12,291 research outputs found
The structure of gauge-invariant ideals of labelled graph -algebras
In this paper, we consider the gauge-invariant ideal structure of a
-algebra associated to a set-finite,
receiver set-finite and weakly left-resolving labelled space
, where is a labelling map assigning
an alphabet to each edge of the directed graph with no sinks. Under the
assumption that an accommodating set is closed under taking
relative complement, it is obtained that there is a one to one correspondence
between the set of all hereditary saturated subsets of and the
gauge-invariant ideals of . For this, we
introduce a quotient labelled space arising
from an equivalence relation on and show the existence
of the -algebra generated by a
universal representation of . Also the
gauge-invariant uniqueness theorem for is
obtained.
For simple labelled graph -algebras
, where is the
smallest accommodating set containing all the generalized vertices, it is
observed that if for each vertex of , a generalized vertex is
finite for some , then is simple if
and only if is strongly cofinal and
disagreeable. This is done by examining the merged labelled graph
of and the common properties that
and
share
Comment on ``Solution of Classical Stochastic One-Dimensional Many-Body Systems''
In a recent Letter, Bares and Mobilia proposed the method to find solutions
of the stochastic evolution operator with a
non-trivial quartic term . They claim, ``Because of the conservation of
probability, an analog of the Wick theorem applies and all multipoint
correlation functions can be computed.'' Using the Wick theorem, they expressed
the density correlation functions as solutions of a closed set of
integro-differential equations.
In this Comment, however, we show that applicability of Wick theorem is
restricted to the case only.Comment: 1 page, revtex style, comment on paper Phys. Rev. Lett. {\bf 83},
5214 (1999
Thermodynamic Volume and the Extended Smarr Relation
We continue to explore the scaling transformation in the reduced action
formalism of gravity models. As an extension of our construction, we consider
the extended forms of the Smarr relation for various black holes, adopting the
cosmological constant as the bulk pressure as in some literatures on black
holes. Firstly, by using the quasi-local formalism for charges, we show that,
in a general theory of gravity, the volume in the black hole thermodynamics
could be defined as the thermodynamic conjugate variable to the bulk pressure
in such a way that the first law can be extended consistently. This, so called,
thermodynamic volume can be expressed explicitly in terms of the metric and
field variables. Then, by using the scaling transformation allowed in the
reduced action formulation, we obtain the extended Smarr relation involving the
bulk pressure and the thermodynamic volume. In our approach, we do not resort
to Euler's homogeneous scaling of charges while incorporating the would-be
hairy contribution without any difficulty.Comment: 1+21 pages, plain LaTeX; v2 typo fixed and references adde
- β¦