Optical symbolic substitution using lenslet arrays

1993 ◽  
Vol 32 (4) ◽  
pp. 847 ◽  
Author(s):  
Kenji Matsushita
Keyword(s):  
Symbolic Substitution

Symbolic substitution modified signed-digit optical adder

1994 ◽  
Vol 33 (8) ◽  
pp. 1498 ◽  
Author(s):  
David Casasent ◽  
Paul Woodford
Keyword(s):  
Symbolic Substitution

Optical production systems using neural networks and symbolic substitution

1988 ◽  
Vol 27 (24) ◽  
pp. 5185 ◽  
Author(s):  
Elizabeth Botha ◽  
David Casasent ◽  
Etienne Barnard
Keyword(s):  
Neural Networks ◽  
Production Systems ◽  
Optical Production ◽  
Symbolic Substitution

scholarly journals -Analogues of Symbolic Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Michael J. Dancs ◽  
Tian-Xiao He
Keyword(s):  
Linear Operators ◽  
Derivative Operator ◽  
Symbolic Summation ◽  
Series Transformation ◽  
Transformation Formulas ◽  
Symbolic Substitution

Here presented are -extensions of several linear operators including a novel -analogue of the derivative operator . Some -analogues of the symbolic substitution rules given by He et al., 2007, are obtained. As sample applications, we show how these -substitution rules may be used to construct symbolic summation and series transformation formulas, including -analogues of the classical Euler transformations for accelerating the convergence of alternating series.

Optical symbolic substitution using diffraction gratings

1990 ◽  
Vol 29 (14) ◽  
pp. 2126 ◽  
Author(s):  
Ruedi Thalmann ◽  
Giancarlo Pedrini ◽  
Kenneth J. Weible
Keyword(s):  
Diffraction Gratings ◽  
Symbolic Substitution
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