The Compact Approximation Property does not imply the Approximation Property

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property

Development potential of Intermittent Combustion (I.C.) aircraft engines for commuter transport applications

An update on general aviation (g/a) and commuter aircraft propulsion research effort is reviewed. The following topics are discussed: on several advanced intermittent combustion engines emphasizing lightweight diesels and rotary stratified charge engines. The current state-of-the-art is evaluated for lightweight, aircraft suitable versions of each engine. This information is used to project the engine characteristics that can be expected on near-term and long-term time horizons. The key enabling technology requirements are identified for each engine on the long-term time horizon

Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms

To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local field, it is a natural idea to try to define a map from the space of directions of analytic automorphisms of G to the space of directions of automorphisms of the Lie algebra L(G) of G, which takes the direction of an analytic automorphism of G to the direction of the associated Lie algebra automorphism. We show that, in general, this map is not well-defined. However, the pathology cannot occur for a large class of linear algebraic groups (called ``generalized Cayley groups'' here). For such groups, the assignment just proposed defines a well-defined isometric embedding from the space of directions of inner automorphisms of G to the space of directions of automorphisms of L(G). Some counterexamples concerning the existence of small joint tidy subgroups for flat groups of automorphisms are also provided.Comment: 20 pages, LaTe

The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group

To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically transitive. Topologically transitive actions of automorphisms of compact groups have been studied extensively in topological dynamics and results obtained transfer, via the nub, to the study of automorphisms of general locally compact groups. A new proof that the contraction group of $\alpha$ is dense in the nub is given, but it is seen that the two-sided contraction group need not be dense. It is also shown that each pair $(G,\alpha)$, with $G$ compact and $\alpha$ topologically transitive, is an inverse limit of pairs that have `finite depth' and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold for pairs with finite depth

Rotary engine performance limits predicted by a zero-dimensional model

A parametric study was performed to determine the performance limits of a rotary combustion engine. This study shows how well increasing the combustion rate, insulating, and turbocharging increase brake power and decrease fuel consumption. Several generalizations can be made from the findings. First, it was shown that the fastest combustion rate is not necessarily the best combustion rate. Second, several engine insulation schemes were employed for a turbocharged engine. Performance improved only for a highly insulated engine. Finally, the variability of turbocompounding and the influence of exhaust port shape were calculated. Rotary engines performance was predicted by an improved zero-dimensional computer model based on a model developed at the Massachusetts Institute of Technology in the 1980's. Independent variables in the study include turbocharging, manifold pressures, wall thermal properties, leakage area, and exhaust port geometry. Additions to the computer programs since its results were last published include turbocharging, manifold modeling, and improved friction power loss calculation. The baseline engine for this study is a single rotor 650 cc direct-injection stratified-charge engine with aluminum housings and a stainless steel rotor. Engine maps are provided for the baseline and turbocharged versions of the engine

Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials)

Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain semistandard tableaux of shape lambda. Let pi be an n-permutation. The type A Demazure character (key polynomial, Demazure polynomial) indexed by lambda and pi is another such polynomial generating function. Reiner and Shimozono and then Postnikov and Stanley studied coincidences between these two families of polynomials. Here their results are sharpened by the specification of unique representatives for the equivalence classes of indexes for both families of polynomials, extended by the consideration of more general beta, and deepened by proving that the polynomial coincidences also hold at the level of the underlying tableau sets. Let R be the set of lengths of columns in the shape of lambda that are less than n. Ordered set partitions of {1,..,n} with block sizes determined by R, called R-permutations, are used to describe the minimal length representatives for the parabolic quotient of the nth symmetric group specified by the set {1,..,n-1}\R. The notion of 312-avoidance is generalized from n-permutations to these set partitions. The R-parabolic Catalan number is defined to be the number of these. Every flagged Schur function arises as a Demazure polynomial. Those Demazure polynomials are precisely indexed by the R-312-avoiding R-permutations. Hence the number of flagged Schur functions that are distinct as polynomials is shown to be the R-parabolic Catalan number. The projecting and lifting processes that relate the notions of 312-avoidance and of R-312-avoidance are described with maps developed for other purposes.Comment: 27 pages, 2 figures. Identical to v.2, except for the insertion of the publication data for the DMTCS journal (dates and volume/issue/number). This is two-thirds of our preprint "Parabolic Catalan numbers count flagged Schur functions; Convexity of tableau sets for Demazure characters", arXiv:1612.06323v

Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities: alg-rk(W)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the maximal $\mathbb{Z}$-rank of abelian subgroups of W, and rk(|W|\_0) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|\_0. We can prove these inequalities under weaker assumptions. We also show that for any integer n \geq 1 there is a topologically simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G)=n and which is not linear