Alternating subgroups of Coxeter groups

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.     

Synthesis,characterization, and application of light‐emitting copolyfluorenes slightly doped with distyrylbenzene derivatives

Copolyfluorenes PFG1～PFG4 slightly doped with 0.006–0.5 mol % of 2,5‐dihexyloxy‐1,4‐bis(2‐phenyl‐2‐cyanovinyl)benzene (green chromophore) were synthesized by the Suzuki coupling reaction to be evaluated as hosts for white‐light electroluminescent (EL) devices. Their optical, thermal and electrochemical properties were almost identical to those of polyfluorene ( PF ) due to minimal chromophore content. However, the electroluminescent (EL) spectra of the PFGn were very different from photoluminescence spectra in film state. Relative intensity of green emission (ca. 521 nm) in EL spectra are much stronger than those in PL spectra, which can be attributed to charges trapping in the chromophores due to its narrow band gap (E_g ≈ 2.56 eV). The performance of EL devices [ITO/PEDOT:PSS/polymer/Ca (50 nm)/Al (100 nm)] were improved with an increase in chromophore content. The PFG4 device revealed the best performance (6790 cd/m², 1.69 cd/A), and the PFG1 and PFG2 devices exhibited comparable intensity in blue and green emissions. Blend EL devices were fabricated by using the PFGn as the hosts and a red iridium complex [Ir(piq)₂(acac)] as dopant. By controlling the amount of the iridium complex, the white‐light emitting device was achieved with PFG2 , with maximum brightness and CIE coordinate being 4120 cd/m² and (0.31, 0.28), respectively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 149–160, 2009     

脉冲光热光谱中波长效应的理论分析

本文从理论上分析了脉冲光热谱中波长效应。讨论了波长调谐对脉冲光热光谱信号的峰值和时间特性的影响。     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

Measuring supersymmetry at the large hadron collider

The large hadron collider (LHC) should have the ability to detect supersymmetric particles if low-energy supersymmetry solves the hierarchy problem. Studies of the LHC detection reach, and the ability to measure properties of supersymmetric particles are currently underway. We highlight some of these, such as the reach in minimal supergravity space and correlation with a fine-tuning parameter, precision measurements of edge variables, anomaly or gauge-mediated supersymmetry breaking. Supersymmetry with baryon-number violation seems at first glance more difficult to detect, but proves to be possible by using leptons from cascade decays.     

Analysis and optimisation of the tuning of the twelfths for a clarinet resonator

Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points of view. First, we systematically review various physical reasons why this inharmonicity may take place, and the effect of different bore perturbations inserted in cylindrical instruments such as bore flare, open and closed holes, taper, temperature gradients, visco-thermal effects, etc. Applications to a real clarinet resonator and comparisons with impedance measurements are then presented. A commonly accepted idea is that the register hole is the dominant cause for this inharmonicity: it is natural to expect that opening this hole will shift the position of the resonances of the instrument to higher frequencies, except of course for the note for which the hole is exactly at the pressure node. We show that the real situation is actually more complicated because other effects, such as open holes or bore taper and bell, introduce resonance shifts that are comparable but with opposite sign, so that a relatively good overall compensation takes place. This is checked by experimental and theoretical studies of the acoustical impedance curves of a clarinet. The origin of the observed inharmonicity in playing frequencies is therefore different, maybe related to the reed or the vocal tract. In a second part, we use an elementary model of the clarinet in order to isolate the effect of the register hole: a perfect cylindrical tube without closed holes. Optimization techniques are then used to calculate an optimum location for the register hole (without taking into account the use of the register hole as a B flat tone hole); the result turns out to be close to the location chosen by clarinet makers. Finally, attempts are made numerically to improve the situation by introducing small perturbations in the higher part of the cylindrical resonator, but no satisfactory improvement is obtained.     

Universality in the length spectrum of integrable systems

The length spectrum of periodic orbits in integrable hamiltonian systems can be expressed in terms of the set of winding numbers {M ₁,…,M _f} on thef-tori. Using the Poisson summation formula, one can thus express the density, Σδ(T−T _M), as a sum of a smooth average part and fluctuations about it. Working with homogeneous separable potentials, we explicitly show that the fluctuations are due to quantal energies. Further, their statistical properties are universal and typical of a Poisson process as in the corresponding quantal energy eigenvalues. It is interesting to note however that even though long periodic orbits in chaotic billiards have similar statistical properties, the form of the fluctuations are indeed very different.     

硅微机械谐振陀螺仪的非线性分析

给出了硅微机械谐振陀螺仪的结构,介绍了硅微机械谐振陀螺仪的工作原理,详细推导并给出了陀螺仪的输出频率和标度因数非线性的计算公式;基于影响谐振陀螺仪标度因数的参数,分析了由谐振器的振幅和梳齿静电驱动力引起的硅微机械谐振陀螺仪的非线性特性,给出了振动幅度与谐振频率关系的表达式.实验结果表明,陀螺仪的整体性能主要取决于谐振器振动幅度的稳定性.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

On lengths,areas and Lipschitz continuity of polyharmonic mappings

In this paper, we continue our investigation of polyharmonic mappings in the complex plane. First, we establish two Landau type theorems. We also show a three circles type theorem and an area version of the Schwarz lemma. Finally, we study Lipschitz continuity of polyharmonic mappings with respect to the distance ratio metric.