scholarly journals The subvariety lattice of the variety of distributive double p-algebras

1985 ◽  
Vol 31 (3) ◽  
pp. 377-387 ◽  
Author(s):  
Wieslaw Dziobiak
Keyword(s):  
Finite Algebra ◽  
Boolean Algebras ◽  
The Other ◽  
High Complexity ◽  
Inclusion Relation ◽  
Other Hand ◽  
Subvariety Lattice ◽  
A Chain ◽  
Proper Filter

Let L denote the subvariety lattice of the variety of distributive double p-algebras, that is, the lattice whose universe consists of all varieties of distributive double p-algebras and whose ordering is the inclusion relation. We prove in this paper that each proper filter in L is uncountable. Moreover, we prove that except for the trivial variety (the zero in L) and the variety of Boolean algebras (the unique atom in L) every other element of L, generated by a finite algebra, has infinitely many covers in L, among which at least one is not generated by any finite algebra. The former result strengthens a result of Urquhart who showed that the lattice L is uncountable. On the other hand, both of our results indicate a high complexity of the lattice L at least in comparison with the subvariety lattice of the variety of distributive p-algebras, since a result of Lee shows that the latter lattice forms a chain of type ω + 1 and every cover in it of the variety generated by a finite algebra is itself generated by a finite algebra.

scholarly journals On the semantics of place/transition Petri nets

1997 ◽  
Vol 7 (4) ◽  
pp. 359-397 ◽  
Author(s):  
JOSÉ MESEGUER ◽  
UGO MONTANARI ◽  
VLADIMIRO SASSONE
Keyword(s):  
Petri Nets ◽  
The Other ◽  
General Category ◽  
Monoidal Categories ◽  
Other Hand ◽  
Models Of Concurrency ◽  
A Chain ◽  
The One ◽  
Algebraic Domains

Place/transition (PT) Petri nets are one of the most widely used models of concurrency. However, they still lack, in our view, a satisfactory semantics: on the one hand the ‘token game’ is too intensional, even in its more abstract interpretations in terms of nonsequential processes and monoidal categories; on the other hand, Winskel's basic unfolding construction, which provides a coreflection between nets and finitary prime algebraic domains, works only for safe nets. In this paper we extend Winskel's result to PT nets. We start with a rather general category PTNets of PT nets, we introduce a category DecOcc of decorated (nondeterministic) occurrence nets and we define adjunctions between PTNets and DecOcc and between DecOcc and Occ, the category of occurrence nets. The role of DecOcc is to provide natural unfoldings for PT nets, i.e., acyclic safe nets where a notion of family is used to relate multiple instances of the same place. The unfolding functor from PTNets to Occ reduces to Winskel's when restricted to safe nets. Moreover, the standard coreflection between Occ and Dom, the category of finitary prime algebraic domains, when composed with the unfolding functor above, determines a chain of adjunctions between PTNets and Dom.

scholarly journals Four games on Boolean algebras

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3389-3395
Author(s):  
Milos Kurilic ◽  
Boris Sobot
Keyword(s):  
Boolean Algebra ◽  
Winning Strategy ◽  
Zero Element ◽  
Boolean Algebras ◽  
The Other ◽  
Complete Boolean Algebra ◽  
Other Hand

The games G2 and G3 are played on a complete Boolean algebra B in ?-many moves. At the beginning White picks a non-zero element p of B and, in the n-th move, White picks a positive pn < p and Black chooses an in ? {0,1}. White wins G2 iff lim inf pin,n = 0 and wins G3 iff W A?[?]? ? n?A pin,n = 0. It is shown that White has a winning strategy in the game G2 iff White has a winning strategy in the cut-and-choose game Gc&c introduced by Jech. Also, White has a winning strategy in the game G3 iff forcing by B produces a subset R of the tree <?2 containing either ??0 or ??1, for each ? ? <?2, and having unsupported intersection with each branch of the tree <?2 belonging to V. On the other hand, if forcing by B produces independent (splitting) reals then White has a winning strategy in the game G3 played on B. It is shown that ? implies the existence of an algebra on which these games are undetermined.

Amalgamation in relation algebras

1998 ◽  
Vol 63 (2) ◽  
pp. 479-484 ◽  
Author(s):  
Maarten Marx
Keyword(s):  
Modal Logic ◽  
Equational Theory ◽  
Weak Form ◽  
Boolean Algebras ◽  
The Other ◽  
Relation Algebras ◽  
Boolean Algebras With Operators ◽  
Other Hand ◽  
Arrow Logic ◽  
Representable Relation

We investigate amalgamation properties of relational type algebras. Besides purely algebraic interest, amalgamation in a class of algebras is important because it leads to interpolation results for the logic corresponding to that class (cf. [15]). The multi-modal logic corresponding to relational type algebras became known under the name of “arrow logic” (cf. [18, 17]), and has been studied rather extensively lately (cf. [10]). Our research was inspired by the following result of Andréka et al. [1].Let K be a class of relational type algebras such that(i) composition is associative,(ii) K is a class of boolean algebras with operators, and(iii) K contains the representable relation algebras RRA.Then the equational theory of K is undecidable.On the other hand, there are several classes of relational type algebras (e.g., NA, WA denned below) whose equational (even universal) theories are decidable (cf. [13]). Composition is not associative in these classes. Theorem 5 indicates that also with respect to amalgamation (a very weak form of) associativity forms a borderline. We first recall the relevant definitions.

On the Glass Transition in Polymer Films: Recent Monte Carlo Results

1998 ◽  
Vol 543 ◽  
Author(s):  
J. Baschnagel ◽  
K. Binder
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Glass Transition ◽  
Polymer Film ◽  
Polymer Films ◽  
The Other ◽  
Strong Tendency ◽  
Other Hand ◽  
A Chain

AbstractThis paper reports results of a Monte Carlo simulation for a simplified lattice modelof a supercooled polymer film. The film geometry is realized by two opposite hard walls.The distance between the walls is varied. The chains exhibit a strong tendency to orientparallel to the walls and are flattened when being very close to them. This deviation of thepolymer structure with respect to the bulk is accompanied by an acceleration of local densityfluctuations. On the other hand, the diffusion coefficient of a chain remains unaffected.

The Means and Methods of War

2021 ◽  
Vol 12 (2) ◽  
pp. 414-436
Author(s):  
Danial Saeed
Keyword(s):  
The Other ◽  
Other Hand ◽  
The Law ◽  
A Chain

The Joint Doctrine and Concepts Center (JDCC) is in charge of distributed Joint Warfare Publications (JWPs) and keeping up a chain of importance of such productions. At the start of any thought of the law of furnished clash, it must be underlined that the privilege of the gatherings to the contention to pick techniques on the other hand method for fighting is not boundless .

Mit Puppen spielen

2017 ◽  
Vol 8 (1) ◽  
pp. 157-176
Author(s):  
Helga Lutz
Keyword(s):  
20Th Century ◽  
The Other ◽  
Other Hand ◽  
A Chain ◽  
The One

"Der Text vergleicht zwei fetischistische Puppenexperimente des 20. Jahrhunderts. Auf der einen Seite steht der vielbeachtete Versuch Oskar Kokoschkas, die verlorene Alma Mahler durch eine lebensechte Puppe zu ersetzen. Auf der anderen Seite geht es um die verborgen gehaltenen Bücher des Schweizer Einsiedlers Armand Schulthess, bevölkert von Hunderten von erotischen Collage-Frauen, die kunstvoll zusammengeklebt, vernäht und ineinander gefaltet sind. So unterschiedlich das zugrundeliegende fetischistische Ritual auch ausfällt, so zeigt sich in beiden Anordnungen doch eine grundlegende Übereinstimmung: In beiden Fällen nimmt das Inkarnieren die Form einer Operationskette an, die das Bild ins Register einer mimetischen Transformationsontologie überstellt. The paper compares two fetishistic experiments with puppets of the 20th century. On the one hand, there is Oskar Kokoschka’s much discussed attempt to replace the lost Alma Mahler with a life-size doll. On the other hand, the paper treats the secret books of Swiss hermit Armand Schulthess, populated by hundreds of erotic women, which are artfully glued, sewn and folded together. However different the underlying fetishistic ritual may be, the two groups show a fundamental agreement: In both cases, the process of incarnating becomes a chain of operations, translating the image into the register of a mimetic ontology of transformation. "

The Powers of Association

1984 ◽  
Vol 32 (1_suppl) ◽  
pp. 264-280 ◽  
Author(s):  
Bruno Latour
Keyword(s):  
Diffusion Model ◽  
The Other ◽  
Central Source ◽  
Translation Model ◽  
Other Hand ◽  
The Social ◽  
A Chain ◽  
The Way

This article starts with a paradox: when an actor simply has power nothing happens and s/he is powerless; when, on the other hand, an actor exerts power it is others who perform the action. It appears that power is not something one can possess – indeed it must be treated as a consequence rather than as a cause of action. In order to explore this paradox a diffusion model of power in which a successful command moves under an impetus given it from a central source is contrasted with a translation model in which such a command, if it is successful, results from the actions of a chain of agents each of whom ‘translates’ it in accordance with his/her own projects. Since, in the translation model, power is composed here and now by enrolling many actors in a given political and social scheme, and is not something that can be stored up and given to the powerful by a pre-existing ‘society’, it follows that debates about the origins of society, the nature of its components, and their relationships become crucial data for the sociologist. It also follows that the nature of society is negotiable, a practical and revisable matter (performative), and not something that can be determined once and for all by the sociologist who attempts to stand outside it (ostensive). The sociologist should, accordingly, seek to analyse the way in which people are associated together, and should, in particular, pay attention to the material and extrasomatic resources (including inscriptions) that offer ways of linking people that may last longer than any given interaction. In the translation model the study of society therefore moves from the study of the social as this is usually conceived, to a study of methods of association.

scholarly journals The left, the right and the sequential topology on Boolean algebras

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4451-4459
Author(s):  
Milos Kurilic ◽  
Aleksandar Pavlovic
Keyword(s):  
Boolean Algebra ◽  
A Priori ◽  
Boolean Algebras ◽  
The Other ◽  
Complete Boolean Algebra ◽  
A Posteriori ◽  
Other Hand ◽  
Convergence Of Sequences ◽  
Algebraic Convergence ◽  
The Right

For the algebraic convergence ?s, which generates the well known sequential topology ?s on a complete Boolean algebra B, we have ?s = ?ls ? ?li, where the convergences ?ls and ?li are defined by ?ls(x) = {lim sup x}? and ?li(x) = {lim inf x+}? (generalizing the convergence of sequences on the Alexandrov cube and its dual). We consider the minimal topology Olsi extending the (unique) sequential topologies O?s (left) and O?li (right) generated by the convergences ?ls and ?li and establish a general hierarchy between all these topologies and the corresponding a priori and a posteriori convergences. In addition, we observe some special classes of algebras and, in particular, show that in (?,2)-distributive algebras we have limOlsi = lim?s = ?s, while the equality Olsi = ?s holds in all Maharam algebras. On the other hand, in some collapsing algebras we have a maximal (possible) diversity.

scholarly journals Circumscribed journeys through soundscape composition

2002 ◽  
Vol 7 (1) ◽  
pp. 1-3 ◽  
Author(s):  
Andra McCartney
Keyword(s):  
The Other ◽  
Sound Sources ◽  
Environmental Sounds ◽  
Daily Lives ◽  
Other Hand ◽  
Memory Time ◽  
A Chain ◽  
The One ◽  
The Relationship

The soundscape composition is the journey that circumscribes the relationship, the conversation between composer and sound sources. (Hildegard Westerkamp)Environmental sounds hold an unusual place in our imaginations. On the one hand, hey make up the often unnoticed ambiences of our daily lives: they are so much with us and surrounding us that it takes a special effort to bring them into the foreground, and pay attention to them. On the other hand, environmental sounds form a powerful conduit to memory. Hearing a particular sound or ambience can launch a chain of related memories, whether experienced consciously or working subconsciously, that reconnects us with particular places and times in our lives. It is precisely these confluences of memory, time and place that interest those who compose with soundscapes.

Intuition and Coherence in the Keystone Loop

2018 ◽  
pp. 108-130
Author(s):  
Keith Lehrer
Keyword(s):  
First Principles ◽  
Knowledge Claim ◽  
The Other ◽  
Wilfrid Sellars ◽  
Thomas Reid ◽  
Other Hand ◽  
A Chain ◽  
Knowledge Claims

Is knowledge and justification a matter of isolated intuition or coherence with a background system? One intuitionist, Thomas Reid, failed to acknowledge the controversy. He argued that knowledge was a matter of first principles, which drive intuition, but also claimed that the first principles depended on each other like links in a chain, as a coherentist might. Wilfrid Sellars, a famous coherentist, argued that all knowledge was explained by coherence with a background system, but, on the other hand, conceded that some knowledge claims were justified noninferentially, as an intuitionist might. This book suggests a resolution to the conflict in terms of a kind of knowledge requiring the knower be able to defend the target knowledge claim. The defense rests on exemplar representation of experience, yielding intuition, tied together in a keystone loop within a system to defend that representation, yielding coherence.

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