Last edited by Gahn
Friday, May 8, 2020 | History

2 edition of Fixed points of some operators defined on free monoids found in the catalog.

Fixed points of some operators defined on free monoids

Wit ForysМЃ

# Fixed points of some operators defined on free monoids

## by Wit ForysМЃ

Written in English

Subjects:
• Fixed point theory.,
• Monoids.

• Edition Notes

Includes bibliographical references (p. -58).

Classifications The Physical Object Statement Wit Foryś. Series Rozprawy habilitacyjne / Uniwersytet Jagielloński,, nr. 237, Rozprawy habilitacyjne (Uniwersytet Jagielloński) ;, nr. 237. LC Classifications QA611.7 .F67 1992 Pagination 58 p. : Number of Pages 58 Open Library OL1521313M ISBN 10 832330579X LC Control Number 93208712

Note there are two parts to the definition of a monoid – the things plus the associated operation. A monoid is not just “a bunch of things”, but “a bunch of things” and “some way of combining them”. So, for example, “the integers” is not a monoid, but “the integers under addition” is a monoid. Semigroups. The set of all finite strings over some fixed alphabet Σ forms a monoid with string concatenation as the operation. The empty string serves as the identity element. This monoid is denoted Σ ∗ and is called the free monoid over Σ.

Algebraic Graph Theory: Morphisms, Monoids and Matrices Ulrich Knauer, Kolja Knauer The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Now, let us define a quasi-property of an operation as a property that holds up to an equivalence relation. For example, list concatenation is quasi-commutative if we consider lists of equal length or with identical contents up to permutation to be equivalent. Here are some quasi-monoids and quasi-commutative monoids and semigroups.

Monoids Transformations monoids A transformation of a set E, is a function from E to itself. The full transformation monoid of E is the set E E of all transformations of E, seen as an algebra with two operations: the constant Id, and the binary operation ০ of composition. A transformation monoid of E is a set M of transformations of E forming an {Id,০}-algebra, M ∈ Sub {Id,০} E E. LOGICS FOR CLASSES OF BOOLEAN MONOIDS • a ⊥=⊥=⊥ a, i.e., the monoid operation is normal. DEFINITION A starred Boolean monoid (BM∗) is a Boolean monoid which satisﬁes the following axioms • 1 +(a∗ a∗)+a ≤ a∗; • 1 +(b b)+a ≤ b implies a∗ ≤ b. LEMMA (Residuation). The operators ∧ and the deﬁned operator ⊃, i.e., a ⊃ b =−a + b, are.

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### Fixed points of some operators defined on free monoids by Wit ForysМЃ Download PDF EPUB FB2

Pedro V. Silva Fixed points for groups and monoids Introduction Virtually free groups Graph groups raceT monoids Inverse monoids Uniformly continuous endomorphisms. We consider involutory antimorphisms ϑ of a free monoid A * and their fixed points, called ϑ -palindromes or pseudopalindromes.

A ϑ -palindrome reduces to a usual palindrome when ϑ is the reversal by:   points of (uniformly continuous) endomorphisms of monoids deﬁned b y special conﬂuent rewriting systems, extending results known for free monoids [11 ].

Th is line of reasearch was. There are many examples of monoids, but there is a special class of them called free monoids. The easiest way to understand what a free monoid is, is to construct one. Just pick a set, any set, and call it the set of generators.

Then define multiplication in the laziest, dumbest possible way. First, add one more element to the set and call it a. Associated with any (connected) topological space X is its fundamental group π 1 (X) or 2-complex (Squier complex) D (X).This can often be specified by means of a presentation.

A presentation of a group G or monoid M consists of a set of generators of G or M, together with a collection of relations amongst these generators, such that any other relation amongst the generators is derivable (in Cited by: 9. The universal condition in Fig.

gives us immediately the left unit law for the monoid. The right unit law: requires a little more work. There is a standard trick that we can use to show that two morphisms, whose source (in this case) is a free algebra, are ’s enough to prove that they are algebra morphisms, and that they are both induced by the same morphism (in this case).

We prove a fixed point theorem for nonlinear operators, acting on some function spaces (of set-valued maps), which satisfy suitable inclusions.

We also show some Cited by: 1. Existence results of fixed points for some convex operators are given by means of fixed point theorem of cone expansion and compression, then they are applied to nonlinear multi-pCited by: 2.

Some Fixed Point Theorems Of Functional Analysis By F.F. Bonsall Notes by K.B. Vedak No part of this book may be reproduced in any form by print, microﬁlm or any other means with-out written permission from the Tata Institute of Fundamental Research, Colaba, Bombay 5 Tata Institute of Fundamental Research Bombay Abstract We consider involutory antimorphisms ϑ of a free monoid A* and their fixed points, called ϑ-palindromes or pseudopalindromes.

A ϑ-palindrome reduces to a usual palindrome when ϑ is the. monoids in characteristic 0 (see [3, Thm. In this article, we obtain some fundamental results on algebraic semigroups and monoids, that include the above structure theorems in slightly more gen-eral versions. We also describe all algebraic semigroup structures on abelian varieties, irreducible curves and complete irreducible varieties.

The notion of a coupled fixed point was introduced and studied by Opoitsev [] and investigated later by Guo-Lakshmikantham [].Among investigations of coupled fixed point results for nonlinear operators in the ordered Banach space setting, there are more results on the existence of coupled fixed points than on the existence of common coupled fixed points of a pair of operators, Author: Nabil Machrafi.

Fixed point theory is a fascinating subject, with an enormous number of applications in various ﬁelds of mathematics. Maybe due to this transversal character, I have always experienced some diﬃculties to ﬁnd a book (unless expressly devoted to ﬁxed points) treating the argument in a unitary fashion.

In most cases, I noticedFile Size: KB. In summary, any monad is by definition an endofunctor, hence an object in the category of endofunctors, where the monadic join and return operators satisfy the definition of a monoid in that particular (strict) monoidal category.

We study the factorization properties of continuous homomorphisms defined on a (dense) submonoid S of a Tychonoff product D = ∏ i ∈ I D i of topological or even topologized monoids. In a number of different situations, we establish that every continuous homomorphism f: S → K to a topological monoid (or group) K depends on at most finitely many : Mikhail Tkachenko.

Monoids in practice. In the previous post, we looked at the definition of a this post, we'll see how to implement some monoids. First, let's revisit the definition: You start with a bunch of things, and some way of combining them two at a time.

Rule 1 (Closure): The result of combining two things is always another one of the things. Rule 2 (Associativity): When combining more than. The purpose of this work is to extend Leech cohomology for monoids (and so Eilenberg-Mac Lane cohomology of groups) to presheaves of monoids on an arbitrary small category.

The main result states and proves a cohomological classification of monoidal prestacks on a category with values in groupoids with abelian isotropy groups. The paper also includes a cohomological classification for Author: Pilar Carrasco, Antonio M.

Cegarra. Monoids and Groups are categories with one object and an (endo-)functor going from that single functor back to itself. So this is the simplest type category that still has some structure.

This is useful to study because: It gives a different approach to monoids and groups which are interesing in their own right. AbstractWe define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and 3 × 3 matrices.

Firstly, we completely characterize these injections that yield commutative monoids of integer triples. Secondly, we determine commutative monoids of Pythagorean triples Author: Nadir Murru, Marco Abrate, Stefano Barbero, Umberto Cerruti.

[deleted] 2 points 3 points 4 points 2 years ago Even if we define a monoid in category terms, the collection of all monoids is a large category/proper class. Fille's question basically translates then to asking whether a small monoid is different from a large one and the answer is no due to the universe axiom.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Understanding free monoids.

Ask Question Asked 3 years, 4 months ago. However, according to the definition of a free monoid, where does it fail to become free? \$\endgroup. You may have heard of some of these, especially if you’ve looked into statically typed functional programming languages such as Haskell, OCaml, F#, or Scala.

Semigroups In talking about Monoids, we actually need to talk about two structures: the Semigroup and the : David Koontz.Fixed Point Theorems This section will discuss three xed point theorems: the Contraction Mapping Theorem, Brouwer’s Theorem and Schauder’s Theorem. De nition 1.

Let (X;d) be a metric space and T: MˆX!Xbe a map. A solution of Tx= xis called a xed point of T. We will see several xed point theorems with di erent assumptions on the space Xand.