6,730 research outputs found
Differential systems associated with tableaux over Lie algebras
We give an account of the construction of exterior differential systems based
on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom
14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie
algebra is revisited and extended in the light of the formalism of the Spencer
cohomology; the question of involutiveness for the associated systems and their
prolongations is addressed; examples are discussed.Comment: 16 pages; to appear in: "Symmetries and Overdetermined Systems of
Partial Differential Equations" (M. Eastwood and W. Miller, Jr., eds.), IMA
Volumes in Mathematics and Its Applications, Springer-Verlag, New Yor
Formal logic: Classical problems and proofs
Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational
Non-Abelian Chern-Simons Particles in an External Magnetic Field
The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons
particles (non-Abelian anyons) in an external magnetic field are addressed. We
derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the Hilbert
space is projected onto the lowest Landau level of the magnetic field. In the
presence of an additional harmonic potential, the N-body spectrum depends
linearly on the coupling (statistics) parameter. We calculate the second virial
coefficient and find that in the strong magnetic field limit it develops a
step-wise behavior as a function of the statistics parameter, in contrast to
the linear dependence in the case of Abelian anyons. For small enough values of
the statistics parameter we relate the N-body partition functions in the lowest
Landau level to those of SU(2) bosons and find that the cluster (and virial)
coefficients dependence on the statistics parameter cancels.Comment: 35 pages, revtex, 3 eps figures include
A class of overdetermined systems defined by tableaux: involutiveness and Cauchy problem
This article addresses the question of involutiveness and discusses the
initial value problem for a class of overdetermined systems of partial
differential equations which arise in the theory of integrable systems and are
defined by tableaux.Comment: 14 page
Towards an efficient prover for the C1 paraconsistent logic
The KE inference system is a tableau method developed by Marco Mondadori
which was presented as an improvement, in the computational efficiency sense,
over Analytic Tableaux. In the literature, there is no description of a theorem
prover based on the KE method for the C1 paraconsistent logic. Paraconsistent
logics have several applications, such as in robot control and medicine. These
applications could benefit from the existence of such a prover. We present a
sound and complete KE system for C1, an informal specification of a strategy
for the C1 prover as well as problem families that can be used to evaluate
provers for C1. The C1 KE system and the strategy described in this paper will
be used to implement a KE based prover for C1, which will be useful for those
who study and apply paraconsistent logics.Comment: 16 page
Emergent Phase Space Description of Unitary Matrix Model
We show that large phases of a dimensional generic unitary matrix
model (UMM) can be described in terms of topologies of two dimensional droplets
on a plane spanned by eigenvalue and number of boxes in Young diagram.
Information about different phases of UMM is encoded in the geometry of
droplets. These droplets are similar to phase space distributions of a unitary
matrix quantum mechanics (UMQM) ( dimensional) on constant time
slices. We find that for a given UMM, it is possible to construct an effective
UMQM such that its phase space distributions match with droplets of UMM on
different time slices at large . Therefore, large phase transitions in
UMM can be understood in terms of dynamics of an effective UMQM. From the
geometry of droplets it is also possible to construct Young diagrams
corresponding to representations and hence different large states of
the theory in momentum space. We explicitly consider two examples : single
plaquette model with terms and Chern-Simons theory on . We
describe phases of CS theory in terms of eigenvalue distributions of unitary
matrices and find dominant Young distributions for them.Comment: 52 pages, 15 figures, v2 Introduction and discussions extended,
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