arXiv subjects
Publications and source records attributed to Marcin Zieliński.
In this paper we show there does not exist any arrangement of degree $7$ consisting of $k\geq 1$ conics and $d\geq 1$ lines admitting certain naturally chosen ${\rm ADE}$-singularities.
We present a phenomenology-driven overview of opportunities and outstanding challenges in baryon electroweak transitions, focusing on hyperon and charmed-baryon processes for which lattice-QCD results are available, including semileptonic decays and selected radiative, dileptonic, and neutrino-induced channels. We identify semileptonic decays of strange and charmed baryons as a particularly promising domain for synergy between phenomenology, experiment, and lattice QCD. Particular emphasis is placed on the determination of vector and axial form factors, the precision and model-independent extraction of $|V_{us}|$ from hyperon semileptonic decays including radiative corrections, and on searches for non-standard interactions through lepton-flavor- and CP-violating observables. We examine the momentum dependence of form factors in ground-state transitions, highlight the emerging $Ξ_c \to Ξ$ semileptonic puzzle stemming from tensions between lattice-QCD predictions and experimental measurements, discuss inclusive decay rates, and outline strategies for extending these studies to transitions involving excited baryon states. For completeness, we review also results involving beauty-baryon decays.
Laface and Ugaglia recently constructed an irrational one-point Seshadri constant on the blow-up of $\mathbb{P}^2$ at nine very general points by combining a dihedral orbit on $\mathbb{P}^1\times\mathbb{P}^1$, a sequence of de Jonquières transformations, and a reflection argument along a $(-4)$-curve with balanced normal bundle. We show that the same mechanism extends uniformly to every odd integer $n\geq 5$. For $n=2k+1$ we prove $$ \varepsilon\bigl(\mathcal{O}_{\mathbb{P}^1\times\mathbb{P}^1}(n-4,1);p_1,\ldots,p_{2n}\bigr)=\sqrt{\frac{n-4}{n}} $$ at $2n$ very general points, and already at a very general free orbit of a fixed dihedral group of order $2n$. For every odd $n\geq 7$ this produces an explicit ample line bundle on the blow-up of $\mathbb{P}^2$ at $k+7=(n+13)/2$ very general points whose one-point Seshadri constant at a very general point equals $$ 2\sqrt{n(n-4)}. $$ More precisely, after one quadratic transformation we obtain the ample divisor $$ L_n=(3n-4)H-nE_1-(n-2)(E_2+\cdots+E_5)-4(E_6+\cdots+E_{k+5})-2(E_{k+6}+E_{k+7}), $$ with $L_n^2=4n(n-4)$ and $\varepsilon(L_n;x)=\sqrt{L_n^2}$. We also isolate an abstract balanced-reflection principle underlying the construction: a nef class on a special fiber can be reflected across a rational curve of square $-2a$ whenever the curve has normal bundle $\mathcal{O}_{\mathbb{P}^1}(-a)^{\oplus 2}$ in the total space, and the reflected class is nef on very general fibers.
We give a complete classification of free arrangement of three smooth conics on complex projective plane admitting only ${\rm ADE}$ singularities and $J_{2,0}$ singularities.
In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangements of bitangents associated with highly symmetric quartic curves. We consider quartic curves from the point of view of the order of their automorphism groups, in order to establish a lower bound on the number of quadruple intersection points for arrangements of bitangents associated with smooth plane quartics, which are smooth members of Ciani's pencil. We then construct new examples of $3$-syzygy reduced plane curves using smooth plane quartics and their bitangents.
In this note, we examine the arrangements of lines and configurations of points that emerge from Fermat (von Dyck) and Komiya-Kuribayashi quartics. These quartics are characterized by having the maximum number of lines of maximal tangency, that is, lines for which the intersection multiplicity at the tangency point is equal to the degree of the curve. Additionally, we delve into the study of sextactic points on these quartics - points at which there exists a conic with the curve having a local intersection multiplicity of at least 6, which is one more than that observed at a general point - alongside the related configurations of conics.
We report on the status of the search for eta-mesic nuclei and the studies of the interaction of the eta meson with nucleons. Recently we have completed the analysis of the new WASA-at-COSY data on the production of the eta meson with polarized proton beam. New results on the analyzing power for the pp->ppeta reaction with more than an order of magnitude improved precision shed a new light on the production mechanism of the eta meson in nucleon-nucleon collisions. Also, the latest results of the search for eta-mesic nuclei are discussed.
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.
This paper describes three methods regarding the production of plastic scintillators. One method appears to be suitable for the manufacturing of plastic scintillator, revealing properties which fulfill the requirements of novel positron emission tomography scanners based on plastic scintillators. The key parameters of the manufacturing process are determined and discussed.