scholarly journals An algebraic weak factorisation system on 01-substitution sets: a constructive proof

2016 ◽  
Author(s):  
Andrew Swan
Keyword(s):  
Constructive Proof ◽  
Weak Factorisation System ◽  
Factorisation System

scholarly journals The identity type weak factorisation system

2008 ◽  
Vol 409 (1) ◽  
pp. 94-109 ◽  
Author(s):  
Nicola Gambino ◽  
Richard Garner
Keyword(s):  
Weak Factorisation System ◽  
Factorisation System

scholarly journals Elementary fibrations of enriched groupoids

2021 ◽  
pp. 1-21
Author(s):  
Jacopo Emmenegger ◽  
Fabio Pasquali ◽  
Giuseppe Rosolini
Keyword(s):  
Type Theory ◽  
First Order ◽  
Weak Factorisation System ◽  
Factorisation System ◽  
Order Equality

Abstract The present paper aims at stressing the importance of the Hofmann–Streicher groupoid model for Martin Löf Type Theory as a link with the first-order equality and its semantics via adjunctions. The groupoid model was introduced by Martin Hofmann in his Ph.D. thesis and later analysed in collaboration with Thomas Streicher. In this paper, after describing an algebraic weak factorisation system $$\mathsf {L, R}$$ on the category $${\cal C}-{\cal Gpd}$$ of $${\cal C}$$ -enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for $$\mathsf {L, R}$$ needed to interpret identity types.

scholarly journals A homotopy-theoretic universal property of Leinster's operad for weak ω-categories

2009 ◽  
Vol 147 (3) ◽  
pp. 615-628 ◽  
Author(s):  
RICHARD GARNER
Keyword(s):  
Universal Property ◽  
Weak Factorisation System ◽  
Factorisation System

AbstractWe explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster's operad for weak ω-categories.

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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