Asymptotic expansions of one-dimensional second-order Helmholtz equation with rapidly oscillating coefficient

2007 ◽  
Vol 188 (2) ◽  
pp. 1921-1929
Author(s):  
Wen-ming He
Keyword(s):  
Helmholtz Equation ◽  
Asymptotic Expansions ◽  
Second Order ◽  
One Dimensional ◽  
Oscillating Coefficient

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

One dimensional polymeric photonic crystal doped with second-order nonlinear optical chromophore

2009 ◽  
Author(s):  
Azusa Inoue ◽  
Shin-ichiro Inoue ◽  
Shiyoshi Yokoyama ◽  
Keisuke Kojima ◽  
Kei Yasui ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Nonlinear Optical ◽  
Second Order ◽  
One Dimensional ◽  
Nonlinear Optical Chromophore
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