Adam Bednorz,1,* Witold Bednorz,2,† and Wolfgang Belzig3 1Faculty of Physics, University of Warsaw, Hoża 69, PL-00681 Warsaw, Poland 2Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland 3Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany (Received 20 August 2013; revised manuscript received 27 January 2014; published 27 Feb...

We prove that a curious generating series identity implies Faber's intersection number conjecture (by showing it combinatorial already given in (Garcia-Failde, Kramer, Lewański, and Shadrin, SIGMA 15 (2019), 080)) give new proof of by directly proving this identity.

We explore the halo structure of four gravitational lenses with well-observed, thin Einstein rings. We find that the gravitational potentials are well described by ellipsoidal density distributions in the sense that the best-fit nonellipsoidal models have parameters consistent with their ellipsoidal counterparts. We find upper limits on the standard parameters for the deviation from an ellipse ...

We develop a theory of Einstein rings and demonstrate it using the infrared Einstein ring images of the quasar host galaxies observed in PG 1115+080, B 1608+656 and B 1938+666. The shape of an Einstein ring accurately and independently determines the shape of the lens potential and the shape of the lensed host galaxy. We find that the host galaxies of PG 1115+080, B 1608+656 and B 1938+666 have...

1 Department of Mathematics, Warsaw University, Warsaw 02-097, Poland. This work was supported in part by The Polish Sciences Foundation under grant NN201006933. 2 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA 3 Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro 22460-320, Brazil 4 Department of Mathematical Sciences, Worcester Polytechnic In...

We consider the influence of (milli/micro)lensing on the spectra of lensed QSOs. We propose a method for the observational detection of microlensing in the spectra of lensed QSOs and apply it to the spectra of the three lensed QSOs (PG 1115+080, QSO 1413+117 and QSO 0957+561) observed with Hubble Space Telescope (HST). We find that the flux ratio between images A1 and A2 of PG 1115+080 is wavel...

We describe a rare case of multiple coronary artery-left ventricular fistulas associated with apical hypertrophic cardiomyopathy in a 62 year asymptomatic old male admitted to our department for a perioperative evaluation of non cardiac surgery, already diagnosed for multiple coronary artery-left fistulae. He underwent transthoracic echocardiography and then to accelerated dipiridamole stress-e...