hyperbolic weight
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2016 ◽  
Vol 25 (08) ◽  
pp. 1650048
Author(s):  
Marco Marengon

We prove that for particular infinite families of [Formula: see text]-spaces, arising as branched double covers, the [Formula: see text]-invariants defined by Ozsváth and Szabó assume arbitrarily large positive and negative values. As a consequence, we generalize a result by Greene and Watson by proving, for every odd number [Formula: see text], the existence of infinitely many non-quasi-alternating homologically thin knots with determinant [Formula: see text], and a result by Hoffman and Walsh concerning the existence of hyperbolic weight [Formula: see text] manifolds, that are not surgery on a knot in [Formula: see text].



2014 ◽  
Vol 96 (5-6) ◽  
pp. 904-913 ◽  
Author(s):  
D. V. Gorbachev ◽  
V. I. Ivanov ◽  
R. A. Veprintsev


It has been observed that for a lead wire, loaded well beyond the elastic limit, the extension after some time becomes proportional to the time, or the flow becomes viscous in character. The rate of this viscous flow varies with the load, and the following work was undertaken to investigate the law of this variation, and the phenomenon in general. Methods of Experiment. The Hyperbolic Weight . The experiments were all done on wires of the metal, and the preliminary observations were all made on lead. To suspend the wires, they were soldered into stout brass hooks. In the first rough experiments the extension registered itself on a clockwork-driven drum; these experiments showed that the rate of extension for a given load became constant for a time, but finally increased, and continued increasing. This is due to two causes: (1) As the wire stretches, the length of wire being experimented on at any moment increases. (2) As the wire stretches, the cross-section diminishes, and thus the load per unit area or stress increases. This is by far the more disturbing cause, since, as shown later, the rate increases much more rapidly with the stress than would be given by a linear law. To obviate this difficulty an automatic method of keeping the stress constant was devised.



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