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Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

100%
Baleanu D., Blaszczyk T., Asad J., Alipour M.
Acta Physica Polonica A
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2016
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vol. 130
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issue 3
688-691
EN
We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations.
2
Content available remote

Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

88%
Lulek B., Lulek T., Łabuz M., Milewski J.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
336-338
EN
Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a finite extension of the prime field Q of rationals. We propose here a geometric interpretation of this symmetry in the interior of the Brillouin zone, in terms of point groups. Explicitly, it is a subgroup of the direct product C₄ × D₄. We present also the appropriate irreducible representations of the group.
3
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Some New Approaches of the XXX Heisenberg Model of the Two-Magnon Sector

88%
Łabuz M., Milewski J., Lulek T.
Acta Physica Polonica A
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2018
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vol. 133
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issue 3
444-446
EN
XXX Heisenberg s-1/2 model has been examined in detail during last decades, however, recently one may find some new insights into that issue. Among several approaches describing the eigenproblem for the finite case, a close look into the structure of Bethe equations (BE) for the two-magnon sector case seems to be particularly interesting. BE enable us to evaluate parameters labeling eigenstates of a magnet, however to find appropriate sets of winding numbers, which parametrize BE, one has to apply the Inverse Bethe Ansatz method. On the other hand, one may choose a different - combinatoric approach - which also parametrizes Bethe eigenstates, with the use of rigging numbers describing string configurations. We present an idea of comparison of the concepts mentioned above for the particular case of two-spin deviations sector.
4
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Magnetic Pentagonal Ring - Galois Extensions and Crystallography

88%
Labuz M., Lulek T.
Acta Physica Polonica A
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2017
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vol. 132
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issue 1
97-99
EN
The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions. Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice ℤ₂×ℤ₂, responsible for extension of the cyclotomic field by the Bethe parameters.
5
Content available remote

Prediction of the Probabilities of the Transmission of Genetic Traits within Bayesian Logical Inference

75%
Cevri M., Üstündağ D.
Acta Physica Polonica A
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2016
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vol. 130
|
issue 1
45-50
EN
Predictions for the transmission of genetic traits along to generations are an important process for patients, their family and genetic counseling. For this purpose, Bayesian analysis in which one can include a priori knowledge taking into account all relevant information into the problem could be a useful tool to examine how disease forecasting affects its probability so that it provides a more straightforward interpretation of predictions. Therefore, we investigate here transmissions of autosomal recessive diseases along to generations within Bayesian framework. In order to do that we develop a computer code that is useful to facilitate genetic transition matrices to forecast predictions of probabilities of transmission of genetic traits by using Mathematica software, well known as an algebraic manipulation language. Furthermore, the symbolic implementation of the code is applied for the cystic fibrosis disease forecasting in humans genetics. All results show that Bayesian analysis plays a central role of prediction for probabilities of transmissions of genetic traits along generations for cystic fibrosis disease or other autosomal recessive disorders.
6
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Covering group and graph of discretized volumes

63%
Makai M., Orechwa Y.
Open Physics
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2004
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vol. 2
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issue 4
660-686
EN
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γv associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.
7
Content available remote

The cubic period-distance relation for the Kate reversible pendulum

63%
Rossi M., Zaninetti L.
Open Physics
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2005
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vol. 3
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issue 4
636-659
EN
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass configurations for which the periods of small oscillations about the two pivots of the pendulum have the same value. We also discuss a real compound Kater pendulum that realizes this property.
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