The Weyl group of the fine grading of sl(n,C)sl(n,\mathbb{C}) 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 $K$ 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 $K$, is just the isometry group of the symplectic abelian group $K$. 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

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