A binary operation on trees and an initial algebra characterization for finite tree types

1979 ◽  
Vol 11 (2) ◽  
Author(s):  
Wolfgang Merzenich
Keyword(s):  
Binary Operation ◽  
Finite Tree ◽  
Initial Algebra ◽  
Algebra Characterization

Using binary operations to construct a transitive set of block transformations

2020 ◽  
Vol 30 (6) ◽  
pp. 375-389
Author(s):  
Igor V. Cherednik
Keyword(s):  
Binary Operation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Binary Operations ◽  
The Family ◽  
Transitive Set ◽  
Necessary And Sufficient

AbstractWe study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.

scholarly journals M-Hazy Vector Spaces over M-Hazy Field

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1118
Author(s):  
Faisal Mehmood ◽  
Fu-Gui Shi
Keyword(s):  
Vector Space ◽  
Linear Transformation ◽  
Binary Operation ◽  
Vector Spaces ◽  
Fundamental Properties ◽  
Classical Algebra ◽  
Important Development ◽  
Fuzzy Algebra ◽  
Convex Spaces

The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces over M-hazy field. Some fundamental properties of M-hazy field, M-hazy vector spaces, and M-hazy subspaces are studied, and some important results are also proved. Furthermore, the linear transformation of M-hazy vector spaces is studied and their important results are also proved. Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space.

The initial algebra of maximal minors of a generalized hankel matrix

1999 ◽  
Vol 27 (1) ◽  
pp. 429-450
Author(s):  
Paulo F. Machado
Keyword(s):  
Hankel Matrix ◽  
Initial Algebra

scholarly journals Weak integer additive set-labeled graphs: A creative review

2015 ◽  
Vol 08 (03) ◽  
pp. 1550052 ◽  
Author(s):  
N. K. Sudev ◽  
K. A. Germina ◽  
K. P. Chithra
Keyword(s):  
Binary Operation ◽  
Labeled Graphs ◽  
Injective Function ◽  
Power Set

For a non-empty ground set [Formula: see text], finite or infinite, the set-valuation or set-labeling of a given graph [Formula: see text] is an injective function [Formula: see text], where [Formula: see text] is the power set of the set [Formula: see text]. A set-valuation or a set-labeling of a graph [Formula: see text] is an injective set-valued function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text] for every [Formula: see text], where [Formula: see text] is a binary operation on sets. Let [Formula: see text] be the set of all non-negative integers and [Formula: see text] be its power set. An integer additive set-labeling (IASL) is defined as an injective function [Formula: see text] such that the induced function [Formula: see text] is defined by [Formula: see text]. An IASL [Formula: see text] is said to be an integer additive set-indexer if [Formula: see text] is also injective. A weak IASL is an IASL [Formula: see text] such that [Formula: see text]. In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.

Initial Algebra Semantics and Continuous Algebras

1977 ◽  
Vol 24 (1) ◽  
pp. 68-95 ◽  
Author(s):  
J. A. Goguen ◽  
J. W. Thatcher ◽  
E. G. Wagner ◽  
J. B. Wright
Keyword(s):  
Initial Algebra ◽  
Initial Algebra Semantics

scholarly journals Initial Algebra Semantics Is Enough!

2007 ◽  
pp. 207-222 ◽  
Author(s):  
Patricia Johann ◽  
Neil Ghani
Keyword(s):  
Initial Algebra ◽  
Initial Algebra Semantics

Deciding Equivalence of Finite Tree Automata

1990 ◽  
Vol 19 (3) ◽  
pp. 424-437 ◽  
Author(s):  
Helmut Seidl
Keyword(s):  
Tree Automata ◽  
Finite Tree

The Fusion as a Novel Binary Operation on Medial Axes

2010 ◽  
Author(s):  
Ivan Mekhedov ◽  
Leonid Mestetskiy
Keyword(s):  
Binary Operation

On Refined Semilattices of Semigroups

2008 ◽  
Vol 15 (02) ◽  
pp. 331-336 ◽  
Author(s):  
Zhengpan Wang ◽  
Yuqi Guo ◽  
K. P. Shum
Keyword(s):  
Binary Operation ◽  
Short Proof ◽  
Semilattice Of Semigroups

We give a short proof for the associativity of the binary operation defined on a refined system of semigroups indexed by a semilattice. The main result given by Zhang, Shum and Zhang in 2001 on the refined semilattice of semigroups is substantially strengthened.

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