904 research outputs found
Trees whose 2-domination subdivision number is 2
A set of vertices in a graph is a -dominating set if every vertex of is adjacent to at least two vertices of . The -domination number of a graph , denoted by , is the minimum size of a -dominating set of . The -domination subdivision number is the minimum number of edges that must be subdivided (each edge in can be subdivided at most once) in order to increase the -domination number. The authors have recently proved that for any tree of order at least , . In this paper we provide a constructive characterization of the trees whose -domination subdivision number is
The Signed Roman Domatic Number of a Digraph
Let be a finite and simple digraph with vertex set .A {\em signed Roman dominating function} on the digraph isa function such that for every , where consists of andall inner neighbors of , and every vertex for which has an innerneighbor for which . A set of distinct signedRoman dominating functions on with the property that for each, is called a {\em signed Roman dominating family} (of functions) on . The maximumnumber of functions in a signed Roman dominating family on is the {\em signed Roman domaticnumber} of , denoted by . In this paper we initiate the study of signed Romandomatic number in digraphs and we present some sharp bounds for . 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
The phase diagram of twisted mass lattice QCD
We use the effective chiral Lagrangian to analyze the phase diagram of
two-flavor twisted mass lattice QCD as a function of the normal and twisted
masses, generalizing previous work for the untwisted theory. We first determine
the chiral Lagrangian including discretization effects up to next-to-leading
order (NLO) in a combined expansion in which m_\pi^2/(4\pi f_\pi)^2 ~ a \Lambda
(a being the lattice spacing, and \Lambda = \Lambda_{QCD}). We then focus on
the region where m_\pi^2/(4\pi f_\pi)^2 ~ (a \Lambda)^2, in which case
competition between leading and NLO terms can lead to phase transitions. As for
untwisted Wilson fermions, we find two possible phase diagrams, depending on
the sign of a coefficient in the chiral Lagrangian. For one sign, there is an
Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is
washed out into a crossover if the twisted mass is non-vanishing. For the other
sign, there is a first order transition for pure Wilson fermions, and we find
that this transition extends into the twisted mass plane, ending with two
symmetrical second order points at which the mass of the neutral pion vanishes.
We provide graphs of the condensate and pion masses for both scenarios, and
note a simple mathematical relation between them. These results may be of
importance to numerical simulations.Comment: 13 pages, 5 figures, small clarifying comments added in introduction,
minor typos fixed. Version to be published in Phys. Rev.
Finite-Temperature Phase Structure of Lattice QCD with Wilson Quark Action
The long-standing issue of the nature of the critical line of lattice QCD
with the Wilson quark action at finite-temperatures, defined to be the line of
vanishing pion screening mass, and its relation to the line of
finite-temperature chiral tansition is examined. Analytical and numerical
evidence are presented that the critical line forms a cusp at a finite gauge
coupling, and the line of chiral transition runs past the tip of the cusp
without touching the critical line. Implications on the continuum limit and the
flavor dependence of chiral transition are discussed.Comment: 13 pages(4 figures), latex (epsf style-file needed), one sentence in
abstract missed in transmission supplied and a few minor modifications in the
text mad
Perturbative Renormalization of Improved Lattice Operators
We derive bases of improved operators for all bilinear quark currents up to
spin two (including the operators measuring the first moment of DIS Structure
Functions), and compute their one-loop renormalization constants for arbitrary
coefficients of the improvement terms. We have thus control over O(a)
corrections, and for a suitable choice of improvement coefficients we are only
left with errors of O(a^2).Comment: 4 pages, LaTeX + 1 eps file + epscrc2.sty (included). Talk given to
the Lattice 97 International Symposium, 22-26 July 1997, Edinburgh, UK. Minor
changes in notatio
Non-Perturbative Renormalisation of Composite Operators
It is shown that the renormalisation constants of two quark operators can be
accurately determined (to a precision of a few per-cent using 18 gluon
configurations) using Chiral Ward identities. A method for computing
renormalisation constants of generic composite operators without the use of
lattice perturbation theory is proposed.Comment: 3 pages, uuencoded compressed postscript file, to appear in the
Proceedings of the International Symposium on Lattice Field Theory, Dallas,
Texas, 12-17 October 1993, Southampton Preprint 93/94-0
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