We construct double cross biproduct and bi-cycle bicrossproduct Lie bialgebras from braided Lie bialgebras. The main result generalizes Majids matched pairs of Lie algebras, Drinfelds quantum double, and Masuokas cross product Lie bialgebras.
Microwave reflectometry is a non-intrusive plasma diagnostic tool which is widely applied in many fusion devices. In 2014, the microwave reflectometry on Experimental Advanced Superconducting Tokamak (EAST) had been upgraded to measure plasma density profile and fluctuation, which covered the frequency range of Q-band (32-56 GHz), V-band (47-76 GHz) and W-band (71-110 GHz). This paper presented a dedicated data acquisition and control system (DAQC) to meet the measurement requirements of high accuracy and temporal resolution. The DAQC consisted of two control modules, which integrated arbitrary waveform generation block (AWG) and trigger processing block (TP), and two data acquisition modules (DAQ) that was implemented base on the PXIe platform from National Instruments (NI). All the performance parameters had satisfied the requirements of reflectometry. The actual performance will be further examined in the experiments of EAST in 2014.
Planar functions in odd characteristic were introduced by Dembowski and Ostrom in order to construct finite projective planes in 1968. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and signal sets. Recently, a new notion of pseudo-planar functions in even characteristic was proposed by Zhou. These new pseudo-planar functions, as an analogue of planar functions in odd characteristic, also bring about finite projective planes. There are three known infinite families of pseudo-planar monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In this paper, three new classes of pseudo-planar binomials are provided. Moreover, we find that each pseudo-planar function gives an association scheme which is defined on a Galois ring.
By introducing a predictive mechanism with small-world connections, we propose a new motion protocol for self-driven flocks. The small-world connections are implemented by randomly adding long-range interactions from the leader to a few distant agents, namely pseudo-leaders. The leader can directly affect the pseudo-leaders, thereby influencing all the other agents through them efficiently. Moreover, these pseudo-leaders are able to predict the leaders motion several steps ahead and use this information in decision making towards coherent flocking with more stable formation. It is shown that drastic improvement can be achieved in terms of both the consensus performance and the communication cost. From the industrial engineering point of view, the current protocol allows for a significant improvement in the cohesion and rigidity of the formation at a fairly low cost of adding a few long-range links embedded with predictive capabilities. Significantly, this work uncovers an important feature of flocks that predictive capability and long-range links can compensate for the insufficiency of each other. These conclusions are valid for both the attractive/repulsive swarm model and the Vicsek model.
