On nn-norm preservers and the Aleksandrov conservative nn-distance problem

The goal of this paper is to point out that the results obtained in the recent papers [7,8,10,11] can be seriously strengthened in the sense that we can significantly relax the assumptions of the main results so that we still get the same conclusions. In order to do this first, we prove that for $n \geq 3$ any transformation which preserves the $n$-norm of any $n$ vectors is automatically plus-minus linear. This will give a re-proof of the well-known Mazur--Ulam-type result that every $n$-isometry is automatically affine ($n \geq 2$) which was proven in several papers, e.g. in [9]. Second, following the work of Rassias and \v{S}emrl [23], we provide the solution of a natural Aleksandrov-type problem in $n$-normed spaces, namely, we show that every surjective transformation which preserves the unit $n$-distance in both directions ($n\geq 2$) is automatically an $n$-isometry

The phase diagram in the vector meson extended linear sigma model

We investigate the chiral phase transition of the strongly interacting matter at nonzero temperature and baryon chemical potential $\mu_B$ within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates. We study the $T-\rho_B$ phase diagram of the model and find that a critical end point exists, although at very low density.Comment: 5 pages, 2 figures, Presented at CPOD 2016, Wrocla

Chiral phase transition in an extended linear sigma model: initial results

We investigate the scalar meson mass dependence on the chiral phase transition in the framework of an SU(3), (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops. We determine the parameters of the Lagrangian at zero temperature in a hybrid approach, where we treat the mesons at tree-level, while the constituent quarks at 1-loop level. We assume two nonzero scalar condensates and together with the Polyakov-loop variables we determine their temperature dependence according to the 1-loop level field equations.Comment: Presented at the Workshop on Unquenched Hadron Spectroscopy: Non-Perturbative Models and Methods of QCD vs. Experiment, At the occasion of Eef van Beveren's 70th birthda

Probing in-medium vector meson decays by double-differential di-electron spectra in heavy-ion collisions at SIS energies

Within a transport code simulation for heavy-ion collisions at bombarding energies around 1 AGeV, we demonstrate that double-differential di-electron spectra with suitable kinematical cuts are useful to isolate (i) the $\rho$ meson peak even in case of strong broadening, and (ii) the in-medium $\omega$ decay contribution. The expected in-medium modifications of the vector meson spectral densities can thus be probed in this energy range via the di-electron channel

Massive Splenic Pseudocysts : Report of 2 cases

Splenic cysts can be classified as parasitic and nonparasitic. Non parasitic cysts can be further divided into true and pseudocysts. Pseudocysts of spleen does not contain an epithelial lining. Pseudocysts of spleen are usually post traumatic and they rarely grow to a large size and most of them are asymptomatic. It can be confused with cystic lesions of spleen or pancreas or from the surrounding structures. These cases require exploration and is both diagnostic and therapeutic. Conservative measures to preserve spleen can be considered only in presence of expertise and if remnant functional splenic parenchyma is more than 25 %. Here we present two cases of giant pseudocysts who were confused with malignancy and referred to our centre and were later found to be pseudocysts of spleen. We would like to report these cases as they are rare and as diagnostic dilemmas

Trajectories of the S-matrix poles in Salamon-Vertse potential

The trajectories of S-matrix poles are calculated in the finite-range phenomenological potential introduced recently by P. Salamon and T. Vertse (SV). The trajectories of the resonance poles in this SV potential are compared to the corresponding trajectories in a cut-off Woods-Saxon (WS) potential for l>0. The dependence on the cut-off radius is demonstrated. The starting points of the trajectories turn out to be related to the average ranges of the two terms in the SV potential

An elementary proof for the non-bijective version of Wigner's theorem

The non-bijective version of Wigner’s theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two elements, is induced by a linear or antilinear isometry. We present a completely new, elementary and very short proof of this famous theorem which is very important in quantum mechanics. We do not assume bijectivity of the mapping or separability of the underlying space like in many other proofs