Approximation of Bellman's function by piecewise constant functions

1978 ◽  
Vol 18 (4) ◽  
pp. 95-107
Author(s):  
E.N. Orel
Keyword(s):  
Piecewise Constant ◽  
Piecewise Constant Functions

scholarly journals Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 994 ◽  
Author(s):  
Adrian Holhoş ◽  
Daniela Roşca
Keyword(s):  
Unit Ball ◽  
Multiresolution Analysis ◽  
Uniform Grid ◽  
Orthonormal Wavelet ◽  
Wavelet Bases ◽  
Piecewise Constant ◽  
Regular Octahedron ◽  
Piecewise Constant Functions ◽  
Local Support ◽  
Volume Preserving

We construct a new volume preserving map from the unit ball B 3 to the regular 3D octahedron, both centered at the origin, and its inverse. This map will help us to construct refinable grids of the 3D ball, consisting in diameter bounded cells having the same volume. On this 3D uniform grid, we construct a multiresolution analysis and orthonormal wavelet bases of L 2 ( B 3 ) , consisting in piecewise constant functions with small local support.

scholarly journals Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 216
Author(s):  
Shahram Rezapour ◽  
Mohammed Said Souid ◽  
Sina Etemad ◽  
Zoubida Bouazza ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Variable Order ◽  
Mawhin’S Continuation Theorem ◽  
Piecewise Constant ◽  
At Resonance ◽  
Piecewise Constant Functions ◽  
The Given ◽  
Continuation Technique

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

scholarly journals Parseval frames of piecewise constant functions

2020 ◽  
pp. 317-331
Author(s):  
Dorin Ervin Dutkay ◽  
Rajitha Ranasinghe
Keyword(s):  
Piecewise Constant ◽  
Piecewise Constant Functions ◽  
Parseval Frames

scholarly journals Mild mixing property for special flows under piecewise constant functions

2007 ◽  
Vol 19 (4) ◽  
pp. 691-710 ◽  
Author(s):  
Krzysztof Frączek ◽  
◽  
M. Lemańczyk ◽  
E. Lesigne ◽  
◽  
...  
Keyword(s):  
Piecewise Constant ◽  
Piecewise Constant Functions ◽  
Mixing Property
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