Single-input and single-output (SISO) controller reduction based on the L1L_1-norm

This paper proposes a new method to solve the controller-reduction problem based on the $L_1$-norm. This method uses a reduced-order closed-loop system to deduce reduced-order controllers. The problem of obtaining the required lower-order closed-loop system was formulated as an $L_1$-norm optimization, and the conditions were provided for guaranteeing the internal stability and the existence of lower-order controllers from the obtained reduced-order closed-loop system. In addition, the particle swarm optimization and sequence linear programming were adopted to solve the resultant $L_1$-norm optimization. Two numerical examples demonstrated the effectiveness of the proposed method

Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Laser opacity in underdense preplasma of solid targets due to quantum electrodynamics effects

We investigate how next-generation laser pulses at 10 PW $-$ 200 PW interact with a solid target in the presence of a relativistically underdense preplasma produced by amplified spontaneous emission (ASE). Laser hole boring and relativistic transparency are strongly restrained due to the generation of electron-positron pairs and $\gamma$-ray photons via quantum electrodynamics (QED) processes. A pair plasma with a density above the initial preplasma density is formed, counteracting the electron-free channel produced by the hole boring. This pair-dominated plasma can block the laser transport and trigger an avalanche-like QED cascade, efficiently transfering the laser energy to photons. This renders a 1-$\rm\mu m$-scalelength, underdense preplasma completely opaque to laser pulses at this power level. The QED-induced opacity therefore sets much higher contrast requirements for such pulse in solid-target experiments than expected by classical plasma physics. Our simulations show for example, that proton acceleration from the rear of a solid with a preplasma would be strongly impaired.Comment: 5 figure

Valosin-containing protein regulates the proteasome-mediated degradation of DNA-PKcs in glioma cells.

DNA-dependent protein kinase (DNA-PK) has an important role in the repair of DNA damage and regulates the radiation sensitivity of glioblastoma cells. The VCP (valosine-containing protein), a chaperone protein that regulates ubiquitin-dependent protein degradation, is phosphorylated by DNA-PK and recruited to DNA double-strand break sites to regulate DNA damage repair. However, it is not clear whether VCP is involved in DNA-PKcs (DNA-PK catalytic subunit) degradation or whether it regulates the radiosensitivity of glioblastoma. Our data demonstrated that DNA-PKcs was ubiquitinated and bound to VCP. VCP knockdown resulted in the accumulation of the DNA-PKcs protein in glioblastoma cells, and the proteasome inhibitor MG132 synergised this increase. As expected, this increase promoted the efficiency of DNA repair in several glioblastoma cell lines; in turn, this enhanced activity decreased the radiation sensitivity and prolonged the survival fraction of glioblastoma cells in vitro. Moreover, the VCP knockdown in glioblastoma cells reduced the survival time of the xenografted mice with radiation treatment relative to the control xenografted glioblastoma mice. In addition, the VCP protein was also downregulated in ~25% of GBM tissues from patients (WHO, grade IV astrocytoma), and the VCP protein level was correlated with patient survival (R(2)=0.5222, P<0.05). These findings demonstrated that VCP regulates DNA-PKcs degradation and increases the sensitivity of GBM cells to radiation

Phase diagram of the frustrated, spatially anisotropic S=1 antiferromagnet on a square lattice

We study the S=1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest neighbor couplings $J_{1x}$, $J_{1y}$ frustrated by a next-nearest neighbor coupling $J_{2}$ numerically using the density-matrix renormalization group (DMRG) method and analytically employing the Schwinger-Boson mean-field theory (SBMFT). Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the N\'{e}el ordered state above the classically stable region. Whereas SBMFT suggests a fluctuation-induced first order transition between the N\'{e}el state and a stripe antiferromagnet for $1/3\leq J_{1x}/J_{1y}\leq 1$ and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic $J_{1}$-$J_{2}$ model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for S=1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.Comment: 10 pages, 10 figure

Spin states and persistent currents in a mesoscopic ring with an embedded magnetic impurity

Spin states and persistent currents are investigated theoretically in a mesoscopic ring with an embedded magnetic ion under a uniform magnetic field including the spin-orbit interactions. The magnetic impurity acts as a spin-dependent $\delta$-potential for electrons and results in gaps in the energy spectrum, consequently suppresses the oscillation of the persistent currents. The competition between the Zeeman splittings and the $s$-$d$ exchange interaction leads to a transition of the electron ground state in the ring. The interplay between the periodic potential induced by the Rashba and Dresselhaus spin-orbit interactions and the $\delta$-potential induced by the magnetic impurity leads to significant variation in the energy spectrum, charge density distribution, and persistent currents of electrons in the ring.Comment: 8 pages, 11 figure

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109