A simple parametrization for G2

We give a simple parametrization of the $G_2$ group, which is consistent with the structure of $G_2$ as a SU(3) fibration. We also explicitly compute the (bi)invariant measure, which turns out to have a simple expression.Comment: 9 page

Local area network with fault-checking, priorities, and redundant backup

This invention is a redundant error detecting and correcting local area networked computer system having a plurality of nodes each including a network connector board within the node for connecting to an interfacing transceiver operably attached to a network cable. There is a first network cable disposed along a path to interconnect the nodes. The first network cable includes a plurality of first interfacing transceivers attached thereto. A second network cable is disposed in parallel with the first cable and, in like manner, includes a plurality of second interfacing transceivers attached thereto. There are a plurality of three position switches each having a signal input, three outputs for individual selective connection to the input, and a control input for receiving signals designating which of the outputs is to be connected to the signal input. Each of the switches includes means for designating a response address for responding to addressed signals appearing at the control input and each of the switches further has its signal input connected to a respective one of the input/output lines from the nodes. Also, one of the three outputs is connected to a repective one of the plurality of first interfacing transceivers. There is master switch control means having an output connected to the control inputs of the plurality of three position switches and an input for receiving directive signals for outputting addressed switch position signals to the three position switches as well as monitor and control computer means having a pair of network connector boards therein connected to respective ones of one of the first interfacing transceivers and one of the second interfacing transceivers and an output connected to the input of the master switch means for monitoring the status of the networked computer system by sending messages to the nodes and receiving and verifying messages therefrom and for sending control signals to the master switch to cause the master switch to cause respective ones of the nodes to use a desired one of the first and second cables for transmitting and receiving messages and for disconnecting desired ones of the nodes from both cables

Classical strings in AdS4×CP3AdS_4\times\mathbb{CP}^3 with three angular momenta

In this paper, rotating strings in three directions of $AdS_4 \times \mathbb{CP}^3$ geometry are studied; its divergent energy limit, and conserved charges are also determined. An interpretation of these configurations as either giant magnons or spiky strings are discussed

Squaring the Magic

We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS, the single-split G\"unaydin-Sierra-Townsend MS, and the double-split Barton-Sudbery MS, we obtain other 7 Euclidean and 10 Lorentzian novel MS's. We elucidate the role and the meaning of the various non-compact real forms of Lie algebras, entering the MS's as symmetries of theories of Einstein-Maxwell gravity coupled to non-linear sigma models of scalar fields, possibly endowed with local supersymmetry, in D = 3, 4 and 5 space-time dimensions. In particular, such symmetries can be recognized as the U-dualities or the stabilizers of scalar manifolds within space-time with standard Lorentzian signature or with other, more exotic signatures, also relevant to suitable compactifications of the so-called M*- and M'- theories. Symmetries pertaining to some attractor U-orbits of magic supergravities in Lorentzian space-time also arise in this framework.Comment: 21 pages, 1 figure, 20 tables; reference adde