Commutative integral bounded residuated lattices with an added involution

A symmetric residuated lattice is an algebra A = (A, ∨, ∧, *, →, ∼, 1, 0) such that (A, ∨, ∧, *, →, 1, 0) is a commutative integral bounded residuated lattice and the equations ∼ ∼ x = x and ∼ (x ∨ y) = ∼ x ∧ ∼ y are satisfied. The aim of the paper is to investigate the properties of the unary operation ε defined by the prescription ε x = ∼ x → 0. We give necessary and sufficient conditions for ε being an interior operator. Since these conditions are rather restrictive (for instance, on a symmetric Heyting algebra ε is an interior operator if and only the equation (x → 0) ∨ ((x → 0) → 0) = 1 is satisfied) we consider when an iteration of ε is an interior operator. In particular we consider the chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator. For instance, we show that these varieties are semisimple. When n = 1, we obtain the variety of symmetric stonean residuated lattices. We also characterize the subvarieties admitting representations as subdirect products of chains. These results generalize and in many cases also simplify, results existing in the literature. © 2009 Elsevier B.V. All rights reserved

Free algebras in varieties of BL-algebras generated by a BL n-chain

Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of L and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the Stone spaces of the Boolean subalgebras of idempotents of free algebras in the variety of MV-algebras generated by L N. © 2006 Australian Mathematical Society.Fil:Busaniche, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued {\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A} \cong \mathbb{RS}$.Comment: 16 page

The kitchen as a pedagogical strategy. Addressing celiac disease from the encounter with "Others" is to build a "We", which leads to accessing a good living

This work arises within the framework of the Pehuajó Solidarity Network (RSP), where a voluntary group, independent since 1997, meets alternating kitchen/s to discuss some issues of interest related to signs and symptoms that a member of their family suffered, without know the condition of Celiac disease. Currently, the fact of being celiac in the social context where one lives and/or in the tourist places that they visit, do not always meet the nutritional needs of children, adolescents, young people, adults, people in general who they suffer from Celiac disease. That is to say, the achievement of Municipal Ordinance 94/2019 in district 079 of the province of Buenos Aires and the Laws: National and Provincial in Argentina are still known and are gradually being complied with, being the Gastronomic offer, sale of food, services of confectionery, among other insufficient. They do not have at least one menu for celiacs, with few exceptions. In other words, the group of aware independent volunteers not only incorporates knowledge to self-manage celiac disease, but as an informal entity it is managing to transpose in formal institutions, the community of the contextterritory, non-profit activities with the objective of: disseminate, raise awareness and make celiac disease visible as a pedagogical strategy. That is, to make visible the advances developed in the 21st century, the very concept of this chronic disease, which went from being defined as a mere food intolerance, to being recognized as a systemic pathology with an autoimmune basis

Diseño de antídotos contra los daños bioquímicos y estructurales causados por el tetracloruro de carbono basados en el conocimiento de su mecanismo de acción

Fil: Cignoli de Ferreyra, Elida Virginia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

El abordaje de la capacidad de resolución de problema en las prácticas de enseñanza para pluriaño de escuelas secundarias del ámbito rural bonaerense

Fil: Cignoli, María de los Ángeles. Universidad Católica de Córdoba. Facultad de Educación; Argentina

Electron-hole asymmetry in two-terminal graphene devices

A theoretical model is proposed to describe asymmetric gate-voltage dependence of conductance and noise in two-terminal ballistic graphene devices. The model is analyzed independently within the self-consistent Hartree and Thomas-Fermi approximations. Our results justify the prominent role of metal contacts in recent experiments with suspended graphene flakes. The contact-induced electrostatic potentials in graphene demonstrate a power-law decay with the exponent varying from -1 to -0.5. Within our model we explain electron-hole asymmetry and strong Fabri-Perot oscillations of the conductance and noise at positive doping, which were observed in many experiments with submicrometer samples. Limitations of the Thomas-Fermi approximation in a vicinity of the Dirac point are discussed.Comment: 7 pages, 8 figure

A representation theorem for MV-algebras

An {\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for every MV-pair $(B,G)$, the effect algebra $B/\sim_G$ is an MV- effect algebra. Moreover, for every MV-effect algebra $M$ there is an MV-pair $(B,G)$ such that $M$ is isomorphic to $B/\sim_G$