Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients

AbstractWe obtain results on the unitary equivalence of weak contractions of class C0 to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool in this paper is the theory of boundary representations due to Arveson. We also generalize and improve previously known results concerning unitary equivalence and similarity to Jordan models when the minimal function is a Blaschke product.

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Form Feature Recognition Using Base Volume Decomposition

20th Design Automation Conference: Volume 1 — Dynamic Mechanical Systems; Geometric Modeling and Features; Concurrent Engineering ◽

10.1115/detc1994-0069 ◽

1994 ◽

Author(s):

James K. Coles ◽

Richard H. Crawford ◽

Kristin L. Wood

Keyword(s):

Real World ◽

Feature Recognition ◽

Recognition Method ◽

Mechanical Parts ◽

Feature Representations ◽

Volume Decomposition ◽

Boundary Representations ◽

New Feature ◽

Form Feature

Abstract A new feature recognition method is presented that generates volumetric feature representations from conventional boundary representations of mechanical parts. Recognition is accomplished by decomposing the known total feature volume of a part into a set of smaller volumes through analytic face extension. The decomposed volumes are combined to generate an initial set of features. Alternative sets of features are generated by maintaining and evaluating information on intersections of the initial feature set. The capabilities of the method are demonstrated through both a hypothetical and a real world design example. The method’s ability to locate features despite interactions with other features, and its ability to generate alternative sets of features, distinguishes it from existing recognition techniques.

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From Modeling to 3D Printing

Advances in Chemical and Materials Engineering - 3D Printing and Its Impact on the Production of Fully Functional Components ◽

10.4018/978-1-5225-2289-8.ch002 ◽

2017 ◽

pp. 25-37 ◽

Cited By ~ 1

Keyword(s):

3D Printing ◽

Internal Representation ◽

Modeling Process ◽

Wire Frame ◽

G Code ◽

3D Printers ◽

Boundary Representations ◽

Code Standard ◽

Printing Parameters ◽

Bézier Spline

Geometric or 3D modeling playing key role in geometry definition. These modelers evolved from wire-frame models to Boundary representations or CSG models in solid modeling or Bezier spline or Non-uniform rational B-spline representation. After modeling process, using internal representation, part will be post-processed for manufacturing. Variety of postprocessors existing, and using unique G-code standard we producing on CNC machines requested parts. 3D Printers use the same G-Code standards with extensions for more than ten M functions that programmers use for setting 3D printing parameters different than we using for CNC manufacturing. List of M functions varies depend of the manufacturer.

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