scholarly journals HARD-PnP: PnP Optimization Using a Hybrid Approximate Representation

2019 ◽  
Vol 41 (3) ◽  
pp. 768-774 ◽  
Author(s):  
Simon Hadfield ◽  
Karel Lebeda ◽  
Richard Bowden
Keyword(s):  
Approximate Representation

XIX.—On the Reciprocation of Certain Matrices

1940 ◽  
Vol 59 ◽  
pp. 195-206 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Moment Matrix ◽  
Approximate Representation ◽  
Reciprocal Matrix ◽  
Image Position

In a recent paper (Frazer, Jones, and Skan, 1937) some methods are discussed for the approximate representation of functions by means of polynomials. The coefficients in the polynomials are determined by the equationwhere c is the column of coefficients, h is a column of known constants, and M is a matrix which depends on the method of representation adopted. The present paper shows how the reciprocal matrix M-1 can be computed rapidly and simply in the two cases where M is a moment matrix or an alternant matrix.

The Propagation of Compressional Waves in a Dispersive Elastic Rod: Part II—Experimental Results and Comparison With Theory

1957 ◽  
Vol 24 (2) ◽  
pp. 240-244
Author(s):  
Julius Miklowitz ◽  
C. R. Nisewanger
Keyword(s):  
Shock Tube ◽  
Longitudinal Mode ◽  
Long Waves ◽  
Experimental Results ◽  
Radial Mode ◽  
Approximate Representation ◽  
Elastic Rod ◽  
Compressional Waves ◽  
Short Waves

Abstract Experimental results, obtained by employing an aerodynamic shock tube for rod excitation, are presented. Comparison of these results with the theoretical information presented in Part I is made. It is shown that the Mindlin-Herrmann theory, through its upper mode (radial), offers a good approximate representation of the moderately short waves that predominate at the later times at a random station of the rod. The very short waves of this same radial mode, however, govern the early disturbance, thus precluding the possibility of representing this portion of the disturbance, which the experiment shows to be composed of relatively long waves, by the longitudinal mode of the theory.

Paper 6: A Thermohydrodynamic Analysis of Journal Bearings

1966 ◽  
Vol 181 (15) ◽  
pp. 117-126 ◽  
Author(s):  
D. Dowson ◽  
C. N. March
Keyword(s):  
Heat Conduction ◽  
Journal Bearing ◽  
Journal Bearings ◽  
General Nature ◽  
Two Dimensional ◽  
Approximate Representation ◽  
Full Account ◽  
Design Procedures ◽  
Experimental Findings ◽  
Energy Equations

A thermohydrodynamic analysis is discussed which takes account of the general nature of the experimental observations in work which forms part of a programme of research designed to develop an improved understanding of better design procedures for journal bearings. The analysis considers compatible solutions of the Reynolds, energy, and heat conduction equations for two-dimensional conditions. It is shown that the solutions are in reasonable agreement with experimental findings. The two-dimensional solutions of the Reynolds and energy equations take full account of the variation of lubricant properties along and across the film. A very simple and approximate representation is used to estimate the temperature distribution in the bush, but the solutions present a reasonable estimate of bush and shaft temperatures. The ‘thermohydrodynamic’ or ‘heat conduction’ solution to journal bearing problems will provide intermediate, and it is hoped more realistic, results between the extreme ‘isothermal’ and ‘adiabatic’ conditions.

Weakly Stable Relations and Inductive Limits ofC*-algebras

2003 ◽  
Vol 46 (4) ◽  
pp. 588-596
Author(s):  
Martha Salerno Monteiro
Keyword(s):  
Exact Representation ◽  
Approximate Representation ◽  
Inductive Limits ◽  
Weakly Stable ◽  
Formal Relations

AbstractWe show that ifAis a class ofC*-algebras for which the set of formal relationsRis weakly stable, thenRis weakly stable for the classBthat containsAand all the inductive limits that can be constructed with theC*-algebras inA.A set of formal relationsRis said to beweakly stablefor a classofC*-algebras if, in anyC*-algebra A ∈, close to an approximate representation of the setRinAthere is an exact representation ofRinA.

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