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Search results for: HOPF THEOREM
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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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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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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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Projekt Hoff
PublicationRozdział w monografii dotyczy działalności projektowej Barbary Hoff, od 1956 roku kiedy w "Przekroju" prezentowała pojedyncze projekty sukienek, poprzez pierwszą "kolekcję masową" w 1967 roku aż do powstania marki Hoffland i stoiska " z kolekcją własną Hoff" w Juniorze w Domach towarowych Centrum w warszawie w 1977 roku
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Hopf bifurcation in time‐delayed gene expression model with dimers
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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On the theorem of Tverberg
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Shift invariant operators and a saturation theorem.
PublicationPraca jest kontynuacją wcześniejszych dwóch prac wydanych w Appl. Math. w latach 2001 i 2002. Główny wynik dotyczy wygładzania specjalnego ciągu zbieżnego słabo, tak iż dostajemy ciąg zbieżny w normie supremum.
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A Measurable Selector in Kadison’s Carpenter’s Theorem
PublicationWe 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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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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Analysis of the reliability of any-hop star network
PublicationZałożono, że sieć ma wielostopniową strukturę gwiaździstą. Jako oceny niezawodności tych sieci przyjęto: 1) średnią liczbę sprawnych par węzłów, które mogą komunikować się wzajemnie; 2) średnią liczbę sprawnych par węzłów, które mogą komunikować się poprzez węzeł centralny; 3) średnią liczbę sprawnych par węzłów, które mogą komunikować się z węzłem centralnym; 4) prawdopodobieństwo zdarzenia, że sprawne węzły mogą komunikować...
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No-local-broadcasting theorem for multipartite quantum correlations
PublicationWe prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational...
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Contra Bellum: Bell's Theorem as a Confusion of Languages
PublicationBell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level k ∈ Z are violated by probabilities at level k+1. We are inclined to think that k=0 corresponds to the classical world, while k=1 — to the quantum one. However, as the k=0 inequalities are violated by k=1 probabilities, the same relation holds between k=1 inequalities violated...
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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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Analysis of the reliability 0f any-hop star network.
PublicationZałożono, że sieć ma wielostopniową strukturę gwiaździstą. Jako oceny niezawodności tych sieci przyjęto: 1) średnią liczbę sprawnych par węzłów, które mogą komunikować się wzajemnie; 2)średnią liczbę sprawnych par węzłów, które mogą komunikować się poprzez węzeł centralny; 3) średnią liczbę sprawnych par węzłów, które mogą komunikować się z węzłem centralnym; 4) prawdopodobieństwo zdarzenia, że sprawne węzły mogą komunikować się...
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The Relationship of Purpose in Life and Hope in Shaping Happiness Among Patients with Cancer in Poland
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Lung Protection by Cathepsin C Inhibition: A New Hope for COVID-19 and ARDS?
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Effective residue-to-binary converter with the Chinese Remainder Theorem
PublicationKonwersja liczb z systemu resztowego do systemu binarnego jest podstawową operacją we wszystkich układach cyfrowego przetwarzania sygnałów, które wykorzystują system resztowy. W niniejszej pracy zaproponowano nową metodę konwersji opartą o chińskie twierdzenie o resztach dla modułów 5- i 6-bitowych. Specyficzną cechą nowej metody jest sposób obliczania tzw. współczynnika nadmiaru w formule chińskiego twierdzenia o resztach, co...
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Application of Mazur-Orlicz`s theorem in AMISE calculation
PublicationW pracy podano nowe wyprowadzenie formuły asymptotycznej błędu aproksymacji dla operatorów całkowych w przestrzeniach niezmienniczych na przesunięcia. Obliczono asymptotykę błędu średniokwakratowego dla estymatora gęstości.
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Can a man also be afraid? Partner communication, anxiety and hope in parents of premature infants
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublicationObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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RNS reverse converter based on the new chinese remainder theorem.
PublicationPrzeanalizowano złożoność układu cyfrowego opartego na nowej odmianie chińskiego twierdzenia o resztach.
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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New aspects of the use of Optical Theorem in the analysis of microcavity lasers
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Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds
PublicationLocal hidden-variable model of singlet-state correlations discussed in M. Czachor, Acta Phys. Polon. A 139, 70, is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring...
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The reliability of any-hop star networks with respect to failures of communication nodes.
PublicationThis paper investigated the reliability of any-hop star networks. The any-hop star topology is used in centralized computer networks. We will assume that the all nodes fail independently, links are failure-free. Following measures of network reliability are assumed: the expected number of nodes, which can communicate with the central node; the expected number of node pairs, which are connected by a path through the central node;...
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Mitigating Traffic Remapping Attacks in Autonomous Multi-hop Wireless Networks
PublicationMultihop wireless networks with autonomous nodes are susceptible to selfish traffic remapping attacks (TRAs). Nodes launching TRAs leverage the underlying channel access function to receive an unduly high Quality of Service (QoS) for packet flows traversing source-to-destination routes. TRAs are easy to execute, impossible to prevent, difficult to detect, and harmful to the QoS of honest nodes. Recognizing the need for providing...
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Research Protocol of the Polish Adaptation and Validation of HOPE Scale: Qualitative Measurement of Patients' Spiritual Needs
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The Indirect Relationship Between Spiritual Experiences and Subjective Wellbeing Through Hope? A Sample of Chilean Students
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Composition and In Vitro Effects of Cultivars of Humulus lupulus L. Hops on Cholinesterase Activity and Microbial Growth
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Fast rns scaling of signed numbers based on the chinese remainder theorem
PublicationPrzedstawiono architekturę szybkiego skalera resztowego dla liczb ze znakiem dla modułów 5-bitowych opartego na chińskim twierdzeniu o resztach. W architekturze zastosowano wyznaczanie projekcji ortogonalnych przy użyciu funkcji logicznych 5 zmiennych, sumator kodulo m/k oraz wejściowy konwerter do systemu resztowego. Operacja modulo m/k jest wykonywana przy zastosowaniu drzewa 4-operandowych sumatorów modulo 2m/k i końcowego...
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Optical theorem helps understand thresholds of lasing in open semiconductor microcavities
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Optical Theorem Helps Understand Thresholds of Lasing in Microcavities With Active Regions
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A note on a Wiener-Wintner theorem for mean ergodic Markov amenable semigroups
PublicationWe prove a Wiener-Wintner ergodic type theorem for a Markov representation of a right amenable semitopological semigroup.
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Indirect Relationship between Alcoholics Anonymous Spirituality and Their Hopelessness: The Role of Meaning in Life, Hope, and Abstinence Duration
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Resilience through multicast – An optimization model for multi-hop wireless sensor networks
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Modeling a Traffic Remapping Attack Game in a Multi-hop Ad Hoc Network
PublicationIn multi-hop ad hoc networks, selfish nodes may unduly acquire high quality of service (QoS) by assigning higher priority to source packets and lower priority to transit packets. Such traffic remapping attacks (TRAs) are cheap to launch, impossible to prevent, hard to detect, and harmful to non-selfish nodes. While studied mostly in single-hop wireless network settings, TRAs have resisted analysis in multi-hop settings. In this paper...
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Selfish Attacks in Two-Hop IEEE 802.11 Relay Networks: Impact and Countermeasures
PublicationIn IEEE 802.11 networks, selfish stations can pursue a better quality of service through selfish MAC-layer attacks. Such attacks are easy to perform, secure routing protocols do not prevent them, and their detection may be complex. Two-hop relay topologies allow a new angle of attack: a selfish relay can tamper with either source traffic, transit traffic, or both. We consider the applicability of selfish attacks and their variants...
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Limits Theorems for Random Walks on Homeo(S1)
PublicationThe central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.
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Theory of systems & cybernetics as a bridge between theory and practice. .
PublicationW pracy przedstawiono sposoby posługiwania się Teorią Systemów i Cybernetyką celem identyfikacji efektu synergii między nauką i działalnością praktyczną.
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Death and Dying, Theories of
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An improved high-speed residue-to-binary converter based on the chinese remainder theorem
Publicationw pracy zaprezentowano nowy szybki konwerter z systemu resztowego do systemu binarnego. Projekcje ortogonalne wyznaczane są przy użyciu funkcji logicznych pięciu zmiennych. Suma projekcji obliczana jest z zastosowaniem drzewa Wallace'a. Wektor sumy i wektor przeniesienia są dzielone na segmenty tak aby liczba reprezentowana łącznie przez obydwa segmenty o młodszych wagach nie przekraczała zakresu systemu resztowego,M. Bity segmentów...
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Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography
PublicationBell’s theorem is supposed to exclude all local hidden-variable models of quantum correlations. However,an explicit counterexample shows that a new class of local realistic models, based on generalized arith-metic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical oftwo-electron singlet states. Observable probabilities are consistent with the usual arithmetic employedby macroscopic observers...
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Distributed protection against non-cooperative node behavior in multi-hop wireless networks
PublicationAn important security problem in today's distributed data networks is the prevention of non-cooperative behavior i.e., attacks consisting in the modification of standard node operation to gain unfair advantage over other system nodes. Such a behavior is currently feasible in many types of computer networks whose communication protocols are designed to maximize the network performance assuming full node cooperation. Moreover, it...
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Maximization of multicast periodic traffic throughput in multi-hop wireless networks with broadcast transmissions
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Throughput vs. Resilience in Multi-hop Wireless Sensor Networks with Periodic Packet Traffic
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A Reputation Scheme to Discourage Selfish QoS Manipulation in Two-Hop Wireless Relay Networks
PublicationIn wireless networks, stations can improve their received quality of service (QoS) by handling packets of source flows with higher priority. Additionally, in cooperative relay networks, the relays can handle transit flows with lower priority. We use game theory to model a two-hop relay network where each of the two involved stations can commit such selfish QoS manipulation. We design and evaluate a reputation-based incentive scheme...
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Borsuk-Ulam type theorems on product spaces II
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A Loophole of All ‘Loophole-Free’ Bell-Type Theorems
PublicationBell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different...
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FPGA realization of the high-speed residue-to-binary converter based on the Chinese Remainder Theorem
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FPGA realization of the high-speed residue-to-binary converter based on chinese remainder theorem
PublicationW pracy przedstawiono architekturę, realizację FPGA oraz symulację numeryczną na poziomie bitowym szybkiego konwertera z systemu resztowego do systemu binarnego dla modułów 5-bitowych opartego na chińskim twierdzeniu o resztach. Algorytm konwertera obejmuje obliczanie projekcji ortogonalnych poprzez odczyt pamięci oraz sumowanie modulo M realizowane dwustopniowo, pierwszy stopień oparty o sumatory CSA umożliwia redukcję do zakresu...