A DIVISION THEOREM FOR THE PSEUDOVARIETY GENERATED BY SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS ON A FINITE CHAIN

2001 ◽  
Vol 29 (1) ◽  
pp. 451-456 ◽  
Author(s):  
Vitor H. Fernandes
Keyword(s):  
Finite Chain ◽  
Division Theorem

scholarly journals On Divisors of Pseudovarieties Generated by Some Classes of Full Transformation Semigroups

2008 ◽  
Vol 15 (04) ◽  
pp. 581-588
Author(s):  
Vítor H. Fernandes
Keyword(s):  
Finite Chain ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Division Theorem

In this paper we present a division theorem for the pseudovariety of semigroups 𝖮𝖣 (𝖮𝖱) generated by all semigroups of order-preserving or order-reversing (orientation-preserving or orientation-reversing) full transformations on a finite chain.

Critical Problem for codes over finite chain rings

2021 ◽  
Vol 76 ◽  
pp. 101900
Author(s):  
Koji Imamura ◽  
Keisuke Shiromoto
Keyword(s):  
Finite Chain ◽  
Critical Problem ◽  
Finite Chain Rings

A New Derivation of Postgel Properties of Network Polymers

1976 ◽  
Vol 49 (5) ◽  
pp. 1219-1231 ◽  
Author(s):  
D. R. Miller ◽  
C. W. Macosko
Keyword(s):  
General Result ◽  
Crosslink Density ◽  
Polymer Network ◽  
Probability Generating Function ◽  
Finite Chain ◽  
Network Polymer ◽  
Network Polymers ◽  
Property Relations ◽  
Recursive Scheme ◽  
Effective Network

Abstract The probability of a finite or dangling chain on an ideal polymer network has been derived by a simple recursive scheme. In contrast to the method of Dobson and Gordon, probability generating function formalism is not required. The general result, Equations (21), and its specific solutions, Equations (23), (24), and (30), give the finite chain probability as a function of reactant type and extent of polymerization. They cover most of the important types of network forming polymerizations. From the finite chain probability, useful property relations such as sol fraction, crosslink density, and the number of elastically effective network chains are developed. Because of their simplicity, we expect these relations to be further developed and applied to network polymer property measurements.

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