scholarly journals Construction and Application of Nine-Tic B-Spline Tensor Product SS

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 675 ◽  
Author(s):  
Abdul Ghaffar ◽  
Mudassar Iqbal ◽  
Mehwish Bari ◽  
Sardar Muhammad Hussain ◽  
Raheela Manzoor ◽  
...  
Keyword(s):  
Tensor Product ◽  
Spectral Radius ◽  
Execution Time ◽  
Computer Programming ◽  
Surface Modeling ◽  
Hölder Regularity ◽  
Subdivision Scheme ◽  
Joint Spectral Radius ◽  
B Spline ◽  
Holder Regularity

In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.

scholarly journals Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 474 ◽  
Author(s):  
Sardar Muhammad Hussain ◽  
Aziz Ur Rehman ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
Abdul Ghaffar ◽  
...  
Keyword(s):  
Error Bound ◽  
Shape Parameter ◽  
Geometric Design ◽  
Hölder Regularity ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Computer Aided Geometric Design ◽  
Approximating Subdivision Scheme ◽  
Computer Aided ◽  
Holder Regularity

The Subdivision Schemes (SSs) have been the heart of Computer Aided Geometric Design (CAGD) almost from its origin, and various analyses of SSs have been conducted. SSs are commonly used in CAGD and several methods have been invented to design curves/surfaces produced by SSs to applied geometry. In this article, we consider an algorithm that generates the 5-point approximating subdivision scheme with varying arity. By applying the algorithm, we further discuss several properties: continuity, Hölder regularity, limit stencils, error bound, and shape of limit curves. The efficiency of the scheme is also depicted with assuming different values of shape parameter along with its application.

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

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