Isotropy of unitary involutions

We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.Comment: final version, to appear in Acta Mat

On standard norm varieties

Let $p$ be a prime integer and $F$ a field of characteristic 0. Let $X$ be the {\em norm variety} of a symbol in the Galois cohomology group $H^{n+1}(F,\mu_p^{\otimes n})$ (for some $n\geq1$), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field $F(X)$ has the following property: for any equidimensional variety $Y$, the change of field homomorphism \CH(Y)\to\CH(Y_{F(X)}) of Chow groups with coefficients in integers localized at $p$ is surjective in codimensions $< (\dim X)/(p-1)$. One of the main ingredients of the proof is a computation of Chow groups of a (generalized) Rost motive (a variant of the main result not relying on this is given in Appendix). Another important ingredient is {\em $A$-triviality} of $X$, the property saying that the degree homomorphism on \CH_0(X_L) is injective for any field extension $L/F$ with $X(L)\ne\emptyset$. The proof involves the theory of rational correspondences reviewed in Appendix.Comment: 38 pages; final version, to appear in Ann. Sci. \'Ec. Norm. Sup\'er. (4

New Developments of EPOS 2

Since 2006, EPOS hadronic interaction model is being used for very high energy cosmic ray analysis. Designed for minimum bias particle physics and used for having a precise description of SPS and RHIC heavy ion collisions, EPOS brought more detailed description of hadronic interactions in air shower development. Thanks to this model it was possible to understand why there were less muons in air shower simulations than observed in real data. With the start of the LHC era, a better description of hard processes and collective effects is needed to deeply understand the incoming data. We will describe the basic physics in EPOS and the new developments and constraints which are taken into account in EPOS 2.Comment: Contributed presentation to the XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010), Batavia, IL, USA (28 June 2 July 2010). 4 pages, 6 figure

Four-Valued Logics BD and DM4: Expansions

The paper discusses functional properties of some four-valued logics which are the expansions of four-valued Belnap’s logic DM4. At first, we consider the logics with two designated values, and then logics defined by matrices having the same underlying algebra, but with a different choice of designated values, i.e. with one designated value. In the preceding literature both approaches were developed independently. Moreover, we present the lattices of the functional expansions of DM4.Zadanie „ Wdrożenie platformy Open Journal System dla czasopisma „ Bulletin of the Section of Logic” finansowane w ramach umowy 948/P-DUN/2016 ze środków Ministra Nauki i Szkolnictwa Wyższego przeznaczonych na działalność upowszechniającą naukę

Jaśkowski's criterion and three-valued paraconsistent logics

A survey is given of three-valued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested

Global hyperon polarization at local thermodynamic equilibrium with vorticity, magnetic field and feed-down

The system created in ultrarelativistic nuclear collisions is known to behave as an almost ideal liquid. In non-central collisions, due to the large orbital momentum, such a system might be the fluid with the highest vorticity ever created under laboratory conditions. Particles emerging from such a highly vorticous fluid are expected to be globally polarized with their spins on average pointing along the system angular momentum. Vorticity-induced polarization is the same for particles and antiparticles, but the intense magnetic field generated in these collisions may lead to the splitting in polarization. In this paper we outline the thermal approach to the calculation of the global polarization phenomenon for particles with spin and we discuss the details of the experimental study of this phenomenon, estimating the effect of feed-down. A general formula is derived for the polarization transfer in two-body decays and, particularly, for strong and electromagnetic decays. We find that accounting for such effects is crucial when extracting vorticity and magnetic field from the experimental data.Comment: 14 pages, 1 figure. Final version published in PRC with one more formula and slightly revised tex

Jets, Bulk Matter, and their Interaction in Heavy Ion Collisions at Several TeV

We discuss a theoretical scheme that accounts for bulk matter, jets, and the interaction between the two. The aim is a complete description of particle production at all transverse momentum ($p_{t}$) scales. In this picture, the hard initial scatterings result in mainly longitudinal flux tubes, with transversely moving pieces carrying the $p_{t}$ of the partons from hard scatterings. These flux tubes constitute eventually both bulk matter (which thermalizes and flows) and jets. We introduce a criterion based on parton energy loss to decide whether a given string segment contributes to the bulk or leaves the matter to end up as a jet of hadrons. Essentially low $p_{t}$ segments from inside the volume will constitute the bulk, high $p_{t}$ segments (or segments very close to the surface) contribute to the jets. The latter ones appear after the usual flux tube breaking via q-qbar production (Schwinger mechanism). Interesting is the transition region: Intermediate $p_{t}$ segments produced inside the matter close to the surface but having enough energy to escape, are supposed to pick up q-qbar pairs from the thermal matter rather than creating them via the Schwinger mechanism. This represents a communication between jets and the flowing bulk matter (fluid-jet interaction). Also very important is the interaction between jet hadrons and the soft hadrons from the fluid freeze-out. We employ the new picture to investigate Pb-Pb collisions at 2.76 TeV. We discuss the centrality and $p_{t}$ dependence of particle production and long range dihadron correlations at small and large $p_{t}$