An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline

1981 ◽  
Vol 7 (3) ◽  
pp. 331-347 ◽  
Author(s):  
David F. McAllister ◽  
John A. Roulier
Keyword(s):  
Shape Preserving ◽  
Quadratic Spline

scholarly journals Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3182
Author(s):  
Gabriela Cristescu ◽  
Vlad-Florin Drăgoi ◽  
Sorin Horaţiu Hoară
Keyword(s):  
Generalized Convexity ◽  
Low Complexity ◽  
Small Error ◽  
Spline Functions ◽  
Shape Preserving ◽  
Quadratic Spline ◽  
Minimal Network ◽  
Convexity Properties ◽  
Minimal Networks ◽  
Accuracy Of Approximation

Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based on both interpolation conditions and shape knowledge. It is proved that the approximant objects preserve both the high-order convexity and some extremum properties of the exact reliability polynomials. It leads to pointing out the area of the network where the maximum number of paths is achieved. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed.

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

Ceramic Nanoparticle Assemblies with Tailored Shapes and Tailored Chemistries via Biosculpting and Shape-Preserving Inorganic Conversion

2005 ◽  
Vol 5 (1) ◽  
pp. 63-67 ◽  
Author(s):  
M.B. Dickerson ◽  
R.R. Naik ◽  
P.M. Sarosi ◽  
G. Agarwal ◽  
M.O. Stone ◽  
...  
Keyword(s):  
Shape Preserving ◽  
Nanoparticle Assemblies
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