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Search results for: PROOF
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International Journal of Evidence & Proof
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An Alternative Proof of a Lower Bound on the 2-Domination Number of a Tree
PublicationA 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in D has a at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. Fink and Jacobson [n-domination in graphs, Graph theory with applications to algorithms and computer science, Wiley, New York, 1985, 283-300] established the following lower bound on the 2-domination...
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Computer Assisted Proof of the Existence of a Periodic Orbit in the Rössler Equations
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Law requirements of explosion proof protection at working with chemical substances
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Porównanie wydajności modyfikacji algorytmu Proof-number search uwzględniających wartości remisowe
PublicationProof-number search to znana rodzina algorytmów służących do wyznaczania wartości pozycji w nielosowych grach dwóch graczy z pełną informacją. W wersji podstawowej pn-search doskonale radzi sobie z wyszukiwaniem strategii wygrywającej jednego z graczy. Jednak istnieje wiele znanych gier, w których obydwaj gracze posiadają jedynie strategię remisującą (Młynek, Awari, Warcaby). W niniejszej pracy porównano wydajność dwóch modyfikacji...
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Network-assisted processing of advanced IoT applications: challenges and proof-of-concept application
PublicationRecent advances in the area of the Internet of Things shows that devices are usually resource-constrained. To enable advanced applications on these devices, it is necessary to enhance their performance by leveraging external computing resources available in the network. This work presents a study of computational platforms to increase the performance of these devices based on the Mobile Cloud Computing (MCC) paradigm. The main...
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Entrained Flow Plasma Gasification of Sewage Sludge–Proof-of-Concept and Fate of Inorganics
PublicationSewage sludge is a residue of wastewater processing that is biologically active and consists of water, organic matter, including dead and living pathogens, polycyclic aromatic hydrocarbons, and heavy metals, as well as organic and inorganic pollutants. Landfilling is on the decline, giving way to more environmentally friendly utilisation routes. This paper presents the results of a two-stage gasification–vitrification system, using...
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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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Ocena poprawności działania algorytmu proof-number search na strukturze digrafu acyklicznego
PublicationAlgorytm proof-number search jest znanym algorytmem służącym do rozwiązywania gier logicznych. Rozwiązanie gry jest jednoznaczne ze znalezieniem optymalnej strategii i pozwala przeprowadzić rozgrywkę w sposób pozwalający na osiągnięcie najlepszego możliwego wyniku. Jedną z największych wad tego algorytmu, naturalnie pracującego na strukturze drzewa, jest wielokrotne rozwijanie identycznych poddrzew gry co prowadzi do nadmiarowego...
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Deformation Analysis of a Composite Bridge during Proof Loading Using Point Cloud Processing
PublicationRemote sensing in structural diagnostics has recently been gaining attention. These techniques allow the creation of three-dimensional projections of the measured objects, and are relatively easy to use. One of the most popular branches of remote sensing is terrestrial laser scanning. Laser scanners are fast and efficient, gathering up to one million points per second. However, the weakness of terrestrial laser scanning is the...
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Proof-of-concept study on improved efficacy of rHuEPO administered as a long-term infusion in rats
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Greening procedures and analytical parameters. The polychlorinated naphthalenes analysis in complex matrices as proof of concept
PublicationDue to the complexity of analytical procedures employed for the determination of wide spectrum of persistent organic pollutants (POPs), it is important to consider the green character of the applied protocols and propose the greenest solutions. In this review, the green aspects of several analytical procedures used for the determination of polychlorinated naphthalenes (PCNs) (as a representatives of POPs) in different types of...
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Proof of Concept of Indoor Location System Using Long RFID Readers and Passive Tags
PublicationThe paper proposes a system for persons and objects location with the use of long radio-frequency identifications (RFIDs) readers. In order to investigate all aspects of the proposed location system, several key elements had to be analyzed, including the distance from which the tagged objects and the possibility of using more than one tag within one RFID range at the same time. When designing the system, it is also necessary to...
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Experimental Investigation of the Performance of an Innovative Implantable Left Ventricular Assist Device—Proof of Concept
PublicationThis paper presents the results of experimental performance of an innovative left ventricular assist device working on a specially designed test stand. The introduced invention is mainly applied for supporting the heart in patients with end-stage heart failure accompanied by mitral valve regurgitation and pulmonary hypertension. Moreover, the developed device has the form of a flexible balloon forming an intracardiac inert gas-filled...
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Open Innovation Competence for a Future-Proof Workforce: A Comparative Study from Four European Universities
PublicationDigital transformation is a key driving force of open innovation to capture and transfer knowledge inside and outside of a company’s bounds. New challenges in organizing multiple knowledge flows imply the need for increased competences related to this paradigm of future employees. In this article, we organize and aggregate the competencies required for open innovation collaboration and develop a competence profile that organizes...
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New Proofs of Some Fibonacci Identities
PublicationLucas proved in 1876 several identities for Fibonacci numbers. We give elementary and short proofs of them.
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Prooftexts: A Journal of Jewish Literary History
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Molecular Characterization of a DNA Polymerase from Thermus thermophilus MAT72 Phage vB_Tt72: A Novel Type-A Family Enzyme with Strong Proofreading Activity
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International Conference on Tests and Proofs
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Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks
PublicationUncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof....
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Electrical measurements of the dewetting of metal thin films
Open Research DataIn situ observations of dewetting of thin films is very complicated. One of the method, that helps to observe it, could be electrical measurements. For experiments, thin gold, silver and gold-silver nanoalloy films were deposited by magnetron sputtering method. Films were deposited on a Corning glass substrates. Samples were measured by four point method...
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The law of the Iterated Logarithm for random interval homeomorphisms
PublicationA proof of the law of the iterated logarithm for random homeomorphisms of the interval is given.
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Path components of the space of gradient vector fields on the two dimensional disc
PublicationWe present a short proof that if two gradient maps on the twodimensional disc have the same degree, then they are gradient homotopic.
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Sensing of anesthetic drugs in blood with Raman spectroscopy
PublicationA proof-of-concept study of a Raman spectroscopy-based approach for measuring the content of anesthesia drugs in blood is presented. Spectra of spiked blood from several patients exhibit prominent changes in regions associated with the drug.
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Distortion in the group of circle homeomorphisms
PublicationLet G be the group PAff+(R/Z) of piecewise affine circle homeomorphisms or the group Diff∞(R/Z) of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.
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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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Partial hyperbolicity and central shadowing
PublicationWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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Degree product formula in the case of a finite group action
PublicationLet V, W be finite dimensional orthogonal representations of a finite group G. The equivariant degree with values in the Burnside ring of G has been studied extensively by many authors. We present a short proof of the degree product formula for local equivariant maps on V and W.
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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Seiberg-Witten invariants the topological degree and wall crossing formula
PublicationFollowing S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b 1 = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.
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PA32 aluminum alloy - tensile properties
Open Research DataIn addition to steel, aluminium alloys are the main building material used in the shipbuilding industry. Due to its undoubted advantages, such as low density (nearly three times lower than in the case of steel for shipbuilding) and high corrosion resistance, it is often used for hulls of yachts and small vessels as well as superstructures. For safety...
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Strucutral steel - tensile test results
Open Research DataModern floating structures such as ships, oil platforms and offshore wind towers are built mostly of structural steel. It is a material that is subject to requirements which, when met, allows the construction and safe operation of the structure throughout its entire work cycle. One of the basic criteria that a material must meet is its strength. The...
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublicationWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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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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Inkjet Printing of Lanthanide–Organic Frameworks for Anti-Counterfeiting Applications
PublicationPhotoluminescent lanthanide−organic frameworks (Ln-MOFs) were printed onto plastic and paper foils with a conventional inkjet printer. Ln-MOF inks were used to reproduce color images that can only be observed under UV light irradiation. This approach opens a new window for exploring Ln-MOF materials in technological applications, such as optical devices (e.g., lab-on-a-chip), as proof of authenticity for official documents.
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A note on simple bifurcation of equilibrium forms of an elastic rod on a deformable foundation
PublicationWe study bifurcation of equilibrium states of an elastic rod on a two-parameter Winkler foundation. In the article "Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation" [Nonlinear Anal., Real World Appl. 39 (2018) 451-463] the existence of simple bifurcation points was proved by the use of the Crandall-Rabinowitz theorem. In this paper we want to present an alternative proof of this fact based...
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Experimental Extraction of Secure Correlations from a Noisy Private State
PublicationWe report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies...
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The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
PublicationWe show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.
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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublicationThe paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations. We investigate weighted difference methods for these problems. A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublicationInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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NO-BROADCASTING OF NON-SIGNALLING BOXES VIA OPERATIONS WHICH TRANSFORM LOCAL BOXES INTO LOCAL ONES
PublicationWe deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider a class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class cannot broadcast a bipartite non-local box with 2 binary inputs and outputs. We consider a function called anti-Robustness which can not decrease under these operations....
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CMOS realisation of analogue processor for early vision processing
PublicationThe architecture concept of a high-speed low-power analogue vision chip, which performs low-level real-time image algorithms ispresented. The proof-of-concept prototype vision chip containing 32 × 32 photosensor array and 32 analogue processors is fabricated usinga 0.35 μm CMOS technology. The prototype can be configured to register and process images with very high speed, reaching 2000 framesper second, or achieve very low power...
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Reconfiguring Minimum Dominating Sets in Trees
PublicationWe provide tight bounds on the diameter of γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. In particular, we prove that for any tree T of order n ≥ 3, the diameter of its γ-graph is at most n/2 in the single vertex replacement adjacency model, whereas in the slide adjacency model, it is at most 2(n − 1)/3. Our proof is constructive, leading to a simple linear-time algorithm for determining...
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Quantumness in Diagnostics of Marine Internal Combustion Engines and Other Ship Power Plant Machines
PublicationThe article provides proof that the diagnostics of marine internal combustion engines and other ship power plant machines should take into account the randomness and unpredictability of certain events, such as wear, damage, the variations of mechanical and thermal loads, etc., which take place during machine operation. In the article, the energy E, like the other forms (methods) that it can be converted into (heat and work), is...
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Alternative Modeling of Volunteer Based Systems
PublicationThe canonical approach to model a flow of a voluntary based computing, as presented in Chapter 7 may tax the capacity of the simulator, especially when a more complex model of Voluntary Computing, proposed in [1], is used which would imply that, for typical heterogeneous groups of volunteers, several thousands of threads would have to be run inside the simulator, to mimic closely the behaviour of every volunteer. This chapter presents...
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublicationBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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The Maslov index and the spectral flow—revisited
PublicationWe give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...
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Analiza i badania systemu antyspoofingowego GPS
PublicationArtykuł dotyczy problemu spoofingu w systemie GPS, polegającego na niepowołanej transmisji sygnałów imitujących sygnały odbierane z satelitów GPS. Takie działanie prowadzi do wyznaczenia przez odbiornik nawigacyjny nieprawidłowego położenia, prędkości i czasu. Zostały opisane metody przeciwdziałania spoofingowi, w szczególności poprzez przestrzenne przetwarzanie sygnałów. Przedstawiono wyniki badań symulacyjnych efektywności tych...
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Voice Multilateration System
PublicationThis paper presents an innovative method of locating airplanes, which uses only voice communication between an air traffic controller and the pilot of an aircraft. The proposed method is described in detail along with its practical implementation in the form of a technology demonstrator (proof of concept), included in the voice communication system (VCS). A complete analysis of the performance of the developed method is presented,...