A priori estimates for the complex Hessian equations

We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $C^n$ and on compact K\"ahler manifolds. We also show optimal $L^p$ integrability for m-subharmonic functions with compact singularities, thus partially confirming a conjecture of Blocki. Finally we obtain a local regularity result for $W^{2,p}$ solutions of the real and complex Hessian equations under suitable regularity assumptions on the right hand side. In the real case the method of this proof improves a result of Urbas.Comment: 18 pages, preliminary versio

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

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

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

Evaporation of light particles from a hot, deformed and rotating nucleus

The dependence of the transmission coefficient on the deformation, the collective rotation and excitation energy of the compound nucleus emitting light particles is introduced in the framework of Wei{\ss}kopf's evaporation theory. The competition between fission and particle evaporation is treated by a~Langevin equation for the fission variable coupled to the emission process. Detailed calculations are presented on the decay of different Gd and Yb isotopes at an excitation energy of about 250~MeV. These calculations demonstrate the importance of the effects of nuclear deformation and of the initial spin distribution on the evaporation.Comment: 22 pages in LaTeX and 26 PS-figures include

Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling

Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections) for processes described by Langevin dynamics. As we demonstrate with numerical examples as well as an exactly solvable model, our method can converge to the desired answer at a rate which is orders of magnitude faster than that achieved with direct simulations of the process in question.Comment: 18 pages + 7 figures, to appear in Nucl.Phys.

Some taxonomic features of small oat (Avena strigosa Schreb.)

Wydano przy pomocy finansowej Uniwersytetu Łódzkiego oraz Komitetu Badań NaukowychPresented are the significant morphological features of small oat (Avena strigosa Schreb.) that should enable proper distinguishing this species from other oats. The morphological observations were based on herbarial material collected in north-eastern Poland.Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę