Weight function for the quantum affine algebra Uq(sl^3)U_q(\hat{sl}_3)

We give a precise expression for the universal weight function of the quantum affine algebra $U_q(\hat{sl}_3)$. The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.Comment: 28 page

Finite-horizon H∞ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements

This technical note deals with the H∞ control problem for a class of discrete time-varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite-horizon. The system measurements are transmitted through fading channels described by a modified stochastic Rice fading model. The purpose of the addressed problem is to design a set of time-varying controllers such that, in the presence of channel fading and randomly occurring nonlinearities, the H∞ performance is guaranteed over a given finite-horizon. The model transformation technique is first employed to simplify the addressed problem, and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite-horizon H∞ performance. Moreover, the time-varying controller parameters are characterized via solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

Quantitative single-cell splicing analysis reveals an ‘economy of scale’ filter for gene expression

In eukaryotic cells, splicing affects the fate of each pre-mRNA transcript, helping to determine whether it is ultimately processed into an mRNA, or degraded. The efficiency of splicing plays a key role in gene expression. However, because it depends on the levels of multiple isoforms at the same transcriptional active site (TAS) in the same cell, splicing efficiency has been challenging to measure. Here, we introduce a quantitative single-molecule FISH-based method that enables determination of the absolute abundances of distinct RNA isoforms at individual TASs. Using this method, we discovered that splicing efficiency behaves in an unexpected ‘economy of scale’ manner, increasing, rather than decreasing, with gene expression levels, opposite to a standard enzymatic process. This behavior could result from an observed correlation between splicing efficiency and spatial proximity to nuclear speckles. Economy of scale splicing represents a non-linear filter that amplifies the expression of genes when they are more strongly transcribed. This method will help to reveal the roles of splicing in the quantitative control of gene expression

Manin-Olshansky triples for Lie superalgebras

Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg, \fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for several series of Lie superalgebras \fa which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward superization of suitable Etingof--Kazhdan's results guarantee then the uniqueness of $q$-quantization of our Lie bialgebras. Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions. To find explicit solutions is a separate (open) problem. It is also an open problem to list (\`a la Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra \fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix

Doping dependent charge injection and band alignment in organic field-effect transistors

We have studied metal/organic semiconductor charge injection in poly(3-hexylthiophene) (P3HT) field-effect transistors with Pt and Au electrodes as a function of annealing in vacuum. At low impurity dopant densities, Au/P3HT contact resistances increase and become nonohmic. In contrast, Pt/P3HT contacts remain ohmic even at far lower doping. Ultraviolet photoemission spectroscopy (UPS) reveals that metal/P3HT band alignment shifts dramatically as samples are dedoped, leading to an increased injection barrier for holes, with a greater shift for Au/P3HT. These results demonstrate that doping can drastically alter band alignment and the charge injection process at metal/organic interfaces.Comment: 5 pages, 4 figure

Charmonium properties in hot quenched lattice QCD

We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above $T_c$. Our analysis suggests that both S wave states ($J/\psi$ and $\eta_c$) and P wave states ($\chi_{c0}$ and $\chi_{c1}$) disappear already at about $1.5 T_c$. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below $T_c$ and approximately $1/\pi T$ at $1.5 T_c\lesssim T\lesssim 3 T_c$.Comment: 32 pages, 19 figures, typo corrected, discussions on isotropic vs anisotropic lattices expanded, published versio

Performance analysis with network-enhanced complexities: On fading measurements, event-triggered mechanisms, and cyber attacks

Copyright © 2014 Derui Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Thermogravimetric kinetics of crude glycerol.

The pyrolysis of the crude glycerol from a biodiesel production plant was investigated by thermogravimetry coupled with Fourier transform infrared spectroscopy. The main gaseous products are discussed, and the thermogravimetric kinetics derived. There were four distinct phases in the pyrolysis process of the crude glycerol. The presence of water and methanol in the crude glycerol and responsible for the first decomposition phase, were shown to catalyse glycerol decomposition (second phase). Unlike the pure compound, crude glycerol decomposition below 500 K leaves behind a large mass fraction of pyrolysis residues (ca. 15%), which eventually partially eliminate in two phases upon reaching significantly higher temperatures (700 and 970 K, respectively). An improved iterative Coats-Redfern method was used to evaluate non-isothermal kinetic parameters in each phase. The latter were then utilised to model the decomposition behaviour in non-isothermal conditions. The power law model (first order) predicted accurately the main (second) and third phases in the pyrolysis of the crude glycerol. Differences of 10-30 kJ/mol in activation energies between crude and pure glycerol in their main decomposition phase corroborated the catalytic effect of water and methanol in the crude pyrolysis. The 3-D diffusion model more accurately reproduced the fourth (last) phase, whereas the short initial decomposition phase was poorly simulated despite correlation coefficients ca. 0.95-0.96. The kinetics of the 3rd and 4th decomposition phases, attributed to fatty acid methyl esters cracking and pyrolysis tarry residues, were sensitive to the heating rate

Bound States of the Heavy Flavor Vector Mesons and Y(4008) and Z1+(4050)Z^{+}_1(4050)

The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{*}\bar{B}^{*}$ molecules should exist, and the $D^{*}\bar{D}^{*}$ bound states with the same quantum numbers very likely exist as well. However, the CP exotic ($1^{-+}$, $2^{+-}$) $B^{*}\bar{B}^{*}$ and $D^{*}\bar{D}^{*}$ states may not be bound by the one boson exchange potential. We find that the I=0 configuration is more deeply bound than the I=1 configuration, hence $Z^{+}_1(4050)$ may not be a $D^{*}\bar{D}^{*}$ molecule. Although Y(4008) is close to the $D^{*}\bar{D}^{*}$ threshold, the interpretation of Y(4008) as a $D^{*}\bar{D}^{*}$ molecule is not favored by its huge width. $1^{--}$ $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ states can be produced copiously in $e^{+}e^{-}$ annihilation, detailed scanning of the $e^{+}e^{-}$ annihilation data near the $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ threshold is an important check to our predictions.Comment: 17 pages,6 figur