A convergence for bivariate functions aimed at the convergence of saddle values

1983 ◽  
pp. 1-42 ◽  
Author(s):  
Hedy Attouch ◽  
Roger J.-B. Wets
Keyword(s):  
Bivariate Functions

scholarly journals Computing the Distance between Piecewise-Linear Bivariate Functions

2016 ◽  
Vol 12 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Guillaume Moroz ◽  
Boris Aronov
Keyword(s):  
Piecewise Linear ◽  
Bivariate Functions

Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces

1998 ◽  
Author(s):  
Helmut Pottmann ◽  
Johannes Wallner ◽  
Georg Glaeser ◽  
Bahram Ravani
Keyword(s):  
Motion Planning ◽  
Sculptured Surfaces ◽  
Global Shape ◽  
Be Star ◽  
Offset Surfaces ◽  
Tool Motion ◽  
Curvature Information ◽  
Bivariate Functions

Abstract The paper presents a geometric investigation of collision-free 3-axis milling of surfaces. We consider surfaces with a global shape condition: they shall be interpretable as graphs of bivariate functions or shall be star-shaped with respect to a point. If those surfaces satisfy a local millability criterion involving curvature information, it is proved that this implies globally gouge-free milling. The proofs are based on general offset surfaces. The results can be applied to tool-motion planning and the computation of optimal cutter shapes.

SOME LIMIT THEOREMS OF DELAYED AVERAGES FOR COUNTABLE NONHOMOGENEOUS MARKOV CHAINS

2019 ◽  
pp. 1-19
Author(s):  
Pingping Zhong ◽  
Weiguo Yang ◽  
Zhiyan Shi ◽  
Yan Zhang
Keyword(s):  
Information Theory ◽  
Markov Chains ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Strong Ergodicity ◽  
Large Numbers ◽  
Nonhomogeneous Markov Chains ◽  
Definition Of ◽  
Bivariate Functions

AbstractThe purpose of this paper is to establish some limit theorems of delayed averages for countable nonhomogeneous Markov chains. The definition of the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for countable nonhomogeneous Markov chains is introduced first. Then a theorem about the generalized C-strong ergodicity and the generalized uniformly C-strong ergodicity for the nonhomogeneous Markov chains is established, and its applications to the information theory are given. Finally, the strong law of large numbers of delayed averages of bivariate functions for countable nonhomogeneous Markov chains is proved.

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