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

Report on the survey for Bursaphelenchus xylophilus and the occurrence of other Bursaphelenchus species in Hungarian coniferous forests.

An ongoing official survey to detect the pine wood nematode Bursaphelenchus xylophilus, a quarantine pest, started in 2003 in coniferous forests in Hungary. Based on the results of the study from 2003–11, B. xylophilus has not yet been detected in Hungary. Two other Bursaphelenchus species (B. mucronatus and B. vallesianus) were identified in samples in 2009. Details of the survey and the measurements of B. mucronatus and B. vallesianus are provided

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

On lines, joints, and incidences in three dimensions

AbstractWe extend (and somewhat simplify) the algebraic proof technique of Guth and Katz (2010) [9], to obtain several sharp bounds on the number of incidences between lines and points in three dimensions. Specifically, we show: (i) The maximum possible number of incidences between n lines in R3 and m of their joints (points incident to at least three non-coplanar lines) is Θ(m1/3n) for m⩾n, and Θ(m2/3n2/3+m+n) for m⩽n. (ii) In particular, the number of such incidences cannot exceed O(n3/2). (iii) The bound in (i) also holds for incidences between n lines and m arbitrary points (not necessarily joints), provided that no plane contains more than O(n) points and each point is incident to at least three lines. As a preliminary step, we give a simpler proof of (an extension of) the bound O(n3/2), established by Guth and Katz, on the number of joints in a set of n lines in R3. We also present some further extensions of these bounds, and give a trivial proof of Bourgain's conjecture on incidences between points and lines in 3-space, which is an immediate consequence of our incidence bounds, and which constitutes a much simpler alternative to the proof of Guth and Katz (2010) [9]

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

Primordial nucleosynthesis

Big Bang nucleosynthesis (BBN) describes the production of light nuclei in the early phases of the Universe. For this, precise knowledge of the cosmological parameters, such as the baryon density, as well as the cross section of the fusion reactions involved are needed. In general, the energies of interest for BBN are so low (E < 1MeV) that nuclear cross section measurements are practically unfeasible at the Earth’s surface. As of today, LUNA (Laboratory for Underground Nuclear Astrophysics) has been the only facility in the world available to perform direct measurements of small cross section in a very low background radiation. Owing to the background suppression provided by about 1400 meters of rock at the Laboratori Nazionali del Gran Sasso (LNGS), Italy, and to the high current offered by the LUNA accelerator, it has been possible to investigate cross sections at energies of interest for Big Bang nucleosynthesis using protons, 3He and alpha particles as projectiles. The main reaction studied in the past at LUNA is the 2H(4He, (Formula presented.))6Li. Its cross section was measured directly, for the first time, in the BBN energy range. Other processes like 2H(p, (Formula presented.))3He , 3He(2H, p)4He and 3He(4He, (Formula presented.))7Be were also studied at LUNA, thus enabling to reduce the uncertainty on the overall reaction rate and consequently on the determination of primordial abundances. The improvements on BBN due to the LUNA experimental data will be discussed and a perspective of future measurements will be outlined. © 2016, SIF, Springer-Verlag Berlin Heidelberg

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.

Small union with large set of centers

Let $T\subset{\mathbb R}^n$ be a fixed set. By a scaled copy of $T$ around $x\in{\mathbb R}^n$ we mean a set of the form $x+rT$ for some $r>0$. In this survey paper we study results about the following type of problems: How small can a set be if it contains a scaled copy of $T$ around every point of a set of given size? We will consider the cases when $T$ is circle or sphere centered at the origin, Cantor set in ${\mathbb R}$, the boundary of a square centered at the origin, or more generally the $k$-skeleton ($0\le k<n$) of an $n$-dimensional cube centered at the origin or the $k$-skeleton of a more general polytope of ${\mathbb R}^n$. We also study the case when we allow not only scaled copies but also scaled and rotated copies and also the case when we allow only rotated copies

Response of Multi-strip Multi-gap Resistive Plate Chamber

A prototype of Multi-strip Multi-gap Resistive Plate chamber (MMRPC) with active area 40 cm $\times$ 20 cm has been developed at SINP, Kolkata. Detailed response of the developed detector was studied with the pulsed electron beam from ELBE at Helmholtz-Zentrum Dresden-Rossendorf. In this report the response of SINP developed MMRPC with different controlling parameters is described in details. The obtained time resolution ($\sigma_t$) of the detector after slew correction was 91.5$\pm$3 ps. Position resolution measured along ($\sigma_x$) and across ($\sigma_y$) the strip was 2.8$\pm$0.6 cm and 0.58 cm, respectively. The measured absolute efficiency of the detector for minimum ionizing particle like electron was 95.8$\pm$1.3 $\%$. Better timing resolution of the detector can be achieved by restricting the events to a single strip. The response of the detector was mainly in avalanche mode but a few percentage of streamer mode response was also observed. A comparison of the response of these two modes with trigger rate was studiedComment: 19 pages, 26 figure