548 research outputs found
Decompositions of edge-colored infinite complete graphs into monochromatic paths
An -edge coloring of a graph or hypergraph is a map . 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 -edge colored countably infinite complete
-uniform hypergraph can be partitioned into monochromatic tight paths
with distinct colors (a tight path in a -uniform hypergraph is a sequence of
distinct vertices such that every set of consecutive vertices forms an
edge),
(2.) for all natural numbers and there is a natural number such
that the vertex set of every -edge colored countably infinite complete graph
can be partitioned into monochromatic powers of paths apart from a
finite set (a power of a path is a sequence of
distinct vertices such that implies that is an
edge),
(3.) the vertex set of every -edge colored countably infinite complete
graph can be partitioned into monochromatic squares of paths, but not
necessarily into ,
(4.) the vertex set of every -edge colored complete graph on
can be partitioned into 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 2003â11, 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 â G such that the preimage of the translate fâ1(B + g) is meager in K for every g â G. The set B is called strongly Haar meager if there is a compact set C â G such that (B + g) â C is meager in C for every g â G. The main open problem in this area is Darjiâs 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 GÎŽ set in â€Ï that is Haar meager but not strongly Haar meager. We also show that no FÏ counterexample exists, hence our result is optimal. © 2019, The Hebrew University of Jerusalem
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):yâR}= dimtHK-1 for the generic f â 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 â C(K) and the generic y â 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 â C(K) and the generic y â 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 â C(K) for every yâintf(K) we have dim H f -1(y) = dim tH K - 1. Finally, we prove that the graph of the generic f â C(K) has the same Hausdorff and topological Hausdorff dimension as K. © 2012 Elsevier Ltd. All rights reserved
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 Î(m1/3n) for mâ©Ÿn, and Î(m2/3n2/3+m+n) for mâ©œn. (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 Earthâs 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 be a fixed set. By a scaled copy of around
we mean a set of the form for some .
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 around every point
of a set of given size? We will consider the cases when is circle or sphere
centered at the origin, Cantor set in , the boundary of a square
centered at the origin, or more generally the -skeleton () of an
-dimensional cube centered at the origin or the -skeleton of a more
general polytope of .
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
- âŠ