The accuracy of heavy-ion optical model calculations

Heavy ion elastic scattering calculations lead to numerical difficulties in the regions of energies and angles where the cross sections are small. Two different approximate methods have been investigated in the case of $^{20}$Ne + $^{24}$Mg scattering at $E_{LAB}$ = 100 MeV. The emerging errors of calculations are traced in detail. It is shown, that the optical model calculations are critically sensitive to some details which are arbitrarily assumed in commonly used approximate methods. The obtained results allow to perform similar calculations with controlled accuracy and some ambiguities of optical model potentials can be removed

Triangle-free geometric intersection graphs with large chromatic number

Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $X$ in $\mathbb{R}^2$ that is not an axis-aligned rectangle and for any positive integer $k$ produces a family $\mathcal{F}$ of sets, each obtained by an independent horizontal and vertical scaling and translation of $X$, such that no three sets in $\mathcal{F}$ pairwise intersect and $\chi(\mathcal{F})>k$. This provides a negative answer to a question of Gyarfas and Lehel for L-shapes. With extra conditions, we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries, and equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the line.Comment: Small corrections, bibliography updat

Triangle-free intersection graphs of line segments with large chromatic number

In the 1970s, Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer $k$, we construct a triangle-free family of line segments in the plane with chromatic number greater than $k$. Our construction disproves a conjecture of Scott that graphs excluding induced subdivisions of any fixed graph have chromatic number bounded by a function of their clique number.Comment: Small corrections, bibliography updat

THE RELATION BETWEEN EMOTIONAL INTELLIGENCE AND INTERNET ADDICTION IN KATOWICE HIGH SCHOOL STUDENTS

Backgroud: Emotional intelligence (EI) is described as the capacity to be aware of, control, and express one\u27s emotions, and to handle interpersonal relationships judiciously and empathetically. It is considered as one of the most important predictors of success, quality of relationships, and overall happiness. Dynamically changing environment of the youth and young adults in recent years may influence their EI development, affecting their lives significantly. The purpose of this study was to analyse the way how the Internet is used by high school students, to determine the amount of time they spend on the Internet, identify the level of EI and to explore if there is any correlation between those factors. Subjects and methods: 1450 high school students from Katowice, at the age from 18 to 21 years took part in an anonymous survey consisting of three parts: The Trait Emotional Intelligence Questionnaire – Short Form (TEIQue-SF), Internet Addiction Test and authorial test giving information about the way of spending time online. The questionnaires were collected from May 2018 to January 2019. Results: 1.03% of the respondents fulfilled the Internet addiction criteria. Students at risk for addiction (33.5%) turned out to be a larger group. A statistically significant correlation between TEIQue-SF and Internet Addiction Test score (P<0.0001, r=-0.3308) was observed. Another significant correlation was found between TEIQue-SF score and amount of time spend on the Internet (p<0.0001, r=-0.162). Conclusion: A significant part of high school students used Internet excessively. Such behaviours were positively correlated with lower EI test results

3D PET image reconstruction based on Maximum Likelihood Estimation Method (MLEM) algorithm

Positron emission tomographs (PET) do not measure an image directly. Instead, they measure at the boundary of the field-of-view (FOV) of PET tomograph a sinogram that consists of measurements of the sums of all the counts along the lines connecting two detectors. As there is a multitude of detectors build-in typical PET tomograph structure, there are many possible detector pairs that pertain to the measurement. The problem is how to turn this measurement into an image (this is called imaging). Decisive improvement in PET image quality was reached with the introduction of iterative reconstruction techniques. This stage was reached already twenty years ago (with the advent of new powerful computing processors). However, three dimensional (3D) imaging remains still a challenge. The purpose of the image reconstruction algorithm is to process this imperfect count data for a large number (many millions) of lines-of-responce (LOR) and millions of detected photons to produce an image showing the distribution of the labeled molecules in space.Comment: 10 pages, 7 figure

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $$X$$ X in $$\mathbb{R }^2$$ R 2 that is not an axis-aligned rectangle and for any positive integer $$k$$ k produces a family $$\mathcal{F }$$ F of sets, each obtained by an independent horizontal and vertical scaling and translation of $$X$$ X , such that no three sets in $$\mathcal{F }$$ F pairwise intersect and $$\chi (\mathcal{F })>k$$ χ ( F ) > k . This provides a negative answer to a question of Gyárfás and Lehel for L-shapes. With extra conditions we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries or equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the lin

Studies of discrete symmetries in decays of positronium atoms

A positronium - a bound state of electron and positron - is an eigenstate of parity and charge conjugation operators which decays into photons. It is a unique laboratory to study discrete symmetries whose precision is limited, in principle, by the effects due to the weak interactions expected at the level of 10−14 and photon-photon interactions expected at the level of 10−9. The Jagiellonian Positron Emission Tomograph (J-PET) is a detector for medical imaging as well as for physics studies involving detection of electronpositron annihilation into photons. The physics case covers the areas of discrete symmetries studies and genuine multipartite entanglement. The J-PET detector has high angular and time resolution and allows for determination of spin of the positronium and the momenta and polarization vectors of annihilation quanta. In this article, we present the potential of the J-PET system for studies of discrete symmetries in decays of positronium atoms

Analysis procedure of the positronium lifetime spectra for the J-PET detector

Positron Annihilation Lifetime Spectroscopy (PALS) has shown to be a powerful tool to study the nanostructures of porous materials. Positron Emissions Tomography (PET) are devices allowing imaging of metabolic processes e.g. in human bodies. A newly developed device, the J-PET (Jagiellonian PET), will allow PALS in addition to imaging, thus combining both analyses providing new methods for physics and medicine. In this contribution we present a computer program that is compatible with the J-PET software. We compare its performance with the standard program LT 9.0 by using PALS data from hexane measurements at different temperatures. Our program is based on an iterative procedure, and our fits prove that it performs as good as LT 9.0.Comment: 4 figures, 8 page