Satellite operators as group actions on knot concordance

Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operators which form a group (unlike traditional satellite operators), modulo a generalization of concordance. This group has an action on the set of knots in homology spheres, using which we recover the recent result of Cochran and the authors that satellite operators with strong winding number $\pm 1$ give injective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture. The notion of generalized satellite operators yields a characterization of surjective satellite operators, as well as a sufficient condition for a satellite operator to have an inverse. As a consequence, we are able to construct infinitely many non-trivial satellite operators P such that there is a satellite operator $\overline{P}$ for which $\overline{P}(P(K))$ is concordant to K (topologically as well as smoothly in a potentially exotic $S^3\times [0,1]$) for all knots K; we show that these satellite operators are distinct from all connected-sum operators, even up to concordance, and that they induce bijective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture.Comment: 20 pages, 9 figures; in the second version, we have added several new results about surjectivity of satellite operators, and inverses of satellite operators, and the exposition and structure of the paper have been improve

Orbital eccentricity of binary radio pulsars in globular clusters and interaction between stars

We analyze the observed distribution of the orbital eccentricity and period of binary radio pulsars in globular clusters using computational tools to simulate binary-single star interactions. Globular clusters have different groups of pulsars arising from separate interaction scenarios. Intermediate eccentricities of cluster pulsars can be mostly accounted by fly-bys although locally lower stellar densities at pulsar positions may alter the situation. Very high eccentricities are likely to be results of exchanges and/or mergers of single stars with the binary companion of the pulsar.Comment: Accepted for publication in ApJ Letters; version modified after referee's comment

Blade Tip Rubbing Stress Prediction

An analytical model was constructed to predict the magnitude of stresses produced by rubbing a turbine blade against its tip seal. This model used a linearized approach to the problem, after a parametric study, found that the nonlinear effects were of insignificant magnitude. The important input parameters to the model were: the arc through which rubbing occurs, the turbine rotor speed, normal force exerted on the blade, and the rubbing coefficient of friction. Since it is not possible to exactly specify some of these parameters, values were entered into the model which bracket likely values. The form of the forcing function was another variable which was impossible to specify precisely, but the assumption of a half-sine wave with a period equal to the duration of the rub was taken as a realistic assumption. The analytical model predicted resonances between harmonics of the forcing function decomposition and known harmonics of the blade. Thus, it seemed probable that blade tip rubbing could be at least a contributor to the blade-cracking phenomenon. A full-scale, full-speed test conducted on the space shuttle main engine high pressure fuel turbopump Whirligig tester was conducted at speeds between 33,000 and 28,000 RPM to confirm analytical predictions

Near-infrared Fabry-Perot imaging of Herbig-Haro energy sources: Collimated, small-scale H2 jets and wide-angled winds

Peer reviewe

Concordance of knots in S1×S2S^1\times S^2

We establish a number of results about smooth and topological concordance of knots in $S^1\times S^2$. The winding number of a knot in $S^1\times S^2$ is defined to be its class in $H_1(S^1\times S^2;\mathbb{Z})\cong \mathbb{Z}$. We show that there is a unique smooth concordance class of knots with winding number one. This improves the corresponding result of Friedl-Nagel-Orson-Powell in the topological category. We say a knot in $S^1\times S^2$ is slice (resp. topologically slice) if it bounds a smooth (resp. locally flat) disk in $D^2\times S^2$. We show that there are infinitely many topological concordance classes of non-slice knots, and moreover, for any winding number other than $\pm 1$, there are infinitely many topological concordance classes even within the collection of slice knots. Additionally we demonstrate the distinction between the smooth and topological categories by constructing infinite families of slice knots that are topologically but not smoothly concordant, as well as non-slice knots that are topologically slice and topologically concordant, but not smoothly concordant.Comment: 25 pages, 19 figures, final version, to appear in Journal of London Mathematical Societ

The Formal Underpinnings of the Response Functions used in X-Ray Spectral Analysis

This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data where they may be identified with the quantities contained in the Ancillary Response File (ARF), the Redistribution Matrix File (RMF), and the Exposure Map. Starting from first-principles, explicit mathematical expressions for these functions, for both imaging and dispersive modes, are arrived at in terms of the underlying instrumental characteristics of the telescope including the effects of pointing motion. The response functions are presented in the context of integral equations relating the expected detector count rate to the source spectrum incident upon the telescope. Their application to the analysis of several source distributions is considered. These include multiple, possibly overlapping, and spectrally distinct point sources, as well as extended sources. Assumptions and limitations behind the usage of these functions, as well as their practical computation are addressed.Comment: 22 pages, 3 figures (LaTeX

Mandamus to Review Administrative Action in West Virginia

Limitation by law of governmental action and legal responsibility of officials are ramparts in defense of constitutional democracy. The American people expect all branches of government-executive and legislative, as well as judicial-to protect us against arbitrary official action. Lawyers, however, are primarily interested in judicial restraints and limitations upon officialdom. This article is an examination of the West Virginia law concerning one of the methods used by courts to control administrative officers-the writ of mandamus