scholarly journals A simple constructive proof of an analogue of the corona theorem

1981 ◽  
Vol 83 (2) ◽  
pp. 299-299 ◽  
Author(s):  
Michael von Renteln
Keyword(s):  
Constructive Proof ◽  
Corona Theorem

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

Two variable implicational calculi of prescribed many-one degrees of unsolvability

1976 ◽  
Vol 41 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Charles E. Hughes
Keyword(s):  
Decision Problems ◽  
Constructive Proof ◽  
Distinct Variable ◽  
The Family ◽  
Propositional Calculi ◽  
Degrees Of Unsolvability

AbstractA constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

A constructive proof for FLP

2004 ◽  
Vol 92 (2) ◽  
pp. 83-87 ◽  
Author(s):  
Hagen Völzer
Keyword(s):  
Constructive Proof

On a Constructive Proof of Kolmogorov’s Superposition Theorem

2009 ◽  
Vol 30 (3) ◽  
pp. 653-675 ◽  
Author(s):  
Jürgen Braun ◽  
Michael Griebel
Keyword(s):  
Constructive Proof ◽  
Superposition Theorem

Constructive Proof of Preisach Right Inverse With Applications to Inverse Compensation of Smart Actuators With Hysteresis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Yangyang Dong ◽  
Hong Hu ◽  
Zijian Zhang
Keyword(s):  
Iterative Algorithm ◽  
Control Design ◽  
Geometric Interpretation ◽  
Constructive Proof ◽  
Preisach Model ◽  
Compensation Scheme ◽  
Fundamental Idea ◽  
Model Inversion ◽  
Significant Challenge ◽  
Piezoelectric Stack Actuator

Hysteresis poses a significant challenge for control of smart material actuators. If unaccommodated, the hysteresis can result in oscillation, poor tracking performance, and potential instability when the actuators are incorporated in control design. To overcome these problems, a fundamental idea in coping with hysteresis is inverse compensation based on the Preisach model. In this paper, we address systematically the problem of Preisach model inversion and its properties, employing the technique of three-step composition mapping and geometric interpretation of the Preisach model. A Preisach right inverse is achieved via the iterative algorithm proposed, which possesses same properties with the Preisach model. Finally, comparative experiments are performed on a piezoelectric stack actuator (PEA) to test the efficacy of the compensation scheme based on the Preisach right inverse.

scholarly journals Constructing Gröbner bases for Noetherian rings

2013 ◽  
Vol 24 (2) ◽  
Author(s):  
HERVÉ PERDRY ◽  
PETER SCHUSTER
Keyword(s):  
Gröbner Basis ◽  
Finite Depth ◽  
Commutative Rings ◽  
Polynomial Ideal ◽  
Constructive Proof ◽  
Noetherian Rings ◽  
Grobner Basis ◽  
Finitely Generated ◽  
Prime Decomposition ◽  
Separate Paper

We give a constructive proof showing that every finitely generated polynomial ideal has a Gröbner basis, provided the ring of coefficients is Noetherian in the sense of Richman and Seidenberg. That is, we give a constructive termination proof for a variant of the well-known algorithm for computing the Gröbner basis. In combination with a purely order-theoretic result we have proved in a separate paper, this yields a unified constructive proof of the Hilbert basis theorem for all Noether classes: if a ring belongs to a Noether class, then so does the polynomial ring. Our proof can be seen as a constructive reworking of one of the classical proofs, in the spirit of the partial realisation of Hilbert's programme in algebra put forward by Coquand and Lombardi. The rings under consideration need not be commutative, but are assumed to be coherent and strongly discrete: that is, they admit a membership test for every finitely generated ideal. As a complement to the proof, we provide a prime decomposition for commutative rings possessing the finite-depth property.

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