An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism

Conformally flat spacetimes with an elastic stress energy tensor having diagonal trace-free anisotropic pressure are investigated using 1+3 formalism. The 1+3 Bianchi and Jacobi identities and Einstein field equations are written for a particular case with a conformal factor dependent on only one spatial coordinate. Solutions with non null anisotropic pressure are obtained.

Two-particle Bose–Einstein correlations in pp collisions at s√= 0.9 and 7 TeV measured with the ATLAS detector

The paper presents studies of Bose--Einstein Correlations (BEC) for pairs of like-sign charged particles measured in the kinematic range pT> 100 MeV and |η|< 2.5 in proton--proton collisions at centre-of-mass energies of 0.9 and 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. The integrated luminosities are approximately 7 μb−1, 190 μb−1 and 12.4 nb−1 for 0.9 TeV, 7 TeV minimum-bias and 7 TeV high-multiplicity data samples, respectively. The multiplicity dependence of the BEC parameters characterizing the correlation strength and the correlation source size are investigated for charged-particle multiplicities of up to 240. A saturation effect in the multiplicity dependence of the correlation source size is observed using the high-multiplicity 7 TeV data sample. The dependence of the BEC parameters on the average transverse momentum of the particle pair is also investigated.