120,797 research outputs found
On symmetric commutator subgroups, braids, links and homotopy groups
In this paper, we investigate some applications of commutator subgroups to
homotopy groups and geometric groups. In particular, we show that the
intersection subgroups of some canonical subgroups in certain link groups
modulo their symmetric commutator subgroups are isomorphic to the (higher)
homotopy groups. This gives a connection between links and homotopy groups.
Similar results hold for braid and surface groups.Comment: 24 pages, 1 figur
Brunnian Braids and Lie Algebras
Brunnian braids have interesting relations with homotopy groups of spheres.
In this work, we study the graded Lie algebra of the descending central series
related to Brunnian subgroup of the pure braid group. A presentation of this
Lie algebra is obtained.Comment: 21 page
A search algorithm for a class of optimal finite-precision controller realization problems with saddle points
With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them
Charge pumping in monolayer graphene driven by a series of time-periodic potentials
We applied the Floquet scattering-matrix formalism to studying the electronic
transport properties in a mesoscopic Dirac system. Using the method, we
investigate theoretically quantum pumping driven by a series of time-periodic
potentials in graphene monolayer both in the adiabatic and non-adiabatic
regimes. Our numerical results demonstrate that adding harmonic modulated
potentials can break the time reversal symmetry when no voltage bias is applied
to the graphene monolayer. Thus, when the system is pumped with proper dynamic
parameters, these scatterers can produce a nonzero dc pumped current. We also
find that the transmission is anisotropic as the incident angle is changed.Comment: 8 pages, 6 figure
An improved closed-loop stability related measure for finite-precision digital controller realizations
The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller, implemented with finite word length (FWL), is used. A new stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure
An improved closed-loop stability related measure for finite-precision digital controller realizations
The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller, implemented with finite word length (FWL), is used. A new stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure
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