Homotopy nilpotent groups

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying $\pi_0$ is the theory of ordinary n-nilpotent groups and that the Goodwillie tower of a connected space is determined by a certain homotopy left Kan extension. We prove that n-excisive functors of the form $\Omega F$ have values in homotopy n-nilpotent groups.Comment: 16 pages, uses xy-pic, improved exposition, submitte

Viscosity measurement in thin lubricant films using shear ultrasonic reflection

When a shear ultrasonic wave is incident on a solid and liquid boundary, the proportion that is reflected depends on the liquid viscosity. This is the basis for some instruments for on-line measurement of bulk liquid viscosity. In machine elements, the lubricant is usually present in a thin layer between two rubbing solid surfaces. The thin film has a different response to an ultrasonic shear wave than liquid in bulk. In this work, this response is investigated with the aim of measuring viscosity in situ in a lubricating film. The proportion of the wave reflected at a thin layer depends on the layer stiffness. A shear wave is reflected by the shear stiffness of the thin layer. For a thin viscous liquid layer, the stiffness is a complex quantity dependent on the viscosity, wave frequency, and film thickness. This stiffness is incorporated into a quasi-static spring model of ultrasonic reflection. In this way, the viscosity can be determined from shear-wave reflection if the oil-film thickness is known. The approach has been experimentally evaluated on some static oil film between Perspex plates. Predictions of the spring model gave good measurement up to layer thicknesses of around 15 μm. For thicker layers, the shear stiffness reduces to such an extent that almost all the wave is reflected and the difference associated with the layer response is hard to distinguish from background noise

Normalizers of tori

We determine the groups which can appear as the normalizer of a maximal torus in a connected 2-compact group. The technique depends on using ideas of Tits to give a novel description of the normalizer of the torus in a connected compact Lie group, and then showing that this description can be extended to the 2-compact case.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper31.abs.htm

Frobenius and the derived centers of algebraic theories

We show that the derived center of the category of simplicial algebras over every algebraic theory is homotopically discrete, with the abelian monoid of components isomorphic to the center of the category of discrete algebras. For example, in the case of commutative algebras in characteristic $p$, this center is freely generated by Frobenius. Our proof involves the calculation of homotopy coherent centers of categories of simplicial presheaves as well as of Bousfield localizations. Numerous other classes of examples are discussed.Comment: 40 page

Setting Standards for Parenting - By What Right?

Mental health professionals, like other professionals involved in familymatters, feel constrained when advocating for the interests of children by the beliefthat parents are entitled to custody and control of their children\u27s lives, regardless ofwhat others may think of their parenting behavior, absent severe harm to the children.This belief is morally untenable, and the legal doctrine of parental rights that is itsconcrete embodiment is inconsistent with other well-established legal principles andshould be abandoned. Children alone should have legal rights in connection with theirupbringing, and those rights should include an entitlement to much higher standardsof parenting than the law presently imposes

Combined forced and free convection in a curved duct

The purpose of this study is to investigate the flow and heat transfer characteristics of a combined forced and free convection flow in a curved duct. Solutions are obtained by solving the low Mach number model of the Navier-Stokes equation using a control volume method. The finite-volume method was developed with the use of a predictor-corrector numerical scheme and some new variations of the classical projection method. Solutions indicated that the existence of a buoyancy force has changed the entire flow structure inside a curved duct. Reversed flow at both inner and outer bend is observed. For moderate Reynolds number, the upstream section of the duct was significantly influenced by the free convection processes. In general, heat transfer is strong at the inner bend of the beginning of the heated section and at the outer bend on the last half of the heated section. The maximum velocity location is strongly influenced by the combined effects of buoyancy and centrifugal forces. A strong buoyancy force can reduce the strength of the secondary flow where it plays an important role in mixing

Bredon Homology of Partition Complexes

We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of Bredon homology and cohomology approximation.Comment: 48 pages. Minor revisions. A typo in the statement of Corollary 1.2 was corrected, along with other typos. Some references have been adde