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7. Sebastian J. Szybka Równania Einsteina i efekt niejednorodności w kosmologii W ,,Ogólna teoria względności a filozofia  sto lat interakcji'', red. P. Polak, J. Mączka, CCPress, pp. 127142 [journal]  Abstract:
 8. Bratek Ł., Sikora S., Jałocha J., Kutschera M. Velocitydensity twin transforms in the thin disk model Mon. Not. R. Astron. Soc. , vol. 451, p. 4018 (2015). [abstract] [preprint] [journal]  Abstract: Ring mass density and the corresponding circular velocity in thin disc model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to onefold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula.  9. Jałocha J., Bratek Ł., Sikora S., Kutschera M. Modelling vertical structure in circular velocity of spiral galaxy NGC 4244 Mon. Not. R. Astron. Soc. , vol. 451, p. 3366 (2015). [abstract] [preprint] [journal]  Abstract: We study the vertical gradient in azimuthal velocity of spiral galaxy NGC 4244 in a thin disc model. With surface density accounting for the rotation curve, we model the gradient properties in the approximation of quasicircular orbits. It is worthy to note that the prediction of our model is consistent with the gradient properties inferred recently from a numerical model implementing the positionvelocity diagram of this galaxy. The confirmation of our prediction by the future measurement of the gradient would provide support for the expectation that the mass distribution in this galaxy is flattened.  10. Sikora S., Bratek Ł., Jałocha J., Kutschera M. Motion of halo tracer objects in the gravitational potential of a lowmass model of the Galaxy Astron. Astrophys. , vol. 579, p. A134 (2015). [abstract] [preprint] [journal]  Abstract: Recently, we determined a lower bound for the Milky Way mass in a point mass approximation. We obtain this result for most general spherically symmetric phasespace distribution functions consistent with a measured radial velocity dispersion. As a stability test of these predictions against a perturbation of the point mass potential, in this paper we make use of a representative of these functions to set the initial conditions for a simulation in a more realistic potential of similar mass and to account for other observations. The predicted radial velocity dispersion profile evolves to forms still consistent with the measured profile, proving structural stability of the point mass approximation and the reliability of the resulting mass estimate of ~2.1 × 10^11 M⊙ within 150 kpc. As a byproduct, we derive a formula in the spherical symmetry relating the radial velocity dispersion profile to a directly measured kinematical observable.  11. Edited by James Ladyman, Stuart Presnell, Gordon McCabe, Michał Eckstein, Sebastian J. Szybka Road to Reality with Roger Penrose CCPress [abstract] [preprint] [journal]  Abstract: Where does the road to reality lie? This fundamental question is addressed in this collection of essays by physicists and philosophers, inspired by the original ideas of Sir Roger Penrose. The topics range from black holes and quantum information to the very nature of mathematical cognition itself.  12. A. Woszczyna, W. Czaja, K. Głód, Z. A. Golda, R. A. Kycia, A. Odrzywołek, P. Plaszczyk, L. M. Sokołowski, S. J. Szybka ccgrg: The symbolic tensor analysis package with tools for general relativity Wolfram Library Archive, vol. 8848 (2014). [abstract] [journal]  Abstract: Riemann and Weyl curvature, covariant derivative, Lie derivative, the first and the second fundamental form on hypersurfaces, as well as basic notions of relativistic hydrodynamics (expansion, vorticity, shear) are predefined functions of the package. New tensors are easy to define. Instructions, basic examples, and some more advanced examples are attached to the package. Characteristic feature of the ccgrg package is the specific coupling between the functional programming and the ParkerChristensen index convention. This causes that no particular tools to rising/lowering tensor indices neither to the tensor contractions are needed. Tensor formulas are written in the form close to that of classical textbooks in GRG, with the only difference that the summation symbol appears explicitly. Tensors are functions, not matrixes, and their components are evaluated lazily. This means that only these components which are indispensable to realize the final task are computed. The memoization technique prevents repetitive evaluation of the same quantities. This saves both, time and memory.  
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