ON QUOTIENTS OF BRAID GROUPS

ABSTRACT.

Let G be the group ?[t, t ^?1] x ?. By studying the action of the braid group B_n on the set Gⁿ , we obtain representations of B_n into a wreath product of the symmetric group and the general linear group over ?[t, t ^?1]. This in particular recovers the Burau representation of the braid group. Furthermore, some quotients of the braid group are obtained by using the representations found.     

The Likelihood of the Parameters of a Continuous Time Vector Autoregressive Model

This paper provides a method of constructing the likelihood function of the parameters of a continuous time vector autoregressive model on the basis of discrete data without requiring the restrictions extant methods impose on the data that are capable of being rejected by a statistical test. In particular, the method does not rely on a steady-state assumption that can rule out unit root processes; it allows for weak assumptions on the innovations; and it allows for a mixture of skip-sampled and temporally-aggregated data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chaotic Dynamics in an Electronic Model of a Genetic Network

We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low (i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics, like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods for characterizing dynamics in these networks.     

Generation of uniform atmospheric pressure argon glow plasma by dielectric barrier discharge

In this paper, atmospheric pressure glow discharges (APGD) in argon generated in parallel plate dielectric barrier discharge system is investigated by means of electrical and optical measurements. Using a high voltage (0–20 kV) power supply operating at 10–30 kHz, homogeneous and steady APGD has been observed between the electrodes with gap spacing from 0.5 mm to 2 mm and with a dielectric barrier of thickness 2 mm while argon gas is fed at a controlled flow rate of 1 l/min. The electron temperature and electron density of the plasma are determined by means of optical emission spectroscopy. Our results show that the electron density of the discharge obtained is of the order of 10¹⁶ cm^???3 while the electron temperature is estimated to be 0.65 eV. The important result is that electron density determined from the line intensity ratio method and stark broadening method are in very good agreement. The Lissajous figure is used to estimate the energy deposited to the glow discharge. It is found that the energy deposited to the discharge is in the range of 20 to 25 μJ with a discharge voltage of 1.85 kV. The energy deposited to the discharge is observed to be higher at smaller gas spacing. The glow discharge plasma is tested to be effective in reducing the hydrophobicity of polyethylene film significantly.     

Characterization of dynamic and steady-state protein phosphorylation using a fluorescent phosphoprotein gel stain and mass spectrometry

Protein phosphorylation plays a vital role in the regulation of most aspects of cellular activity, being key to propagating messages within signal transduction pathways and to modulating protein function. Pro-Q Diamond phosphoprotein gel stain is suitable for the fluorescence detection of phosphoserine-, phosphothreonine-, and phosphotyrosine-containing proteins directly in sodium dodecyl sulfate (SDS)-polyacrylamide gels. The technology is especially appropriate for profiling steady-state and dynamic phosphorylation on a proteome-wide scale, as demonstrated through detection of the native phosphorylation of cardiac mitochondrial phosphoproteins and changes in this profile arising from the activity of a protein kinase. For example, Pro-Q Diamond phosphoprotein gel stain was employed to demonstrate that among the 46 subunits of the mitochondrial respiratory chain complex, NADH:ubiquinone oxidoreductase (complex I), a 42 kDa subunit is phosphorylated in the steady-state. However, exposure of mitochondria to cAMP-dependent protein kinase increases phosphorylation of this 42 kDa subunit and results in de novo phosphorylation of an 18 kDa subunit as well. Since Pro-Q Diamond dye binds to phosphorylated residues noncovalently, the staining technology is fully compatible with modern microchemical analysis procedures, such as peptide mass profiling by matrix assisted laser desorption/ionization-time of flight (MALDI-TOF) mass spectrometry and post-source decay analysis of peptide phosphorylation.     

聚氨酯与铁电陶瓷粉复合物的电致感应性能研究

利用双辊制备了一系列热塑性弹性体聚氨酯（PU）和铁电钛酸锆酸铅盐（PZT）的电感应PZT／PU复合物。X－衍射和SE镜结果显示,复合物中,在铁电相中PZT陶瓷粉呈现结晶态并且均匀分布在PU基体中,复合物的弹性模量和相对电容率随着复合物中PZT体积分数增加而升高,在高压电场下,低PZT含量的复合物呈现负的电致伸缩应力,当PZT体积分数增加到6％以上时,在某个临界电场下,复合物呈现出电致伸缩应力反转的特性,即电致伸缩应力从负转变为正,并且发生应力反转的临界电场随着复合物中PZT体积分数的增加而降低,PU的电致伸缩特性与PZT在高电场下极化反转效应结合,导致了PZT／PU复合物这种有趣的性能,因此PZT／PU复合物将在高电压场方面作为传感器开关材料得到广泛应用。     

A combined experimental and quantum chemistry study of selenium chemical shift tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.