperm quality and low sperm count. The advanced fertility treatment methods like ICSI are nowadays supported by vision systems to assist embryologists in selecting good quality sperm. Computer-Assisted Semen Analysis (CASA) provides quantitative and qualitative sperm analysis concerning concentration, motility, morphology, vitality, and fragmentation....
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Electronic and ionic relaxations in strontium-borate glass and glass-ceramics containing bismuth and vanadium oxides
PublicationThe topography, microstructure and electrical properties of strontium-borate glass and SBO glass containing bismuth and vanadium oxides, were studied. The structure was measured using X-ray diffraction (XRD), Energy Dispersive X-ray Spectrometer (EDS) and Scanning electron microscope (SEM) methods. The A.C. complex conductivity was investigated as a function of temperature and frequency. The influence of the quantity of bismuth...
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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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Evaluation of Glass Powder-Based Geopolymer Stabilized Road Bases Containing Recycled Waste Glass Aggregate
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From Structure to Luminescent Properties of B2O3-Bi2O3-SrF2 Glass and Glass-Ceramics Doped with Eu3+ Ions
PublicationGlass-ceramics with the composition B2O3 -Bi2O3 -SrF2 were synthesized by the conventional melt-quenching technique and subsequent crystallization of the parental glasses. The temperature at which the ceramization was carried out was selected based on differential scanning calorimetry (DSC) analysis. The structure of the studied materials and the formation of SrF2 nanocrystals were confirmed by the Fourier-transform infrared spectroscopy...
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Through the looking-glass of the grazing bifurcation
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