Core compressor exit stage study. 1: Aerodynamic and mechanical design

The effect of aspect ratio on the performance of core compressor exit stages was demonstrated using two three stage, highly loaded, core compressors. Aspect ratio was identified as having a strong influence on compressors endwall loss. Both compressors simulated the last three stages of an advanced eight stage core compressor and were designed with the same 0.915 hub/tip ratio, 4.30 kg/sec (9.47 1bm/sec) inlet corrected flow, and 167 m/sec (547 ft/sec) corrected mean wheel speed. The first compressor had an aspect ratio of 0.81 and an overall pressure ratio of 1.357 at a design adiabatic efficiency of 88.3% with an average diffusion factor or 0.529. The aspect ratio of the second compressor was 1.22 with an overall pressure ratio of 1.324 at a design adiabatic efficiency of 88.7% with an average diffusion factor of 0.491

High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion

The present paper is devoted to the study of sample paths of G-Brownian motion and stochastic differential equations (SDEs) driven by G-Brownian motion from the view of rough path theory. As the starting point, we show that quasi-surely, sample paths of G-Brownian motion can be enhanced to the second level in a canonical way so that they become geometric rough paths of roughness 2 < p < 3. This result enables us to introduce the notion of rough differential equations (RDEs) driven by G-Brownian motion in the pathwise sense under the general framework of rough paths. Next we establish the fundamental relation between SDEs and RDEs driven by G-Brownian motion. As an application, we introduce the notion of SDEs on a differentiable manifold driven by GBrownian motion and construct solutions from the RDE point of view by using pathwise localization technique. This is the starting point of introducing G-Brownian motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin. The last part of this paper is devoted to such construction for a wide and interesting class of G-functions whose invariant group is the orthogonal group. We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian motion of independent interest

A requirement for bone morphogenetic protein-7 during development of the mammalian kidney and eye.

BMP-7/OP-1, a member of the transforming growth factor-beta (TGF-beta) family of secreted growth factors, is expressed during mouse embryogenesis in a pattern suggesting potential roles in a variety of inductive tissue interactions. The present study demonstrates that mice lacking BMP-7 display severe defects confined to the developing kidney and eye. Surprisingly, the early inductive tissue interactions responsible for establishing both organs appear largely unaffected. However, the absence of BMP-7 disrupts the subsequent cellular interactions required for their continued growth and development. Consequently, homozygous mutant animals exhibit renal dysplasia and anophthalmia at birth. Overall, these findings identify BMP-7 as an essential signaling molecule during mammalian kidney and eye development