ON THE EXTENSION OF SHARKOVSKIĬ'S THEOREM TO CONNECTED GRAPHS WITH NON-POSITIVE EULER CHARACTERISTIC

1995 ◽  
Vol 05 (05) ◽  
pp. 1395-1405 ◽  
Author(s):  
J. LLIBRE ◽  
J. PARAÑOS ◽  
J. A. RODRIGUEZ

This paper contains a characterization of all possible sets of periods for all continuous self-maps on a connected topological graph with zero Euler characteristic having all branching points fixed. A characterization in terms of linear orderings is given for the simplest connected topological graph with zero Euler characteristic that has a branching point, the topological graph shaped like the letter σ. In this case a proof follows by lifting the continuous self-map on σ. We show the difficulties that arise in the simplest connected topological graphs with negative Euler characteristic, like for instance the topological graph shaped like the figure 8.

2003 ◽  
Vol 13 (07) ◽  
pp. 1743-1754 ◽  
Author(s):  
Jaume Llibre ◽  
José Paraños ◽  
J. Ángel Rodríguez

Let 8 be the graph shaped like the number 8. This paper contains a characterization of all possible sets of periods for all continuous self-maps of 8 with the branching point fixed. We remark that this characterization is the first complete classification of the sets of periods for all continuous self-maps on a connected graph with negative Euler characteristic with fixed branching points.


2019 ◽  
Vol 342 (11) ◽  
pp. 3047-3056
Author(s):  
Chengfu Qin ◽  
Weihua He ◽  
Kiyoshi Ando

2018 ◽  
Vol 50 (3) ◽  
pp. 706-725
Author(s):  
Julie Fournier

Abstract A deterministic application θ:ℝ2→ℝ2 deforms bijectively and regularly the plane and allows the construction of a deformed random field X∘θ:ℝ2→ℝ from a regular, stationary, and isotropic random field X:ℝ2→ℝ. The deformed field X∘θ is, in general, not isotropic (and not even stationary), however, we provide an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X∘θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. We prove that deformed fields satisfying this property are strictly isotropic. In addition, we are able to identify θ, assuming that the mean Euler characteristic of excursion sets of X∘θ over some basic domain is known.


2020 ◽  
Vol 232 ◽  
pp. 01003
Author(s):  
Michael Paul ◽  
Moshe Tessler ◽  
Shlomi Halfon ◽  
Elad Korngut ◽  
Arik Kreisel ◽  
...  

We report on recent experiments at the Soreq Applied Research Accelerator Facility Liquid-Lithium Target (SARAF-LiLiT) laboratory dedicated to the study of s-process neutron capture reactions. The kW-power proton beam at 1.92 MeV (1-2 mA) from SARAF Phase I yields high-intensity 30 keV quasi-Maxwellian neutrons (3-5×1010 n/s). The high neutron intensity enables Maxwellian averaged cross sections (MACS) measurements of low-abundance or radioactive targets. Neutron capture reactions on the important s-process branching points 147Pm and 171Tm were investigated by activation in the LiLiT neutron beam and γ-measurements of their decay products. MACS values at 30 keV extracted from the experimental spectrum-averaged cross sections are obtained and will be discussed. The Kr region, at the border between the so-called weak and strong s-process was also investigated. Atom Trap Trace Analysis (ATTA) was used for the first time for the measurement of a nuclear reaction cross section. After activation in the quasi-Maxwellian neutron flux at SARAF-LiLiT, isotopic ratios were determined for 81Kr(230 ky)/80Kr and 85gKr(10.8 y)/84Kr. The latter ratio was confirmed both by low-level β counting and γ spectrometry. The shorter-lived capture products 79,85m,87Kr were detected by γ -spectrometry and the corresponding neutron-capture MACS of the respective target nuclei 78,84,86Kr were determined. The MACS of the 80Kr(n, γ)81Kr and 84Kr(n, γ)85gKr reactions are still under study. The partial MACS leading to 85mKr(4.5 h) measured in this experiment has interesting implications since this state decays preferentially by γ decay (79%) to 85Rb on a faster time scale than does 85gKr and behaves thus as an s-process branching point.


1990 ◽  
Vol 84 (1) ◽  
pp. 105-108 ◽  
Author(s):  
Nicola Martinov
Keyword(s):  

2020 ◽  
Vol 86 (6) ◽  
Author(s):  
Sora Yu ◽  
Eun Ju Yun ◽  
Dong Hyun Kim ◽  
So Young Park ◽  
Kyoung Heon Kim

ABSTRACT Vibrio sp. strain EJY3 is an agarolytic marine bacterium that catabolizes 3,6-anhydro-l-galactose (AHG), a monomeric sugar unit of agarose. While the AHG catabolic pathway in EJY3 has been discovered recently, the complete agarolytic system of EJY3 remains unclear. We have identified five enzymes, namely, the β-agarases VejGH50A, VejGH50B, VejGH50C, and VejGH50D and the α-neoagarooligosaccharide (NAOS) hydrolase VejGH117, involved in the agarolytic system of EJY3. Based on the characterization of recombinant enzymes and intracellular metabolite analysis, we found that EJY3 catabolizes agarose via two different agarolytic pathways. Among the four β-agarases of EJY3, VejGH50A, VejGH50B, and VejGH50C were found to be extracellular agarases, producing mainly neoagarotetraose (NeoDP4) and neoagarobiose. By detecting intracellular NeoDP4 in EJY3 grown on agarose, NeoDP4 was observed being taken up by cells. Intriguingly, intracellular NeoDP4 acted as a branching point for the two different downstream agarolytic pathways. First, via the well-known agarolytic pathway, NeoDP4 was depolymerized into monomeric sugars by the exo-type β-agarase VejGH50D and the α-NAOS hydrolase VejGH117. Second, via the newly found alternative agarolytic pathway, NeoDP4 was depolymerized into AHG and agarotriose (AgaDP3) by VejGH117, and AgaDP3 then was completely depolymerized into monomeric sugars by sequential reactions of the agarolytic β-galactosidases (ABG) VejABG and VejGH117. Therefore, by experimentally verifying agarolytic enzymatic activity and transport of NeoDP4 into EJY3 cells, we revealed that EJY3 possesses both the known pathway and the newly discovered alternative pathway that involves α-NAOS hydrolase and ABG. IMPORTANCE Agarose is the main polysaccharide of red macroalgae and is composed of galactose and 3,6-anhydro-l-galactose. Many marine bacteria possess enzymes capable of depolymerizing agarose into oligomers and then depolymerizing the oligomers into monomers. Here, we experimentally verified that both a well-known agarolytic pathway and a novel agarolytic pathway exist in a marine bacterium, Vibrio sp. strain EJY3. In agarolytic pathways, agarose is depolymerized mainly into 4-sugar-unit oligomers by extracellular enzymes, which are then transported into cells. The imported oligomers are intracellularly depolymerized into galactose and 3,6-anhydro-l-galactose by two different agarolytic pathways, using different combinations of intracellular enzymes. These results elucidate the depolymerization routes of red macroalgal biomass in the ocean by marine bacteria and provide clues for developing industrial processes for efficiently producing sugars from red macroalgae.


2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
T. Asir

A subset D of the vertex set of a graph G, is a dominating set if every vertex in V−D is adjacent to at least one vertex in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset of V−D, which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number γ′(G) is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with γ(G)+γ′(G)=n, where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and γ(G)+γ′(G)=n−1.


2009 ◽  
Vol 2 (1) ◽  
Author(s):  
Yi Lu ◽  
Ling Ding ◽  
Jianping Yu

The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.


2013 ◽  
Vol 95 (2) ◽  
pp. 169-188
Author(s):  
S. KALISZEWSKI ◽  
NURA PATANI ◽  
JOHN QUIGG

AbstractFor a countable discrete space $V$, every nondegenerate separable ${C}^{\ast } $-correspondence over ${c}_{0} (V)$ is isomorphic to one coming from a directed graph with vertex set $V$. In this paper we demonstrate why the analogous characterizations fail to hold for higher-rank graphs (where one considers product systems of ${C}^{\ast } $-correspondences) and for topological graphs (where $V$ is locally compact Hausdorff), and we discuss the obstructions that arise.


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