One dimensional estimates for the Bergman kernel and logarithmic capacity

Carleson showed that the Bergman space for a domain on the plane is trivial if and only if its complement is polar. Here we give a quantitative version of this result. One is the Suita conjecture, established by the first-named author in 2012, the other is an upper bound for the Bergman kernel in terms of logarithmic capacity. We give some other estimates for those quantities as well. We also show that the volume of sublevel sets for the Green function is not convex for all regular non simply connected domains, generalizing a recent example of Forn\ae ss.Comment: 8 page

On the Ohsawa-Takegoshi extension theorem

Motivated by a recent work by B.-Y. Chen we prove a new estimate for the $\bar\partial$, which easily implies the Ohsawa–Takegoshi extension theorem. We essentially only use the classical H¨ormander estimate. This method gives the same constant as the one recently obtained by Guan–Zhou–Zhu

Estimates for the Bergman kernel and the multidimensional Suita conjecture

We study the lower bound for the Bergman kernel in terms of volume of sublevel sets of the pluricomplex Green function. We show that it implies a bound in terms of volume of the Azukawa indicatrix which can be treated as a multidimensional version of the Suita conjecture. We also prove that the corresponding upper bound holds for convex domains and discuss it in bigger detail on some convex complex ellipsoids.Comment: 11 pages, 2 figure

On the Ohsawa–Takegoshi extension theorem

Motivated by a recent work by B.-Y. Chen we prove a new estimate for the @-operator, which easily implies the Ohsawa{Takegoshi extension theorem. We essentially only use the classical Hormander estimate. This method gives the same constant as the one recently obtained by Guan{Zhou{Zhu

Kilka uwag o reformie szkolnictwa wyższego

Based on selected indicators, such as university rankings, ERC grants and publications in most important scientific journals, the performance of Polish science in international competition is analyzed. New regulations needed to improve the situation are then discussed. The most important change concerns the management of our universities, especially the way their leadership is selected.Na podstawie wybranych danych, takich jak rankingi uczelni, granty ERC oraz publikacje w najważniejszych czasopismach naukowych, analizowane jest miejsce polskiej nauki w światowej konkurencji. Następnie omówione są konieczne regulacje, które powinny zostać wprowadzone, by to miejsce poprawić. Najważniejszą z nich jest zmiana sposobu zarządzania naszymi uniwersytetami, a przede wszystkim inny sposób wyboru ich władz

Alpha Cluster Model of Atomic Nuclei

Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. These terms, together with the standard symmetry term, are responsible for appearance of the $\alpha$-like clusters in the ground state configurations of the N=Z even-even nuclei. At the nuclear surface these clusters can be identified as alpha particles. A correction for the surface effects is introduced for atomic nuclei. Taking into account an additional interaction between clusters the binding energies and sizes of the considered nuclei are very accurately described. The limits of the EoS parameters are established from the properties of the $\alpha$, $^{3}$He and $t$ particles.Comment: 27 pages, 10 figure

Dissipative orbiting in ^{136}Xe+^{209}Bi reactions at 28 and 62 AMeV

Correlations between the energy, charge and the deflection angle of the projectile-like fragments were studied for the ^{136}Xe + ^{209}Bi reaction at E∕A = 28 and 62 MeV. These correlations are seen to exhibit features characteristic of dissipative orbiting, commonly found at bombarding energies of a few MeV/nucleon above the interaction barrier, but also reported in the Fermi-energy domain. It was found, that in the studied bombarding energy range, the reaction cross section is still dominated by the dissipative binary reactions of well defined projectile- and target-like fragments