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Search results for: SYMMETRIES
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Taking advantage of symmetries: gathering of asynchronous oblivious robots on a ring
PublicationW pracy rozważano problem rendezvous (spotkania, zebrania) dla zbioru bezpamięciowych robotów umieszczonych na wierzchołkach cyklu nieskierowanego, niewyposażonych w urządzenia komunikacyjne. Przyjęto model systemu rozproszonego występujący w literaturze pod nazwą asynchronicznego systemu z cyklami Look-Compute-Move. Problem istnienia rozwiązania rozwiązano dla wszystkich konfiguracji poczatkowych składających się z więcej niż...
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Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring
PublicationOne of the recently considered models of robot-based computing makes use of identical, memoryless mobile units placed in nodes of an anonymous graph. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of the nodes adjacent to its current position (Compute), and in the latter case makes an instantaneous...
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Multiple bifurcation in the solution set of the von Karman equations with S^{1}-symmetries
PublicationRozważmy cienką, sprężystą, kołową płytę, położoną na sprężystym podłożu, poddawaną działaniu sił ściskających koncentrycznie wzdłuż jej brzegu. Formy równowagi takiej płyty są rozwiązaniami równań von Karmana z dwoma parametrami określonych na dysku w R^{2}. Są to równania różniczkowe cząstkowe rzędu czwartego. Można je zapisać jako równanie operatorowe F(x,p)=0 w przestrzeniach Höldera, gdzie zmienna x odpowiada formom równowagi...
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Electronic structure of intertwined kagome, honeycomb, and triangular sublattices of the intermetallics MCo2Al9 ( M = Sr, Ba)
PublicationIntermetallics are an important playground to stabilize a large variety of physical phenomena, arising from their complex crystal structure. The ease of their chemical tunabilty makes them suitable platforms to realize targeted electronic properties starting from the symmetries hidden in their unit cell. Here, we investigate the family of the recently discovered intermetallics MCo2Al9 (M=Sr, Ba) and we unveil their electronic structure....
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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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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Jahn-Teller and related conical intersections in the benzene radical cation and the monofluoro derivate
PublicationThe multi-state multi-mode vibronic interactions in the benzene radical cation and its monofluoro derivative have been investigated theoretically, based on high-level electronic structure calculations for the system parameters and a quantum treatment of the nuclear motion. The available experimental data are well reproduced. The interplay of different vibronic coupling mechanisms is pointed out leading to multiple nonadiabatic...
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Characterizing the Performance of <span class="sc">xor</span> Games and the Shannon Capacity of Graphs
PublicationIn this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party xor game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games...
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublicationIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains
PublicationTwo mobile agents, modeled as points starting at differentlocations of an unknown terrain, have to meet. The terrain is a polygon with polygonal holes. We consider two versions of this rendezvous problem: exact RV, when the points representing the agents have to coincide at some time, and epsilon-RV, when these points have to get at distance less than epsilon in the terrain. In any terrain, each agent chooses its trajectory, but...
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Tuning the ferromagnetic phase in the CDW compound SmNiC2 via chemical alloying
PublicationWe report a study on tuning the charge density wave (CDW) ferromagnet SmNiC2 to a weakly coupled superconductor by substituting La for Sm. X-ray diffraction measurements show that the doped compounds obey Vegard’s law, where La (Lu) alloying expands (shrinks) the lattice due to its larger (smaller) atomic size than Sm. In the series Sm1−xLaxNiC2, CDW transition (TCDW =148K) for SmNiC2 is gradually suppressed, while the ferromagnetic...
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Lanthanide ions (Eu3+, Er3+, Pr3+) as luminescence and charge carrier centers in Sr2TiO4
PublicationA series of strontium orthotitanate (Sr2TiO4) samples doped with 2% of a mole of europium, praseodymium, and erbium were obtained using the solid-state synthesis method. The X-ray diffraction (XRD) technique confirms the phase purity of all samples and the lack of the influence of dopants at a given concentration on the structure of materials. The optical properties indicate, in the case of Sr2TiO4:Eu3+, two independent emission...
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Study of Integer Spin S = 1 in the Polar Magnet β-Ni(IO3)2
PublicationPolar 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...