25,790 research outputs found

    Octonion X,Y-Product G2G_{2} Variants

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    The automorphism group G2G_{2} of the octonions changes when octonion X,Y-product variants are used. I present here a general solution for how to go from G2G_{2} to its X,Y-product variant.Comment: 5 pages, latex, no figure

    Classical String in Curved Backgrounds

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    The Mathisson-Papapetrou method is originally used for derivation of the particle world line equation from the covariant conservation of its stress-energy tensor. We generalize this method to extended objects, such as a string. Without specifying the type of matter the string is made of, we obtain both the equations of motion and boundary conditions of the string. The world sheet equations turn out to be more general than the familiar minimal surface equations. In particular, they depend on the internal structure of the string. The relevant cases are classified by examining canonical forms of the effective 2-dimensional stress-energy tensor. The case of homogeneously distributed matter with the tension that equals its mass density is shown to define the familiar Nambu-Goto dynamics. The other three cases include physically relevant massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc

    Legislative Apportionment and the Federal Constitution

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    Hydraulic servo system increases accuracy in fatigue testing

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    Hydraulic servo system increases accuracy in applying fatigue loading to a specimen under test. An error sensing electronic control loop, coupled to the hydraulic proportional closed loop cyclic force generator, provides an accurately controlled peak force to the specimen

    Spinning branes in Riemann-Cartan spacetime

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    We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form. In the particle case, the resultant world-line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of a zero-size particle does not couple to the background curvature. In the string case, the world-sheet dynamics is studied for some special choices of spin and torsion. As a result, the known coupling to the Kalb-Ramond antisymmetric external field is obtained. Geometrically, the Kalb-Ramond field has been recognized as a part of the torsion itself, rather than the torsion potential

    Active vibration isolator for flexible bodies Patent

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    Vibration control of flexible bodies in steady accelerating environmen

    Improved active vibration isolator

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    Active vibration isolator simultaneously isolates a flexible structure or payload from disturbances, attenuates the response of a flexible structure to transient disturbances, and maintains the equilibrium position of the payload within predetermined limits over a wide range of steady loads and accelerators

    Some finite solvable groups with non-trivial lattice endomorphisms

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    The main purpose of this paper is to exhibit a doubly-infinite family of examples which are extensions of a p-group by a p′-group, with the action satisfying some conditions of Zappa (1951), arising from his study of dual-standard (meet-distributive) subgroups. The examples show that Zappa's conditions do not bound the nilpotency class (or even the derived length) of the p-group. The key to this work is found in closely related conditions of Hartley (published here for the first time). The examples use some exceptional relationships between primes
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