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Search results for: ARNOLD CONJECTURE
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publicationn this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T 2n
PublicationWe show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983.
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet 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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Conjectured strong complementary-correlations tradeoff
PublicationWe conjecture uncertainty relations that restrict correlations between the results of measurements performed by two separate parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from the Maassen-Uffink uncertainty relation and is much stronger...
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Arnold Mathematical Journal
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Artnord
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Modeling of acoustics of hearing aid earmold systems
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Waveguide model of the hearing aid earmold system
PublicationBackground The earmold system of the Behind-The-Ear hearing aid is an acoustic system that modifies the spectrum of the propagated sound waves. Improper selection of the earmold system may result in deterioration of sound quality and speech intelligibility. Computer modeling methods may be useful in the process of hearing aid fitting, allowing physician to examine various earmold system configurations and choose the optimum one...
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Waveguide model of the hearing aid earmold system
PublicationBackground The earmold system of the Behind-The-Ear hearing aid is an acoustic system that modifies the spectrum of the propagated sound waves. Improper selection of the earmold system may result in deterioration of sound quality and speech intelligibility. Computer modeling methods may be useful in the process of hearing aid fitting, allowing physician to examine various earmold system configurations and choose the optimum one...
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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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Harold Pinter Review-Essays on Contemporary Drama
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Hat problem on odd cycles
PublicationThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can...
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Arnold Adamczyk mgr inż.
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Computing dynamical curlicues
Open Research DataA curlicue is a piece-wise linear curve in the complex plane which can be generated by an arbitrary sequence of real numbers u_n. It can be interpreted as a trajectory of a particle in the plane which starts in the origin at time t=0 and moves with a constant velocity, changing its direction at instances t=0,1,2,3,..., where the new direction is given...
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Kontrolki ActiveX - Projektowanie kontrolek ActiveX wykorzystujących klasy MFC
PublicationPrzedstawiono środowisko edycyjne MFC ActiveX ControlWizard do projektowania komponentów ActiveX. Opisano zasady wizualizacji kontrolek, metody przekazywania właściwości do kontrolek oraz podano instruktaż pisania własnych funkcji i procedur obsługi zdarzeń w ramach komponentu ActiveX. Wszystkie etapy projektowania zilustrowano przykładami.
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Kontrolki ActiveX - Osadzanie kontrolek ActiveX w dokumentach WWW
PublicationW artykule opisano cechy i zasady funkcjonowania kontrolek ActiveX. Przedstawiono rozwój technologii Active na przestrzeni ostatnich lat. Na zasadzie lekcji omówiono metody edycji dokumentów WWW wykorzystujących technologię Active i sposób konfigurowania kontrolek w języku HTML.
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ActiveX dla serwera ASP
PublicationPrzedstawiono instruktaż projektowania komponentu ActiveX, rozszerzającego funkcjonalność serwera WWW o usługę chat-room. Opisano zasady osadzania komponentu w środowisku Active Server Pages i metody wymiany informacji pomiędzy komponentem a dokumentem hipertekstowym.
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Projektowanie kontrolek ActiveX za pomocą ATL
PublicationW artykule przedstawiono zasady projektowania komponentów ActiveX z wykorzystaniem szablonów Active Template Library. Opisano narzędzie wspomagające edycję kodu: kreator ATL COM AppWizard oraz kreator ATL Object Wizard. Porównano zalety i wady podejścia bazującego na szablonach ATL względem podejścia wykorzystującego klasy MFC.
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Internetowa telediagnostyka urządzeń w obsłudze serwisowej.
PublicationPrzedstawiono system diagnostyczny do zdalnego testowania i lokalizowania uszkodzeń w elektronicznych podzespołach urządzeń powszechnego użytku. System składa się ze stanowiska doświadczalnego do konfigurowania i weryfikowania procedur diagnostycznych oraz prototypowego układu testera wbudowanego z dostępem internetowym. Zdalna diagnostyka jest rozpatrywana w aspekcie obsługi posprzedażnej w systemach CRM.
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The micro implementation of a Web server.
PublicationArtykuł prezentuje techniczne zasady projektowania mikroserwerów internetowych o zredukowanej złożoności konstrukcyjnej i niewielkim poborze energii.
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Medyczne serwisy internetowe w promocji wysokiego zaufania.
PublicationW artykule poddano dyskusji problematykę internetowej reklamy leków w aspekcie kosztów, efektywności, postrzegania i akceptacji przekazu reklamowego. Porównując wydajność kampanii reklamowych zamawianych w portach medycznych z promocją leków prowadzoną we własnym serwisie tematycznym. Na przykładzie praktycznego wdrożenia serwisu dla lekarzy wykazano korzyści marketingowe wynikające z prowadzenia własnych stron tematycznych...
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Internetowa telediagnostyka układów elektronicznych.
PublicationPrzedstawiono realizację sprzętową i programistyczną prototypowej usługi sieciowej, której zadaniem jest testowanie i lokalizowanie uszkodzeń w mieszanych sygnałowo układach elektronicznych za pośrednictwem Internetu.
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Internetowa akwizycja sygnałów życiowych.
PublicationPrzedstawiono rozwiązanie techniczne systemu do zdalnej akwizycji sygnałów życiowych pacjentów w stanach nagłych z wykorzystaniem protokołów internetowych. Celem projektu jest dążenie do rozwiązań mobilnych z dostępem internetowym o niewielkiej złożoności konstrukcyjnej i małym poborze energii.
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The Implementation of a Microserver.
PublicationArtykuł prezentuje zasady projektowania mikroserwerów o ograniczonej złożoności obliczeniowej i niewielkim poborze energii. Zaproponowana redukcja funkcjonalności protokołow TCP/IP, pomimo niewielkiego zapotrzebowania na obliczenia, pozwala na realizację wydajnego połączenia klient-serwer w układach mikrokontrolerowych.
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Lokalizacja uszkodzeń w układach mieszanych-sygnałowo metodą sygnaturową
PublicationPrzedstawiono metodę detekcji i lokalizacji uszkodzeń w układach mieszanych-sygnałowo przeznaczoną do implementacji w testerach wbudowanych BIST wraz z algorytmem doboru jego optymalnych parametrów układowych.
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Trust and Distrust in e-Democracy
PublicationIn the digital government research literature, the concept of trust is typically used as a precondition for the adoption of digital technology in the public sector or an outcome of a roadmap leading up to such adoption. The concept plays a central role in many decisions linked to the planning, adoption and management of the public sector technology. In contrast, the concept of distrust is almost neglected in such literature but,...
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Complexation of amino acids derivatives in water by calix[4]arene phosphonic acids
PublicationSeries of the calix[4]arene phosphonic acids with various substituents at the lower rim was synthesized. Complexing properties of these receptors towards methyl esters of six amino acids strongly depended on the calix[4]arene conformation flexibility. The complex formation processes were monitored using 1H NMR spectroscopy (deuterated phosphate buffer at pD 7.3, 22 oC) and association constant values were evaluated. Inherently...
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On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs
PublicationIn the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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Trust and Distrust in e-Democracy
PublicationIn the digital government research literature, the concept of trust is typically used as a precondition for the adoption of digital technology in the public sector or an outcome of a roadmap leading up to such adoption. The concept plays a central role in many decisions linked to the planning, adoption and management of the public sector technology. In contrast, the concept of...
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A note on total reinforcement in graphs
PublicationIn this note we prove a conjecture and inprove some results presendet in a recent paper of N. Sridharan, M.D. Elias, V.S.A. Subramanian, Total reinforcement number of a graph, AKCE Int. J. Graphs Comb. 4 (2) (2007) 197-202.
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A Note on a Problem Posed by D. E. Knuth on a Satisfiability Recurrence
PublicationWe resolve a conjecture proposed by D.E. Knuth concerning a recurrence arising in the satisfiability problem. Knuth's recurrence resembles recurrences arising in the analysis of tries, in particular PATRICIA tries, and asymmetric leader election. We solve Knuth's recurrence exactly and asymptotically, using analytic techniques such as the Mellin transform and analytic depoissonization.
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On structural physical approximations and entanglement breaking maps
PublicationVery recently, a conjecture saying that the so-called structural physical approximations (SPAs) to optimal positive maps (optimal entanglement witnesses) give entanglement breaking (EB) maps (separable states) has been posed (Korbicz et al 2008 Phys. Rev. A 78 062105). The main purpose of this contribution is to explore this subject. First, we extend the set of entanglement witnesses supporting the conjecture. Then, we ask whether...
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On Computing Curlicues Generated by Circle Homeomorphisms
PublicationThe dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...
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On some open questions for Ramsey and Folkman numbers
PublicationWe discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Folkman numbers. For the classical two-color Ramsey numbers, we first focus on constructive bounds for the difference between consecutive Ramsey numbers. We present the history of progress on the Ramsey number R(5,5) and discuss the conjecture that it is equal to 43.
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Sytuacje traumatyczne w pracy funkcjonariuszy Służby Więziennej
PublicationBezpośredni kontakt ze skazanymi czyni pracę personelu więziennego niebezpieczną i stresującą. Celem artykułu była analiza sytuacji zagrażających, pojawiających się w więzieniu, mogących wywołać u funkcjonariuszy ostrą reakcję stresową, zespół stresu ostrego (ASD) i zaburzenie po stresie traumatycznym (PTSD). Sytuacje te związane są z przemocą wewnętrzną, jak i skierowaną ze strony więźniów do funkcjonariuszy. Przedstawiono sposoby...
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Fixed point indices of iterates of a low-dimensional diffeomorphism at a fixed point which is an isolated invariant set
PublicationLet f be an R^n-diffeomorphism, where n = 2, 3, for which {0} is an isolated invariant set. We determine all possible forms of the sequences of fixed point indices of iterates of f at 0, {ind(f n, 0)}_n, confirming in R3 the conjecture of Ruiz del Portal and Salazar (J Differ Equ 249, 989–1013, 2010).
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Total chromatic sum for trees
PublicationThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublicationWe 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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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet 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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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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Performance evaluation of unified memory and dynamic parallelism for selected parallel CUDA applications
PublicationThe aim of this paper is to evaluate performance of new CUDA mechanisms—unified memory and dynamic parallelism for real parallel applications compared to standard CUDA API versions. In order to gain insight into performance of these mechanisms, we decided to implement three applications with control and data flow typical of SPMD, geometric SPMD and divide-and-conquer schemes, which were then used for tests and experiments. Specifically,...
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Study of the Effectiveness of Model Order Reduction Algorithms in the Finite Element Method Analysis of Multi-port Microwave Structures
PublicationThe purpose of this paper is to investigate the effectiveness of model order reduction algorithms in finite element method analysis of multi-port microwave structures. Consideration is given to state of the art algorithms, i.e. compact reduced-basis method (CRBM), second-order Arnoldi method for passive-order reduction (SAPOR), reduced-basis methods (RBM) and subspace-splitting moment-matching MOR (SSMM-MOR)
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A construction for the hat problem on a directed graph
PublicationA team of n players plays the following game. After a strategy session, each player is randomly fitted with a blue or red hat. Then, without further communication, everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. Visibility is defined by a directed graph; that is, vertices correspond to players, and a player can see each player to whom he is connected by an arc. The...
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Early Stages of RNA-Mediated Conversion of Human Prions
PublicationPrion diseases are characterized by the conversion of prion proteins from a PrPC fold into a disease-causing PrPSC form that is self-replicating. A possible agent to trigger this conversion is polyadenosine RNA, but both mechanism and pathways of the conversion are poorly understood. Using coarse-grained molecular dynamic simulations we study the time evolution of PrPC over 600 μs. We find that both the D178N mutation and interacting...
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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms
PublicationWe apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff...
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Simple SIR models with Markovian control
PublicationWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving...
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Wideband Macromodels in Finite Element Method
PublicationThis letter proposes a novel projection technique for accelerating Finite Element Method simulations. The algorithm is based on the Second-order Arnoldi Method for Passive Order Reduction (SAPOR). It involves generation of two projection bases and thanks to this it is applicable to the systems of equations, which contain the quadratic frequency-dependence in the input term, that arise when projection is applied locally in the selected...
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Optimal edge-coloring with edge rate constraints
PublicationWe consider the problem of covering the edges of a graph by a sequence of matchings subject to the constraint that each edge e appears in at least a given fraction r(e) of the matchings. Although it can be determined in polynomial time whether such a sequence of matchings exists or not [Grötschel et al., Combinatorica (1981), 169–197], we show that several questions about the length of the sequence are computationally intractable....
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Research on Biosimilars: pivotal trials and principles
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Kinetic and equilibrium studies of the proton and deuteron transfer reaction between bis(2,4-dinitrophenyl)methane and strong nitrogen bases in acetonitrile
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