455 research outputs found
On finitely ambiguous B\"uchi automata
Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one
accepting run per word, are a useful restriction of B\"uchi automata that is
well-suited for probabilistic model-checking. In this paper we propose a more
permissive variant, namely finitely ambiguous B\"uchi automata, a
generalisation where each word has at most accepting runs, for some fixed
. We adapt existing notions and results concerning finite and bounded
ambiguity of finite automata to the setting of -languages and present a
translation from arbitrary nondeterministic B\"uchi automata with states to
finitely ambiguous automata with at most states and at most accepting
runs per word
Symplectic Dirac-K\"ahler Fields
For the description of space-time fermions, Dirac-K\"ahler fields
(inhomogeneous differential forms) provide an interesting alternative to the
Dirac spinor fields. In this paper we develop a similar concept within the
symplectic geometry of phase-spaces. Rather than on space-time, symplectic
Dirac-K\"ahler fields can be defined on the classical phase-space of any
Hamiltonian system. They are equivalent to an infinite family of metaplectic
spinor fields, i.e. spinors of Sp(2N), in the same way an ordinary
Dirac-K\"ahler field is equivalent to a (finite) mulitplet of Dirac spinors.
The results are interpreted in the framework of the gauge theory formulation of
quantum mechanics which was proposed recently. An intriguing analogy is found
between the lattice fermion problem (species doubling) and the problem of
quantization in general.Comment: 86 pages, late
Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\"ahler Fermion Mechanism
We propose a twisted D=N=2 superspace formalism. The relation between the
twisted super charges including the BRST charge, vector and pseudo scalar super
charges and the N=2 spinor super charges is established. We claim that this
relation is essentially related with the Dirac-K\"ahler fermion mechanism. We
show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral
superfields is equivalent to the quantized version of BF theory with the Landau
type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino
action. We then construct a Yang-Mills action described by the twisted N=2
chiral and vector superfields, and show that the action is equivalent to the
twisted version of the D=N=2 super Yang-Mills action, previously obtained from
the quantized generalized topological Yang-Mills action with instanton gauge
fixing.Comment: 36 page
Cavitation inception of a van der Waals fluid at a sack-wall obstacle
Cavitation in a liquid moving past a constraint is numerically investigated
by means of a free-energy lattice Boltzmann simulation based on the van der
Waals equation of state. The fluid is streamed past an obstacle and, depending
on the pressure drop between inlet and outlet, vapor formation underneath the
corner of the sack-wall is observed. The circumstances of cavitation formation
are investigated and it is found that the local bulk pressure and mean stress
are insufficient to explain the phenomenon. Results obtained in this study
strongly suggest that the viscous stress, interfacial contributions to the
local pressure, and the Laplace pressure are relevant to the opening of a vapor
cavity. This can be described by a generalization of Joseph's criterion that
includes these contributions. A macroscopic investigation measuring mass flow
rate behavior and discharge coefficient was also performed. As theoretically
predicted, mass flow rate increases linearly with the square root of the
pressure drop. However, when cavitation occurs, the mass flow growth rate is
reduced and eventually it collapses into a choked flow state. In the cavitating
regime, as theoretically predicted and experimentally verified, the discharge
coefficient grows with the Nurick cavitation number
A holomorphic representation of the Jacobi algebra
A representation of the Jacobi algebra by first order differential operators with polynomial
coefficients on the manifold is presented. The
Hilbert space of holomorphic functions on which the holomorphic first order
differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the
Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI:
10.1142/S0129055X12920018, references update
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
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