Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper is to study generalized Clifford algebras in a similar manner and extend the results of Albuquerque, Majid and Bulacu to the generalized setting. In particular, by taking full advantage of the gauge transformations in symmetric linear Gr-categories, we derive the decomposition theorem and provide categorical weak Hopf structures for generalized Clifford algebras in a conceptual and simpler manner

Performance Scaling Law for Multi-Cell Multi-User Massive MIMO

This work provides a comprehensive scaling law based performance analysis for multi-cell multi-user massive multiple-input-multiple-output (MIMO) downlink systems. Imperfect channel state information (CSI), pilot contamination, and channel spatial correlation are all considered. First, a sum- rate lower bound is derived by exploiting the asymptotically deterministic property of the received signal power, while keeping the random nature of other components in the signal-to-interference-plus-noise-ratio (SINR) intact. Via a general scaling model on important network parameters, including the number of users, the channel training energy and the data transmission power, with respect to the number of base station antennas, the asymptotic scaling law of the effective SINR is obtained, which reveals quantitatively the tradeoff of the network parameters. More importantly, pilot contamination and pilot contamination elimination (PCE) are considered in the analytical framework. In addition, the applicability of the derived asymptotic scaling law in practical systems with large but finite antenna numbers are discussed. Finally, sufficient conditions on the parameter scalings for the SINR to be asymptotically deterministic in the sense of mean square convergence are provided, which covers existing results on such analysis as special cases and shows the effect of PCE explicitly.Comment: 14 pages, 7 figures, accepted by IEEE Transactions on Vehicular Technolog

Interleaved Training and Training-Based Transmission Design for Hybrid Massive Antenna Downlink

In this paper, we study the beam-based training design jointly with the transmission design for hybrid massive antenna single-user (SU) and multiple-user (MU) systems where outage probability is adopted as the performance measure. For SU systems, we propose an interleaved training design to concatenate the feedback and training procedures, thus making the training length adaptive to the channel realization. Exact analytical expressions are derived for the average training length and the outage probability of the proposed interleaved training. For MU systems, we propose a joint design for the beam-based interleaved training, beam assignment, and MU data transmissions. Two solutions for the beam assignment are provided with different complexity-performance tradeoff. Analytical results and simulations show that for both SU and MU systems, the proposed joint training and transmission designs achieve the same outage performance as the traditional full-training scheme but with significant saving in the training overhead.Comment: 16 Pages (double column), 11 figures. This work has been accepted by the IEEE Journal of Selected Topics in Signal Processing (JSTSP), Special Issue on Hybrid Analog - Digital Signal Processing for Hardware-Efficient Large Scale Antenna Arrays. This version is different from the former one due to the revisions made for the comments of 1st and 2nd round revie

Analysis of Weak-Interaction Effects in High Energy Hadron-Hadron Collisions

Parity-violating (pv) effects in inclusive hadron and jet productions in high energy hadron-hadron collisions are analyzed. Such effects arise from the interference between strong and weak amplitudes. This interference gives rise to a nonzero value of the pv parameters $A_L$ and $P_L$, where $A_L$ measures the difference in the inclusive cross sections of, for example, p+p\ri {\rm jet}+X ($X$=anything), with one of incident proton beams in a state of $\pm$ helicity, and $P_L$ denotes the longitudinal polarization of a high-energy baryon (e.g., $\Lambda$) produced in p+p\ri\Lambda+X with the initial proton beams unpolarized. In the present paper, the single helicity asymmetry $A_L$ in one-jet, two-jet and two-jet plus photon productions as well as in the Drell-Yan process p+p\ri\ell^+\ell^-+{\rm jet}+X is probed, and the longitudinal polarization $P_L$ of the $\Lambda$ produced in unpolarized $pp$ collisions is studied. We conclude that the pv effects in high energy proton-proton collisions are in general only sensitive to the spin dependent valence quark distributions.Comment: Latex, 20 pages, 10 figures available upon request, ITP-SB-93-07 and IP-ASTP-05-9

pH-responsive gas–water–solid interface for multiphase catalysis

© 2015 American Chemical Society. Despite their wide utility in laboratory synthesis and industrial fabrication, gas-water-solid multiphase catalysis reactions often suffer from low reaction efficiency because of the low solubility of gases in water. Using a surface-modification protocol, interface-active silica nanoparticles were synthesized. Such nanoparticles can assemble at the gas-water interface, stabilizing micrometer-sized gas bubbles in water, and disassemble by tuning of the aqueous phase pH. The ability to stabilize gas microbubbles can be finely tuned through variation of the surface-modification protocol. As proof of this concept, Pd and Au were deposited on these silica nanoparticles, leading to interface-active catalysts for aqueous hydrogenation and oxidation, respectively. With such catalysts, conventional gas-water-solid multiphase reactions can be transformed to H 2 or O 2 microbubble reaction systems. The resultant microbubble reaction systems exhibit significant catalysis efficiency enhancement effects compared with conventional multiphase reactions. The significant improvement is attributed to the pronounced increase in reaction interface area that allows for the direct contact of gas, water, and solid phases. At the end of reaction, the microbubbles can be removed from the reaction systems through changing the pH, allowing product separation and catalyst recycling. Interestingly, the alcohol oxidation activation energy for the microbubble systems is much lower than that for the conventional multiphase reaction, also indicating that the developed microbubble system may be a valuable platform to design innovative multiphase catalysis reactions