Improved Currents for Heavy Quarks

We discuss lattice artifacts for matrix elements of hadrons containing one or more heavy quark. In particular, we analyze interrelations between lattice artifacts and the $1/m_Q$ expansion. The implications for calculations of heavy-light decay constants and of semi-leptonic form factors are discussed.Comment: 3 pages, no figures, uuencoded PostScript, proceedings of Lattice '94. LaTeX at ftp://fnth06.fnal.gov/pub/Fermilab-Pub/95.00

The Charm Quark on the Lattice

We formulate lattice fermions in a way that encompasses Wilson fermions as well as the static and non-relativistic approximations. In particular, we treat $m_qa$ systematically ($m_q$ is the fermion mass) showing how to understand the Wilson action as an effective action for systems with \vek{p}\ll m_q. The results show how to extract matrix elements and the spectrum from simulations with $m_qa\approx1$, which is relevant for the charm quark.Comment: 4 pages LaTeX using espcrc2.sty and epsf.sty. FERMILAB-CONF-92/329-

Binding Energies in Nonrelativistic Field Theories

Relativistic corrections communicate the binding energy of a bound state to its kinetic mass. This mechanism is reviewed and used to explain anomalous results of Collins, Edwards, Heller, and Sloan (hep-lat/9512026), which compared rest and kinetic masses of heavy-light mesons and quarkonia.Comment: 4 pages, 1 figure, poster presented at LATTICE96(heavy quarks

Trees whose 2-domination subdivision number is 2

A set $S$ of vertices in a graph $G = (V,E)$ is a $2$-dominating set if every vertex of $V\setminus S$ is adjacent to at least two vertices of $S$. The $2$-domination number of a graph $G$, denoted by $\gamma_2(G)$, is the minimum size of a $2$-dominating set of $G$. The $2$-domination subdivision number $sd_{\gamma_2}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the $2$-domination number. The authors have recently proved that for any tree $T$ of order at least $3$, $1 \leq sd_{\gamma_2}(T)\leq 2$. In this paper we provide a constructive characterization of the trees whose $2$-domination subdivision number is $2$

The Signed Roman Domatic Number of a Digraph

Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v]$ consists of $v$ andall inner neighbors of $v$, and every vertex $u\in V(D)$ for which $f(u)=-1$ has an innerneighbor $v$ for which $f(v)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct signedRoman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le 1$ for each$v\in V(D)$, is called a {\em signed Roman dominating family} (of functions) on $D$. The maximumnumber of functions in a signed Roman dominating family on $D$ is the {\em signed Roman domaticnumber} of $D$, denoted by $d_{sR}(D)$. In this paper we initiate the study of signed Romandomatic number in digraphs and we present some sharp bounds for $d_{sR}(D)$. In addition, wedetermine the signed Roman domatic number of some digraphs. Some of our results are extensionsof well-known properties of the signed Roman domatic number of graphs

Fouling Characteristics of a Light Australian Crude Oil

Australian crude oils, which generally contain little asphaltenes, nevertheless give rise to fouling in refinery pre-heat trains. In this research, fouling of a series of such crude oils and their blends is being assessed. The present work focuses on thermal fouling resulting from heating Gippsland crude oil at moderate temperatures. The oil is maintained under nitrogen at a pressure of 379 kPa, and re-circulated at bulk temperatures of 80-120°C through an electrically heated annular probe at velocities in the range 0.25 to 0.65 m/s with surface temperatures from 180-260°C. Experiments are run for periods up to 90 hours at constant heat flux. Fouling is detected by the increase of wall temperature of the probe. The oil is characterized by its filterable solids content, density and viscosity both before and after the fouling run. The trends in fouling rates are compared to predictions of the threshold-fouling model proposed by Ebert and Panchal (1995). Data on deposit composition are presented, and the fouling mechanism discussed