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1. Direct measurement of the muonic content of extensive air showers between $$\mathbf { 2\times 10^{17}}$$ and $$\mathbf {2\times 10^{18}}~$$eV at the Pierre Auger Observatory

   https://doi.org/10.1140/epjc/s10052-020-8055-y  

   Aab, A. ; Abreu, P. ; Aglietta, M. ; Albury, J. M. ; Allekotte, I. ; Almela, A. ; Alvarez Castillo, J. ; Alvarez-Muñiz, J. ; Anastasi, G. A. ; Anchordoqui, L. ; et al ( August 2020 , The European Physical Journal C)

   Abstract The hybrid design of the Pierre Auger Observatory allows for the measurement of the properties of extensive air showers initiated by ultra-high energy cosmic rays with unprecedented precision. By using an array of prototype underground muon detectors, we have performed the first direct measurement, by the Auger Collaboration, of the muon content of air showers between $$2\times 10^{17}$$ 2 × 10 17 and $$2\times 10^{18}$$ 2 × 10 18 eV. We have studied the energy evolution of the attenuation-corrected muon density, and compared it to predictions from air shower simulations. The observed densities are found to be larger than those predicted by models. We quantify this discrepancy by combining the measurements from the muon detector with those from the Auger fluorescence detector at $$10^{{17.5}}\, {\mathrm{eV}} $$ 10 17.5 eV and $$10^{{18}}\, {\mathrm{eV}} $$ 10 18 eV . We find that, for the models to explain the data, an increase in the muon density of $$38\%$$ 38 % $$\pm 4\% (12\%)$$ ± 4 % ( 12 % ) $$\pm {}^{21\%}_{18\%}$$ ± 18 % 21 % for EPOS-LHC , and of $$50\% (53\%)$$ 50 % ( 53 % ) $$\pm 4\% (13\%)$$ ± 4 % ( 13 % ) $$\pm {}^{23\%}_{20\%}$$more »± 20 % 23 % for QGSJetII-04 , is respectively needed.« less
2. Uniqueness of some Calabi–Yau metrics on $${\mathbf {C}}^{{n}}$$

   https://doi.org/10.1007/s00039-020-00543-3  

   Székelyhidi, Gábor ( August 2020 , Geometric and Functional Analysis)
3. $$\mathbf {2\times 2}$$-Convexifications for convex quadratic optimization with indicator variables

   https://doi.org/10.1007/s10107-023-01924-w  

   Han, Shaoning ; Gómez, Andrés ; Atamtürk, Alper ( January 2023 , Mathematical Programming)

   In this paper, we study the convex quadratic optimization problem with indicator variables. For the$${2\times 2}$$$2\times 2$case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the$${2\times 2}$$$2\times 2$case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including the optimal perspective relaxation and the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems.
4. Topological degeneracy (Majorana zero-mode) and 1  +  1D fermionic topological order in a magnetic chain on superconductor via spontaneous $\text{Z}_{\mathbf{2}}^{\text{f}}$ symmetry breaking

   https://doi.org/10.1088/0953-8984/27/40/405601  

   Klassen, Joel ; Wen, Xiao-Gang ( September 2015 , Journal of Physics: Condensed Matter)
5. Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation

   https://doi.org/10.1140/epjc/s10052-019-6566-1  

   Jackura, A. ; Fernández-Ramírez, C. ; Mathieu, V. ; Mikhasenko, M. ; Nys, J. ; Pilloni, A. ; Saldaña, K. ; Sherrill, N. ; Szczepaniak, A. P. ( January 2019 , The European Physical Journal C)