Decompositions of edge-colored infinite complete graphs into monochromatic paths

An $r$-edge coloring of a graph or hypergraph $G=(V,E)$ is a map $c:E\to \{0, \dots, r-1\}$. Extending results of Rado and answering questions of Rado, Gy\'arf\'as and S\'ark\"ozy we prove that (1.) the vertex set of every $r$-edge colored countably infinite complete $k$-uniform hypergraph can be partitioned into $r$ monochromatic tight paths with distinct colors (a tight path in a $k$-uniform hypergraph is a sequence of distinct vertices such that every set of $k$ consecutive vertices forms an edge), (2.) for all natural numbers $r$ and $k$ there is a natural number $M$ such that the vertex set of every $r$-edge colored countably infinite complete graph can be partitioned into $M$ monochromatic $k^{th}$ powers of paths apart from a finite set (a $k^{th}$ power of a path is a sequence $v_0, v_1, \dots$ of distinct vertices such that $1\le|i-j| \le k$ implies that $v_iv_j$ is an edge), (3.) the vertex set of every $2$-edge colored countably infinite complete graph can be partitioned into $4$ monochromatic squares of paths, but not necessarily into $3$, (4.) the vertex set of every $2$-edge colored complete graph on $\omega_1$ can be partitioned into $2$ monochromatic paths with distinct colors

The structure of sets with few sums along a graph

AbstractWe present common generalizations of some structure results of Freiman, Ruzsa, Balog–Szemerédi and Laczkovich–Ruzsa. We also give some applications to Combinatorial Geometry and Algebra, some of which generalize the aforementioned structure results even further

Topological Hausdorff dimension and level sets of generic continuous functions on fractals

In an earlier paper we introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. For a compact metric space K let dim H K and dim tH K denote its Hausdorff and topological Hausdorff dimension, respectively. We proved that this new dimension describes the Hausdorff dimension of the level sets of the generic continuous function on K, namely sup{ dimHf- 1(y):y∈R}= dimtHK-1 for the generic f ∈ C(K), provided that K is not totally disconnected, otherwise every non-empty level set is a singleton. We also proved that if K is not totally disconnected and sufficiently homogeneous then dim H f -1(y) = dim tH K - 1 for the generic f ∈ C(K) and the generic y ∈ f(K). The most important goal of this paper is to make these theorems more precise. As for the first result, we prove that the supremum is actually attained on the left hand side of the first equation above, and also show that there may only be a unique level set of maximal Hausdorff dimension. As for the second result, we characterize those compact metric spaces for which for the generic f ∈ C(K) and the generic y ∈ f(K) we have dim H f -1(y) = dim tH K - 1. We also generalize a result of B. Kirchheim by showing that if K is self-similar then for the generic f ∈ C(K) for every y∈intf(K) we have dim H f -1(y) = dim tH K - 1. Finally, we prove that the graph of the generic f ∈ C(K) has the same Hausdorff and topological Hausdorff dimension as K. © 2012 Elsevier Ltd. All rights reserved

Problematic Internet Use and Problematic Online Gaming Are Not the Same: Findings from a Large Nationally Representative Adolescent Sample

There is an ongoing debate in the literature whether problematic internet use (PIU) and problematic online gaming (POG) are two distinct conceptual and nosological entities or whether they are the same. The present study contributes to this question by examining the interrelationship and the overlap between PIU and POG in terms of gender, school achievement, time spent using the internet and/or online gaming, psychological wellbeing, and preferred online activities. Questionnaires assessing these variables were administered to a nationally representative sample of adolescent gamers (N=2,073; mean age 16.4 years, SD=0.87, 68.4% male). Data showed that internet use was a common activity among adolescents while online gaming was engaged in by a considerably smaller group. Similarly, more adolescents met the criteria for PIU than for POG and a small group of adolescents showed symptoms of both problem behaviors. The most notable difference between the two problem behaviors was in terms of gender. POG was much more strongly associated with being male. Self-esteem had low effect sizes on both behaviors, while depressive symptoms were associated with both PIU and POG, affecting PIU slightly more. In terms of preferred online activities, PIU was positively associated with online gaming, online chatting, and social networking while POG was only associated with online gaming. Based on our findings POG appears to be a conceptually different behavior than PIU and therefore data support the notion that Internet Addiction Disorder and Internet Gaming Disorder are separate nosological entities

A Haar meager set that is not strongly Haar meager

Following Darji, we say that a Borel subset B of an abelian Polish group G is Haar meager if there is a compact metric space K and a continuous function f: K → G such that the preimage of the translate f−1(B + g) is meager in K for every g ∈ G. The set B is called strongly Haar meager if there is a compact set C ⊆ G such that (B + g) ⋂ C is meager in C for every g ∈ G. The main open problem in this area is Darji’s question asking whether these two notions are the same. Even though there have been several partial results suggesting a positive answer, in this paper we construct a counterexample. More specifically, we construct a Gδ set in ℤω that is Haar meager but not strongly Haar meager. We also show that no Fσ counterexample exists, hence our result is optimal. © 2019, The Hebrew University of Jerusalem

High precision 89^{89}Y(α\alpha,α\alpha)89^{89}Y scattering at low energies

Elastic scattering cross sections of the $^{89}$Y($\alpha$,$\alpha$)$^{89}$Y reaction have been measured at energies E$_{c.m.}$ = 15.51 and 18.63 MeV. The high precision data for the semi-magic $N = 50$ nucleus $^{89}$Y are used to derive a local potential and to evaluate the predictions of global and regional $\alpha$-nucleus potentials. The variation of the elastic alpha scattering cross sections along the $N = 50$ isotonic chain is investigated by a study of the ratios of angular distributions for $^{89}$Y($\alpha$,$\alpha$)$^{89}$Y and $^{92}$Mo($\alpha$,$\alpha$)$^{92}$Mo at E$_{c.m.} \approx$ 15.51 and 18.63 MeV. This ratio is a very sensitive probe at energies close to the Coulomb barrier, where scattering data alone is usually not enough to characterize the different potentials. Furthermore, $\alpha$-cluster states in $^{93}$Nb = $^{89}$Y $\otimes$ $\alpha$ are investigated

70Ge(p,gamma)71As and 76Ge(p,n)76As cross sections for the astrophysical p process: sensitivity of the optical proton potential at low energies

The cross sections of the 70Ge(p,gamma)71As and 76Ge(p,n)76As reactions have been measured with the activation method in the Gamow window for the astrophysical p process. The experiments were carried out at the Van de Graaff and cyclotron accelerators of ATOMKI. The cross sections have been derived by measuring the decay gamma-radiation of the reaction products. The results are compared to the predictions of Hauser-Feshbach statistical model calculations using the code NON-SMOKER. Good agreement between theoretical and experimental S factors is found. Based on the new data, modifications of the optical potential used for low-energy protons are discussed.Comment: Accepted for publication in Phys. Rev.

Precise half-life measurement of 110Sn and 109In isotopes

The half-lives of 110Sn and 109In isotopes have been measured with high precision. The results are T1/2 =4.173 +- 0.023 h for 110Sn and T1/2 = 4.167 +-0.018 h for 109In. The precision of the half-lives has been increased by a factor of 5 with respect to the literature values which makes results of the recently measured 106Cd(alpha,gamma)110Sn and 106Cd(alpha,p)109In cross sections more reliable.Comment: 3 pages, 2 figures, accepted for publication in Phys. Rev C as brief repor

Psychoactive substance use and problematic Internet use as predictors of bullying and cyberbullying victimization

Research exploring the relationship between addictions and experiences of bullying suggests that problem behaviors may generally be associated with an increased risk of victimization. The aim of the present study was to examine the role of psychoactive substance use, excessive Internet use, and social support in both traditional offline bullying and online Bcyberbullying^ victimization in a nationally representative sample of adolescents (N = 6237; 51% male; Mage = 16.62 years, SD = 0.95). Results demonstrated that traditional bullying victimization was associated with cyberbullying victimization. Furthermore, psychoactive substance use and problematic Internet use predicted both traditional bullying and cyberbullying victimization. Finally, perceived social support was found to be an important protective factor against both traditional and cyberbullying victimization. However, psychoactive substance use and problematic Internet use accounted for only a small proportion of variance in victimization

Precise half-life measurement of the 10 h isomer in 154Tb

The precise knowledge of the half-life of the reaction product is of crucial importance for a nuclear reaction cross section measurement carried out with the activation technique. The cross section of the 151Eu(alpha,n)154Tb reaction has been measured recently using the activation method, however, the half-life of the 10 h isomer in 154Tb has a relatively high uncertainty and ambiguous values can be found in the literature. Therefore, the precise half-life of the isomeric state has been measured and found to be 9.994 h +- 0.039 h. With careful analysis of the systematic errors, the uncertainty of this half-life value has been significantly reduced.Comment: Accepted for publication in Nuclear Physics