Glueball relevant study on isoscalars from Nf=2N_f=2 lattice QCD

We perform a glueball-relevant study on isoscalars based on anisotropic $N_f=2$ lattice QCD gauge configurations. In the scalar channel, we identify the ground state obtained through gluonic operators to be a single-particle state through its dispersion relation. When $q\bar{q}$ operator is included, we find the mass of this state does not change, and the $q\bar{q}$ operator couples very weakly to this state. So this state is most likely a glueball state. For pseudoscalars, along with the exiting lattice results, our study implies that both the conventional $q\bar{q}$ state $\eta_2$ (or $\eta'$ in flavor $SU(3)$) and a heavier glueball-like state with a mass of roughly 2.6 GeV exist in the spectrum of lattice QCD with dynamical quarks.Comment: 8 pages, 3 figures, 3 tables, talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Minus total domination in graphs

summary:A three-valued function $f\: V\rightarrow \{-1,0,1\}$ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^{-}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^{-}(G)$

Investors’ preference order of fuzzy numbers

AbstractNowadays greater and greater realistic financial problems are modeled by using the stochastic programming in the fuzzy environment. Hence, ranking a set of fuzzy numbers that is consistent with the investors’ preference becomes important for modelling a realistic problem. In this paper, we will provide a new ranking procedure that is consistent with the preference of the conservative investors. Our ranking procedure satisfies the axioms of three order relations for the separable fuzzy numbers or the triangle fuzzy numbers. We found that our ranking procedure has a better capability of discriminating the order of two fuzzy numbers. For the LR-type fuzzy numbers, our ranking procedure reduces the computational time substantially