92,089 research outputs found
The Weyl group of the fine grading of associated with tensor product of generalized Pauli matrices
We consider the fine grading of sl(n,\mb C) induced by tensor product of
generalized Pauli matrices in the paper. Based on the classification of maximal
diagonalizable subgroups of PGL(n,\mb C) by Havlicek, Patera and Pelantova,
we prove that any finite maximal diagonalizable subgroup of PGL(n,\mb C)
is a symplectic abelian group and its Weyl group, which describes the symmetry
of the fine grading induced by the action of , is just the isometry group of
the symplectic abelian group . For a finite symplectic abelian group, it is
also proved that its isometry group is always generated by the transvections
contained in it
Derivatives of Entropy Rate in Special Families of Hidden Markov Chains
Consider a hidden Markov chain obtained as the observation process of an
ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how,
in principle, one can explicitly compute the derivatives of the entropy rate of
at extreme values of the noise. Namely, they showed that the derivatives of
standard upper approximations to the entropy rate actually stabilize at an
explicit finite time. We generalize this result to a natural class of hidden
Markov chains called ``Black Holes.'' We also discuss in depth special cases of
binary Markov chains observed in binary symmetric noise, and give an abstract
formula for the first derivative in terms of a measure on the simplex due to
Blackwell.Comment: The relaxed condtions for entropy rate and examples are taken out (to
be part of another paper). The section about general principle and an example
to determine the domain of analyticity is taken out (to be part of another
paper). A section about binary Markov chains corrupted by binary symmetric
noise is adde
Linear Temporal Logic for Hybrid Dynamical Systems: Characterizations and Sufficient Conditions
This paper introduces operators, semantics, characterizations, and
solution-independent conditions to guarantee temporal logic specifications for
hybrid dynamical systems. Hybrid dynamical systems are given in terms of
differential inclusions -- capturing the continuous dynamics -- and difference
inclusions -- capturing the discrete dynamics or events -- with constraints.
State trajectories (or solutions) to such systems are parameterized by a hybrid
notion of time. For such broad class of solutions, the operators and semantics
needed to reason about temporal logic are introduced. Characterizations of
temporal logic formulas in terms of dynamical properties of hybrid systems are
presented -- in particular, forward invariance and finite time attractivity.
These characterizations are exploited to formulate sufficient conditions
assuring the satisfaction of temporal logic formulas -- when possible, these
conditions do not involve solution information. Combining the results for
formulas with a single operator, ways to certify more complex formulas are
pointed out, in particular, via a decomposition using a finite state automaton.
Academic examples illustrate the results throughout the paper.Comment: 35 pages. The technical report accompanying "Linear Temporal Logic
for Hybrid Dynamical Systems: Characterizations and Sufficient Conditions"
submitted to Nonlinear Analysis: Hybrid Systems, 201
Recommended from our members
Sufficient Conditions for Temporal Logic Specifications in Hybrid Dynamical Systems.
In this paper, we introduce operators, semantics, and conditions that, when possible, are solution-independent to guarantee basic temporal logic specifications for hybrid dynamical systems. Employing sufficient conditions for forward invariance and finite time attractivity of sets for such systems, we derive such sufficient conditions for the satisfaction of formulas involving temporal operators and atomic propositions. Furthermore, we present how to certify formulas that have more than one operator. Academic examples illustrate the results throughout the paper
Limit cycle bifurcations from a nilpotent focus or center of planar systems
In this paper, we study the analytical property of the Poincare return map
and the generalized focal values of an analytical planar system with a
nilpotent focus or center. Then we use the focal values and the map to study
the number of limit cycles of this kind of systems with parameters, and obtain
some new results on the lower and upper bounds of the maximal number of limit
cycles near the nilpotent focus or center.Comment: This paper was submitted to Journal of Mathematical Analysis and
Application
TeV resonances in top physics at the LHC
We consider the possibility of studying novel particles at the TeV scale with
enhanced couplings to the top quark via top quark pair production at the LHC
and VLHC. In particular we discuss the case of neutral scalar and vector
resonances associated with a strongly interacting electroweak symmetry breaking
sector. We constrain the couplings of these resonances by imposing appropriate
partial wave unitarity conditions and known low energy constraints. We evaluate
the new physics signals via WW -> tt~ for various models without making
approximation for the initial state W bosons, and optimize the acceptance cuts
for the signal observation. We conclude that QCD backgrounds overwhelm the
signals in both the LHC and a 200 TeV VLHC, making it impossible to study this
type of physics in the tt~ channel at those machines.Comment: 15p, add. comments to clarify model, +2 ref., version to appear PR
- …