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Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots, Cornelia A. Van Cott
Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots, Cornelia A. Van Cott
Mathematics
We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants τ and s on Km,n, the (m,n)–cable of a knot K where m and n are relatively prime. We show that for every knot K and for any fixed positive integer m, both of the invariants evaluated on Km,n differ from their value on the torus knot Tm,n by fixed constants for all but finitely many n>0. Combining this result together with Hedden’s extensive work on the behavior of τ on (m,mr+1)–cables yields bounds on the value of τ on any (m,n)–cable of K. In addition, several …
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ", Stephen Devlin, T Treloar
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ", Stephen Devlin, T Treloar
Mathematics
We respond to the comment of Zhu et al. [Phys. Rev. E 82, 038101 (2010)] and show that the results in question are not misleading.
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Mathematics
The standard plan for the assessment of the variation due to a measurement system involves a number of operators repeatedly measuring a number of parts in a balanced design. In this article, we consider the performance of two types of (unbalanced) assessment plans. In each type, we use a standard plan augmented with a second component. In type A augmentation, each operator measures a different set of parts once each. In type B augmentation, each operator measures the same set of parts once each. The goal of the paper is to identify good augmented plans for estimating the gauge repeatability …