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Search results for: BELL THEOREM
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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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On the theorem of Tverberg
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The outline of percolation theory in reference to Solid Oxide Fuel Cell composite anodes
PublicationPrzedstawiono podstawy teoretyczne dotyczące zjawiska perkolacji w układach nieuporządkowanych. Zaprezentowano obecny stan wiedzy na temat wykorzystania teorii perkolacji w materiałach elektrodowych dla tlenkowych ogniw paliwowych.
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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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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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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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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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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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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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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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Employee Well-being in the Perspective of Positive Psychology and of the Job Demands-Resources Theory. The Role of Trust Within the Organization
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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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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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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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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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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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Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
PublicationEinstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements,...
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Bounding conditional entropy of bipartite states with Bell operators
PublicationQuantum information theory explores numerous properties that surpass classical paradigms, offering novel applications and benefits. Among these properties, negative conditional von Neumann entropy (CVNE) is particularly significant in entangled quantum systems, serving as an indicator of potential advantages in various information-theoretic tasks, despite its indirect observability. In this paper, we investigate the relationship...
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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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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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Intrinsic asymmetry with respect to adversary: a new feature of Bell inequalities
PublicationIt is known that the local bound of a Bell inequality is sensitive to the knowledge of the external observer about the settings statistics. Here we ask how that sensitivity depends on the structure of that knowledge. It turns out that in some cases it may happen that the local bound is much more sensitive to the adversaryʼs knowledge about the settings of one party than the other. Remarkably, there are Bell inequalities which are...
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Strong Monogamies of No-Signaling Violations for Bipartite Correlation Bell Inequalities
PublicationThe phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as...
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Quantum communication complexity advantage implies violation of a Bell inequality
PublicationWe obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics which violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily...
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Trade-offs in multiparty Bell-inequality violations in qubit networks
PublicationTwo overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations...
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Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
PublicationIt is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 × n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007)], quantum mechanical correlations...
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Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus
PublicationA class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory
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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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Borsuk-Ulam type theorems on product spaces II
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Rotating rod and ball
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Rotating rod and ball
PublicationWe consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...
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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...
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FPGA realization of the high-speed residue-to-binary converter based on the Chinese Remainder Theorem
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About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof
PublicationRecently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether's type Theorem, in particular ([9],Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis...
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Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
PublicationWe study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the...
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Vibration-Based Investigation of a Historic Bell Tower to Understand the Occurrence of Damage
PublicationABSTRACT The paper presents a survey of the historic Arch-cathedral bell tower in Vilnius induced by the appearance of cracks in the structure after a new bell system installation. An attempt is undertaken to identify the reason for the crack occurrence and to check a possible crack influence on global structural behaviour. The research is based on dynamic measurements made in the tower during ambient vibrations and during vibrations...
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Cell Membrane Transport Mechanisms: Ion Channels and Electrical Properties of Cell Membranes
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Theory of industrial clusters
PublicationW niniejszym rozdziale zostały przedstawione podstawy teoretyczne klastrów, a w szczególności stosowane definicje i klasyfikacje gron oraz determinanty ich rozwoju. Autorka wyjaśnia również zjawisko powstawania klastrów i przedstawia korzyści płynące ze współpracy w gronie. Obszerną część artykułu stanowi przegląd metod stosowanych w badaniach struktur klastrowych. Autorka zamieściła również charakterystyki wybranych regionów opartych...
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RNS reverse high-speed converter with quasi-regular structure based on the Chinese Remainder Theorem
PublicationPrzedstawiono dwie nowe architektury szybkiego konwertera z systemuresztowego do systemu binarnego oparte o chińskie tw. o resztach. Zastosowano nowe struktury 4-operandowych sumatorów modulo 2M. Pierwsza ze struktur oparta jest o wstępne sumowanie najstarszych bitów wektorów sumy i przeniesienia na wyjściu sumatora CSA, natomiast druga o bezpośrednie wykrywanie przekroczenia 2M. Konwerter wykorzystujący drugą ze struktur charakteryzuje...
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Germ cell-like telomeric length homeostasis in nonseminomatous testicular germ cell tumors
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Entangled rendezvous: a possible application of Bell non-locality for mobile agents on networks
PublicationRendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, are striving to meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern and future applications. Quantum non-locality, like Bell inequality violation, has shown that in many...