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Wyniki wyszukiwania dla: topological invariants
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Conformational solution studies of the SDS micelle-bound 11-28 fragment of two Alzheimer's β-amyloid variants (E22K and A21G) using CD, NMR, and MD techniques
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Targeting Spike‐ACE2 Interface of SARS‐CoV‐2 and its Omicron Variant: A Comparative Screening of Potential Inhibitors for Existing and Anticipating Variants Using Molecular Modelling Approach
PublikacjaThe recent COVID pandemic has shown major impact on public health and economic crisis. Despite the development of many vaccines and drugs against the severe acute respiratory syndrome (SARS) coronavirus 2, the pandemic still persists. The continued spread of the virus is largely driven by the emergence of viral variants such as α, β, γ, delta, epsilon spike, omicron and its subvariants (BA.1,2,3) which can evade the current vaccines...
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The Importance of Contextual Topology in the Process of Harmonization of the Spatial Databases on Example BDOT500
PublikacjaIn 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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Dedukcja zachowań węzłów sieci ad hoc na podstawie potwierdzeń końcowych: ocena dokładności
PublikacjaPrzebadano precyzję algorytmu dedukcji rzeczywistych spolegliwości węzłów sieci MANET w oparciu o potwierdzenia end-to-end i bez użycia mechanizmu watchdog. W przeprowadzonych eksperymentach numerycznych wskazano charakterystyki topologiczne wpływające na tę precyzję.
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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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Persistent homology as a new method of the assessment of heart rate variability
PublikacjaHeart 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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Three-dimensional Weyl topology in one-dimensional photonic structures
PublikacjaTopological 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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CRVG - a new model for wireless networks topology generation
PublikacjaThis 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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Mechanism of Li nucleation at graphite anodes and mitigation strategies
PublikacjaLithium metal plating is a critical safety issue in Li-ion cells with graphite anodes, and contributes significantly to ageing, drastically limiting the lifetime and inducing capacity loss. Nonetheless, the nucleation mechanism of metallic Li on graphite anodes is still poorly understood. But in-depth understanding is needed to rationally design mitigation measures. In this work, we conducted FirstPrinciples studies to elucidate...
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Synthesis, Molecular Structure, Metabolic Stability and QSAR Studies of a Novel Series of Anticancer N-Acylbenzenesulfonamides
PublikacjaA series of novel N-acyl-4-chloro-5-methyl-2-(R1-methylthio)benzenesulfonamides 18–47 have been synthesized by the reaction of N-[4-chloro-5-methyl-2-(R1-methylthio) benzenesulfonyl]cyanamide potassium salts with appropriate carboxylic acids. Some of them showed anticancer activity toward the human cancer cell lines MCF-7, HCT-116 and HeLa, with the growth percentages (GPs) in the range from 7% to 46%. Quantitative structure-activity relationship...
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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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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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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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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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Deterministic Rendezvous in Restricted Graphs
PublikacjaIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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PI observer stability and application in an induction motor control system
PublikacjaThe paper discusses the problem of stability of a proportional-integral Luenberger observer, designated for the state variables reconstruction of a linear, time-invariant dynamical system.
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The effect of social media communication on consumer perceptions of brands
PublikacjaResearchers and brand managers have limited understanding of the effects social media communication has on how consumers perceive brands. We investigated 504 Facebook users in order to observe the impact of firm-created and user-generated (UG) social media communication on brand equity (BE), brand attitude (BA) and purchase intention (PI) by using a standardized online survey throughout Poland. To test the conceptual model, we...
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DETERMINATION OF THE CITY CENTRE. STUDY FOR THE TROJMIASTO AGGLOMERATION
PublikacjaDetermination of the centre of the city or agglomeration or generally the geographic area is a task which is often undertaken as part of the promotional actions realized by local authorities or directly by inhabitants. Nowadays, especially due to the development and availability of positioning technology and satellite imaging, this job is undertaken within the framework of general didactic tasks and group projects during the study...
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Conley index in Hilbert spaces and the Leray-Schauder degree
PublikacjaZdefiniowane 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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On homotopy Conley index for multivalued flows in Hilbert spaces
PublikacjaPodano 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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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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An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems
PublikacjaW 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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Almost homoclinic solutions for the second order Hamiltonian systems
PublikacjaW niniejszej pracy badam istnienie rozwiązań prawie homoklinicznych (almost homoclinic) dla układu Hamiltona rzędu drugiego (układu Newtona): ü(t) + V_{u}(t,u) = f(t), gdzie t є R, u є R^{n}, V(t,u) = -K(t,u) + W(t,u), K,W: R x R^{n} → R są klasy C^{1}, K spełnia warunek ''pinching'', W_{u}(t,u)=o(|u|), gdy |u| → 0 jednostajnie względem t, f: R → R^{n} jest funkcją ciągłą, niezerową i odpowiednio małą w L^{2}(R,R^{n}). Przy tych...
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Homoclinic solutions for a class of autonomous second order Hamiltonian systems with a superquadratic potential
PublikacjaW niniejszej pracy udowodniliśmy istnienie nietrywialnego rozwiązania homoklinicznego dla autonomicznych układów Hamiltona drugiego rzędu z nadkwadratowym potencjałem. Orbitę homokliniczną otrzymaliśmy jako słabą granicę ciągu punktów prawie krytycznych, stosując zasadę minimaks do odpowiedniego funkcjonału akcji oraz prosty argument typu ''concentration-compactness''.
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The Conley index and spectral sequences
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On the space of equivariant local maps
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Spectral sequences and detailed connection matrices
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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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Computer assisted method for proving existence of periodic orbits
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On the theorem of Tverberg
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Borsuk-Ulam type theorems on product spaces II
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Fixed point index for $G$-equivariant multivalued maps
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Fixed point indices of iterations of planar homeomorphisms.
PublikacjaW pracy bada się postać indeksów iteracji lokalnych homeomorfizmów płaszczyzny.
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The relative cup-length in local Morse cohomology
PublikacjaLocal Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds M. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions...
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Selections and approximations of convex-valued equivariant mappings
PublikacjaUdowodniono szereg twierdzeń o współzmienniczych selekcjach i aproksymacjach ciągłych, mierzalnych i typu Caratheodory'ego dla odwzorowań G-współzmienniczych o wartościach wypukłych, gdzie G jest grupą zwartą Liego. Tw. typu Michaela, Celliny, Browdera, Kuratowskiego-Ryll-Nardzewskiego, Castaing itd.
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublikacjaWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublikacjaWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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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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Turre cum capellis suis – identification of an earlier phase of the Holy Cross church at Tar – Stancija Blek (Tar-Vabriga – Torre-Abrega, Istria)
PublikacjaThe paper reports the results of the first campaign of excavations at the Church of the Holy Cross near Stancija Blek (Tar-Vabriga – Torre-Abrega municipality, Istria), which is close to the multiphase settlement of Old Tar. A trial trench behind the rear wall of the church and along its southern perimetral wall revealed an earlier building and one grave. Though the uncovered remains are scanty, several distinct architectural...
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Study of Integer Spin S = 1 in the Polar Magnet β-Ni(IO3)2
PublikacjaPolar magnetic materials exhibiting appreciable asymmetric exchange interactions can potentially host new topological states of matter such as vortex-like spin textures; however, realizations have been mostly limited to half-integer spins due to rare numbers of integer spin systems with broken spatial inversion lattice symmetries. Here, we studied the structure and magnetic properties of the S = 1 integer spin polar magnet β-Ni(IO3)2...
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A hyperelastic model for soils with stress-induced and inherent anisotropy
PublikacjaIn this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is8presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced9anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to10introduce constant inherent cross-anisotropic component. A convenient...
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Single-phase, Five-level Inverter with SPWM-Based Neutral Point Voltage Balancing Scheme
PublikacjaMultilevel inverter topologies provide several advantages over two-level inverter configuration. These benefits are the reason for the growing interest in multilevel topologies among research society. One of the most popular topological concepts (diode and active switch clamping) requires neutral-point potential balancing due to series-connected capacitor banks across the input dc link in such derived inverter configurations. This...
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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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Equivariant Morse equation
PublikacjaThe 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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Module structure in Conley theory with some applications
PublikacjaA multiplicative structure in the cohomological versjon of Conley index is described . In the case of equivariant flows we apply the normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is then applied to obtain a mountain pass type theorem. Another application is a result on multiple bifurcations for some elliptic PDE.
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A Measurable Selector in Kadison’s Carpenter’s Theorem
PublikacjaWe show the existence of a measurable selector in Carpenter’s Theorem due to Kadison. This solves a problem posed by Jasper and the first author in an earlier work. As an application we obtain a characterization of all possible spectral functions of shift-invariant subspaces of L 2 (R d ) and Carpenter’s Theorem for type I ∞ von Neumann algebras.
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Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet
PublikacjaThe long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition....
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PSYCHOMETRIC PROPERTIES OF THE POLISH VERSION OF THE GENERALIZED ANXIETY DISORDER 7-ITEM SCALE (GAD-7) IN A NON-CLINICAL SAMPLE OF EMPLOYEES DURING PANDEMIC CRISIS
PublikacjaObjectives: The COVID-19 outbreak is an example of a crisis that triggered an increase in generalized anxiety disorder. The study aims to validate the Polish version of the Generalized Anxiety Disorder 7-item scale (GAD-7) by Spitzer et al. among a non-clinical sample of employees and examine the invariance depending on the gender and age of working adults. Material and Methods: For assessing factor structure of the Polish version...
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OBRONA SIECI INFORMACJOCENTRYCZNEJ PRZED ZATRUWANIEM TREŚCI PRZEZ NIEZAUFANYCH WYDAWCÓW Z UŻYCIEM MODELU INFEKCJI W GRAFACH
PublikacjaSieci informacjocentryczne narażone są na ataki zatruwania treści przez intruza, który przejął klucz prywatny wydawcy treści. Efektem jest podmiana treści oryginalnych na zatrute. W pracy zaproponowano model ataku opierający się na analogii z procesami infekcji w grafach i przeanalizowano prosty mechanizm obronny. Symulacje przeprowadzone w sieciach informacjocentrycz-nych o topologiach...
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Quasi-resonant dc-link inverter with a reduced number of active elements
PublikacjaW artykule przedstawiono nową topologię równoległego quasi-rezonansowego obwodu pośredniczącego falownika napięcia. Opisano sekwencje miękkiej komutacji falownika w dwukierunkowym trybie pracy falowniczej i prostowniczej. Analiza układu została zweryfikowana badaniami symulacyjnymi i eksperymentalnymi. Przedstawiona topologia odznacza się prostą strukturą oraz małą ilością elementów aktywnych. Dzięki zastosowaniu krzepkiej strategii...