scholarly journals Erratum: Spherical representation of omnipotent Smith chart

2009 ◽  
Vol 51 (9) ◽  
pp. 2255-2255
Author(s):  
Yongle Wu ◽  
Haiyu Huang ◽  
Yuanan Liu ◽  
Zehua Gao
Keyword(s):  
Spherical Representation ◽  
Smith Chart

Spherical representation of omnipotent Smith chart

2008 ◽  
Vol 50 (9) ◽  
pp. 2452-2455 ◽  
Author(s):  
Yongle Wu ◽  
Haiyu Huang ◽  
Yuanan Liu ◽  
Zehua Gao
Keyword(s):  
Spherical Representation ◽  
Smith Chart

Concentric Spherical Representation for Omnidirectional Soft Shadow

2013 ◽  
Vol 32 (6) ◽  
pp. 201-213 ◽  
Author(s):  
Yi Xiao ◽  
Chi Sing Leung ◽  
Tze Yui Ho ◽  
Liang Wan ◽  
Tien Tsing Wong
Keyword(s):  
Spherical Representation ◽  
Soft Shadow

Selecting a Compressor Meridional Topology: Axial, Mixed, Radial

2021 ◽  
Author(s):  
Jonathan M. Smyth ◽  
Robert J. Miller
Keyword(s):  
Design Optimization ◽  
Early Stage ◽  
New Products ◽  
Systems Design ◽  
Blade Design ◽  
Improved Method ◽  
Stage Design ◽  
Specific Speed ◽  
Early Stage Design ◽  
Smith Chart

Abstract This paper proposes a new duty-based Smith Chart as part of an improved method of selecting the geometric topology of compressors (axial, mixed or radial) in the earliest stage of design. The method has a number of advantages over previous methods: it is based on the non-dimensional flow and the non-dimensional work, which aligns with the aerodynamic function of the compressor and is therefore more intuitive than specific speed and specific diameter. It is based on a large number of consistently designed compressor rotors which have been computationally predicted using RANS CFD. Most importantly, it provides the designer not only with a choice of topology but also with the complete meridional geometry of the compressor, its blade design and the number of blades. This fidelity of geometry at the very early stage of design allows the designer to undertake a true systems design optimization (noise, manufacturing, packaging constraints and cost). This has the major advantage of significantly reducing early stage design times and costs and allows the designer to explore completely new products more quickly.

Images, Imagination, and Movement: Pictorial Representations and Their Development in the Work of James Gibson

Perception ◽  
10.1068/p2976 ◽  
2000 ◽  
Vol 29 (6) ◽  
pp. 635-648 ◽  
Author(s):  
James E Cutting
Keyword(s):  
Vector Field ◽  
Optical Flow ◽  
Spherical Representation ◽  
Pictorial Representations ◽  
The Relationship

For more than 30 years James Gibson studied pictures and he studied motion, particularly the relationship between movement through an environment and its visual consequences. For the latter, he also struggled with how best to present his ideas to students and fellow researchers, and employed various representations and formats. This article explores the relationships between the concepts of the fidelity of pictures (an idea he first promoted and later eschewed) and evocativeness as applied to his images. Gibson ended his struggle with an image of a bird flying over a plane surrounded by a spherical representation of a vector field, an image high in evocativeness but less than completely faithful to optical flow.

scholarly journals Casselman’s Basis of Iwahori Vectors and the Bruhat Order

2011 ◽  
Vol 63 (6) ◽  
pp. 1238-1253 ◽  
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Weyl Group ◽  
Bruhat Order ◽  
Group Element ◽  
The Other ◽  
Intertwining Operators ◽  
Transition Matrices ◽  
Natural Basis ◽  
Spherical Representation ◽  
Langlands Parameters ◽  
Combinatorial Condition

AbstractW. Casselman defined a basis fu of Iwahori fixed vectors of a spherical representation of a split semisimple p-adic group G over a nonarchimedean local field F by the condition that it be dual to the intertwining operators, indexed by elements u of the Weyl group W. On the other hand, there is a natural basis , and one seeks to find the transition matrices between the two bases. Thus, let and . Using the Iwahori–Hecke algebra we prove that if a combinatorial condition is satisfied, then , where z are the Langlands parameters for the representation and α runs through the set S(u, v) of positive coroots (the dual root systemof G) such that with rα the reflection corresponding to α. The condition is conjecturally always satisfied if G is simply-laced and the Kazhdan–Lusztig polynomial Pw0v,w0u = 1 with w0 the long Weyl group element. There is a similar formula for conjecturally satisfied if Pu,v = 1. This leads to various combinatorial conjectures.

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