scholarly journals Modified Operators Interpolating at Endpoints

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2051
Author(s):  
Ana Maria Acu ◽  
Ioan Raşa ◽  
Rekha Srivastava
Keyword(s):  
Affine Functions

Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.

TRANSFORMATION OF NESTED LOOPS WITH MODULO INDEXING TO AFFINE RECURRENCES

1994 ◽  
Vol 04 (03) ◽  
pp. 271-280 ◽  
Author(s):  
FLORIN BALASA ◽  
FRANK H.M. FRANSSEN ◽  
FRANCKY V.M. CATTHOOR ◽  
HUGO J. DE MAN
Keyword(s):  
Code Generation ◽  
State Of The Art ◽  
Transformation Method ◽  
Control Flow ◽  
Code Optimization ◽  
Transformation Techniques ◽  
Hermite Normal Form ◽  
Nested Loops ◽  
Affine Functions ◽  
Systems Transformation

For multi-dimensional (M-D) signal and data processing systems, transformation of algorithmic specifications is a major instrument both in code optimization and code generation for parallelizing compilers and in control flow optimization as a preprocessor for architecture synthesis. State-of-the-art transformation techniques are limited to affine index expressions. This is however not sufficient for many important applications in image, speech and numerical processing. In this paper, a novel transformation method is introduced, oriented to the subclass of algorithm specifications that contains modulo expressions of affine functions to index M-D signals. The method employs extensively the concept of Hermite normal form. The transformation method can be carried out in polynomial time, applying only integer arithmetic.

Criteria for approximation of linear and affine functions

1986 ◽  
Vol 46 (4) ◽  
pp. 371-384 ◽  
Author(s):  
Christian Ronse
Keyword(s):  
Affine Functions

Some conditions for absence of affine functions in NFSR output stream

2021 ◽  
Vol 89 (11) ◽  
pp. 2433-2443
Author(s):  
Michail I. Rozhkov ◽  
Alexander V. Sorokin
Keyword(s):  
Output Stream ◽  
Affine Functions

Kolmogorov's Theorem Is Relevant

1991 ◽  
Vol 3 (4) ◽  
pp. 617-622 ◽  
Author(s):  
Věra Kůrková
Keyword(s):  
Neural Networks ◽  
Continuous Functions ◽  
Sigmoidal Function ◽  
Linear Combinations ◽  
Affine Functions ◽  
The One ◽  
Upper Estimate ◽  
Kolmogorov's Theorem

We show that Kolmogorov's theorem on representations of continuous functions of n-variables by sums and superpositions of continuous functions of one variable is relevant in the context of neural networks. We give a version of this theorem with all of the one-variable functions approximated arbitrarily well by linear combinations of compositions of affine functions with some given sigmoidal function. We derive an upper estimate of the number of hidden units.

scholarly journals A Beurling-Helson type theorem for modulation spaces

2009 ◽  
Vol 7 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Kasso A. Okoudjou
Keyword(s):  
Type Theorem ◽  
Modulation Spaces ◽  
Affine Functions ◽  
Special Case

We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only𝒞1changes of variables that leave invariant the modulation spacesℳp,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.

scholarly journals A Choquet-Deny theorem for affine functions on a Choquet simplex

1969 ◽  
Vol 16 (4) ◽  
pp. 325-327 ◽  
Author(s):  
H. A. Priestley
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Present Note ◽  
Continuous Functions ◽  
Choquet Simplex ◽  
Affine Functions ◽  
Stone Theorem

The closed wedges in C(X) (the space of real continuous functions on a compact Hausdorff space X) which are also inf-lattices have been characterized by Choquet and Deny (2); see also (5). The present note extends their result to certain wedges of affine continuous functions on a Choquet simplex, the generalization being in the same spirit as the generalization of the Kakutani- Stone theorem obtained by Edwards in (4).I should like to thank my supervisor, Dr D. A. Edwards, for suggesting this problem and for his subsequent help. I am also grateful to the referee for correcting several slips.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

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