scholarly journals Upper bounds on derivatives of the logarithm of the heat kernel

1998 ◽  
Vol 6 (4) ◽  
pp. 669-685 ◽  
Author(s):  
Daniel W. Stroock ◽  
James Turetsky
Keyword(s):  
Heat Kernel ◽  
Upper Bounds ◽  
Derivatives Of

scholarly journals An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1382
Author(s):  
Ye Tian ◽  
Tao Ning ◽  
Jixing Li ◽  
Jianmin Zheng ◽  
Zhitong Chen
Keyword(s):  
Upper Bounds ◽  
Basis Functions ◽  
Nurbs Surface ◽  
Degree Reduction ◽  
B Spline ◽  
Partial Derivatives ◽  
Spline Basis ◽  
Rational Bézier Surface ◽  
Nurbs Surfaces ◽  
Derivatives Of

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

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