THE DUAL NOTION OF MULTIPLICATION MODULES

Causal-consistent reversible debugging is an innovative technique for debugging concurrent systems. It allows one to go back in the execution focusing on the actions that most likely caused a visible misbehavior. When such an action is selected, the debugger undoes it, including all and only its consequences. This operation is called a causal-consistent rollback. In this way, the user can avoid being distracted by the actions of other, unrelated processes. In this work, we introduce its dual notion: causal-consistent replay. We allow the user to record an execution of a running program and, in contrast to traditional replay debuggers, to reproduce a visible misbehavior inside the debugger including all and only its causes. Furthermore, we present a unified framework that combines both causal-consistent replay and causal-consistent rollback. Although most of the ideas that we present are rather general, we focus on a popular functional and concurrent programming language based on message passing: Erlang.

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Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽

10.3390/math9121441 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1441

Author(s):

Juan-De-Dios González-Hedström ◽

Juan-José Miñana ◽

Oscar Valero

Keyword(s):

Equivalence Relation ◽

Fuzzy Relations ◽

Measure Of Similarity ◽

Dual Notion ◽

The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

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Mutual Determination, Concrescence and Transition. Whitehead’s Speculative Conception of Temporal Subjectivity Interpreted from a Merleau-Pontyan Standpoint

Chiasmi International ◽

10.5840/chiasmi20202215 ◽

2020 ◽

Vol 22 ◽

pp. 101-117

Author(s):

Luca Vanzago ◽

Keyword(s):

Mathematical Concepts ◽

Material World ◽

Natural Knowledge ◽

Constant Change ◽

Interpretive Approach ◽

Dual Notion ◽

Mathematics And Physics ◽

Processual Approach

The interpretive approach adopted in this paper is influenced by Merleau-Ponty’s philosophy and in particular by his understanding of Nature, which in turn takes into consideration Whitehead’s work. Whitehead’s philosophy of organism is seen by its author as the metaphysical generalization of problems found in his investigation of natural knowledge. Whitehead admits that a speculative approach is necessitated by the very questions arising from the mathematical concepts of the material world and the revolutions undergone in logic, mathematics and physics at the turn of the century.Whitehead’s understanding of nature is framed from the beginning in terms of a processual approach. However, this notion of process is not fully worked out in the epistemological works and requires a metaphysical deepening. This is due to the fact that the notion of duration adopted in the epistemological works is not sufficient to convey the notion of process. This lack of adequacy is coupled by Whitehead with the need to interpret process in terms of experience. In turn, this notion of experience is wider than the usual one, for it implies that there is experience from the lowest levels onwards. Matter itself experiences. Seen in this perspective, reality is thus conceived in terms of a whole in constant change, whose parts are in mutual connection. This conception derives from Whitehead’s criticism of Aristotle’s substantialism and from his preference for a relationist ontology. The outcome of this approach is a speculative conception of reality in terms of a twofold notion of process: concrescence and transition, which Whitehead sees as the two faces of the creative advance of nature. This dual notion of process is interpreted in this essay in a merleau-pontyan perspective.

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Cartan-Whitehead decomposition as Adams cocompletion

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700028214 ◽

1987 ◽

Vol 42 (2) ◽

pp. 223-226 ◽

Cited By ~ 1

Author(s):

A. Behera ◽

S. Nanda

Keyword(s):

Connected Space ◽

Dual Notion

AbstractDeleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, the Adams cocompletion of an object in a category. In this paper the different stages of the Cartan-Whitehead decomposition of a 0-connected space are shown to be the cocompletions of the space with respect to suitable sets of morphisms.

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On the Dual Notion of Prime Submodules

Algebra Colloquium ◽

10.1142/s1005386712000880 ◽

2012 ◽

Vol 19 (spec01) ◽

pp. 1109-1116 ◽

Cited By ~ 17

Author(s):

H. Ansari-Toroghy ◽

F. Farshadifar

Keyword(s):

Commutative Ring ◽

Prime Submodules ◽

Dual Notion

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of prime submodules (that is, second submodules of M) and investigate the conditions under which the number of maximal second submodules of M is finite. Furthermore, we introduce the concept of coisolated submodules of M and obtain some related characterizations.

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The Dual Notion of Content Modules

Communications in Algebra ◽

10.1080/00927872.2015.1110587 ◽

2016 ◽

Vol 44 (11) ◽

pp. 4709-4723 ◽

Cited By ~ 1

Author(s):

H. Ansari-Toroghy ◽

S. S. Pourmortazavi

Keyword(s):

Dual Notion

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On the Dual Notion of Multiplication Modules

Arabian Journal for Science and Engineering ◽

10.1007/s13369-011-0088-y ◽

2011 ◽

Vol 36 (6) ◽

pp. 925-932 ◽

Cited By ~ 1

Author(s):

H. Ansari-Toroghy ◽

F. Farshadifar

Keyword(s):

Dual Notion

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Lyric, Nation, and Dialogism

Poetics Today ◽

10.1215/03335372-8720085 ◽

2020 ◽

Vol 41 (4) ◽

pp. 595-617

Author(s):

Morani Kornberg

Keyword(s):

Political Activism ◽

Nationalist Discourse ◽

Right Of Return ◽

Close Analysis ◽

Ethical Role ◽

Dual Notion ◽

Law Of Return ◽

First Time ◽

The Relationship

This article introduces, for the first time, the marginalized writings of Israeli-statehood-generation poet Maxim Ghilan (1931–2005), who lived in self-exile in Paris as a result of his political activism. By investigating the relationship between lyric poetry and nationalism, the article introduces Ghilan’s early poetry, followed by a close analysis of his groundbreaking and understudied poem “In Enemy Land,” written upon his return to Israel. Ghilan’s poetry overturns nationalist discourse by revisiting the events of 1948 and evoking the dual notion of return, namely, the Israeli Law of Return and the Palestinian Right of Return. In an effort to contribute to New Lyric Studies, the article offers a new form of lyric reading, the “trans-national lyric,” a hyphenated form of transnationalism used to emphasize crossing over and moving beyond the nation. The trans-national lyric dismantles the lyric speaker’s sovereign position and consequently uncovers the silent — and silenced — dialogic voices that are an inseparable part of the genre. The article concludes with an analysis of lyric address and the ethical role of reading, whereby readers are implicated in the process of forced remembering and historical revision.

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Cotorsion radicals and projective modules

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700047122 ◽

1971 ◽

Vol 5 (2) ◽

pp. 241-253 ◽

Cited By ~ 4

Author(s):

John A. Beachy

Keyword(s):

Projective Module ◽

Projective Modules ◽

Left Module ◽

Perfect Ring ◽

Artinian Rings ◽

Trace Ideal ◽

Dual Notion ◽

Rings Of Quotients ◽

Torsion Radical ◽

Natural Way

We study the notion (for categories of modules) dual to that of torsion radical and its connections with projective modules.Torsion radicals in categories of modules have been studied extensively in connection with quotient categories and rings of quotients. (See [8], [12] and [13].) In this paper we consider the dual notion, which we have called a cotorsion radical. We show that the cotorsion radicals of the category RM correspond to the idempotent ideals of R. Thus they also correspond to TTF classes in the sense of Jans [9].It is well-known that the trace ideal of a projective module is idempotent. We show that this is in fact a consequence of the natural way in which every projective module determines a cotorsion radical. As an application of these techniques we study a question raised by Endo [7], to characterize rings with the property that every finitely generated, projective and faithful left module is completely faithful. We prove that for a left perfect ring this is equivalent to being an S-ring in the sense of Kasch. This extends the similar result of Morita [15] for artinian rings.

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Spherical diagrams and equations over groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100062150 ◽

1984 ◽

Vol 96 (2) ◽

pp. 255-268 ◽

Cited By ~ 5

Author(s):

James Howie

Keyword(s):

Group Presentations ◽

Equations Over Groups ◽

Dual Notion ◽

Original Approach

Spherical diagrams were introduced by Lyndon and Schupp[14] in order to study asphericity in group presentations and in 2-complexes. They have since been studied by several authors [2, 3, 5]. In particular, some technical loopholes in the original approach were closed in [5]. For many purposes the dual notion of pictures, introduced by Rourke[17], is more useful. These arise naturally through transversality. Pictures have also been studied and applied in [2, 5, 6, 12, 19].

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