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

Why has China grown so fast? The role of physical and human capital formation

Cross-province growth regressions for China are estimated for the reform period. Two research questions are asked. Can the regressions help us to understand why China as a whole has grown so fast? What types of investment matter for China's growth? We address the problem of model uncertainty by adopting two approaches to model selection to consider a wide range of candidate predictors of growth. Starting from the baseline equation, the growth impact of physical and human capital is examined using panel data techniques. Both forms of capital promote economic growth. ‘Investment in innovation’ and private investment are found to be particularly important. Secondary school enrolment contributes to growth, and higher education enrolment even more so

Pattern Synthesis of Dual-band Shared Aperture Interleaved Linear Antenna Arrays

This paper presents an approach to improve the efficiency of an array aperture by interleaving two different arrays in the same aperture area. Two sub-arrays working at different frequencies are interleaved in the same linear aperture area. The available aperture area is efficiently used. The element positions of antenna array are optimized by using Invasive Weed Optimization (IWO) to reduce the peak side lobe level (PSLL) of the radiation pattern. To overcome the shortness of traditional methods which can only fulfill the design of shared aperture antenna array working at the same frequency, this method can achieve the design of dual-band antenna array with wide working frequency range. Simulation results show that the proposed method is feasible and efficient in the synthesis of dual-band shared aperture antenna array

Length Dependent Thermal Conductivity Measurements Yield Phonon Mean Free Path Spectra in Nanostructures

Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. However, nearly all of these measurements have been interpreted using an average MFP even though phonons in many crystals possess a broad MFP spectrum. Here, we present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements. Using this method, we investigate recently reported length-dependent thermal conductivity measurements on SiGe alloy nanowires and suspended graphene ribbons. We find that the recent measurements on graphene imply that 70 % of the heat in graphene is carried by phonons with MFPs longer than 1 micron

Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding

It is often of interest to decompose a total effect of an exposure into the component that acts on the outcome through some mediator and the component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator-outcome confounding

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