scholarly journals Almost structural completeness; an algebraic approach

10.29007/59qg ◽  
2018 ◽  
Author(s):  
Wojciech Dzik ◽  
Michał Stronkowski
Keyword(s):  
Algebraic Approach ◽  
Free Algebras ◽  
Deductive Systems ◽  
Structural Completeness

The notion of structural completeness has received considerable attention for many years. A translating to algebra gives: a quasivariety is structurally complete if it is generated by its free algebras. It appears that many deductive systems (quasivarieties), like S5 or MV<sub>n</sub> fails structural completeness for a rather immaterial reason. Therefore the adjusted notion was introduced: almost structural completeness. We investigate almost structural completeness from an algebraic perspective and obtain a characterization of this notion for quasivarieties.

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

scholarly journals A linear-algebraic tool for conditional independence inference

2015 ◽  
Vol 6 (2) ◽  
Author(s):  
Kentaro Tanaka ◽  
Milan Studeny ◽  
Akimichi Takemura ◽  
Tomonari Sei
Keyword(s):  
Computational Result ◽  
Conditional Independence ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Positive Density ◽  
Implication Problem ◽  
Algebraic Tool ◽  
Linear Algebraic Method

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables. 

scholarly journals Almost structural completeness; an algebraic approach

2016 ◽  
Vol 167 (7) ◽  
pp. 525-556 ◽  
Author(s):  
Wojciech Dzik ◽  
Michał M. Stronkowski
Keyword(s):  
Algebraic Approach ◽  
Structural Completeness

scholarly journals The Max-Plus Algebra of the Natural Numbers has no Finite Equational Basis

1999 ◽  
Vol 6 (33) ◽  
Author(s):  
Luca Aceto ◽  
Zoltán Ésik ◽  
Anna Ingólfsdóttir
Keyword(s):  
Equational Theory ◽  
Geometric Characterization ◽  
Independent Interest ◽  
Free Algebras ◽  
Finitely Based ◽  
Natural Numbers ◽  
Equational Basis ◽  
Stepping Stone

This paper shows that the collection of identities which hold in<br />the algebra N of the natural numbers with constant zero, and binary<br />operations of sum and maximum is not finitely based. Moreover, it<br />is proven that, for every n, the equations in at most n variables that<br />hold in N do not form an equational basis. As a stepping stone in<br />the proof of these facts, several results of independent interest are<br />obtained. In particular, explicit descriptions of the free algebras in the<br />variety generated by N are offered. Such descriptions are based upon<br />a geometric characterization of the equations that hold in N, which<br />also yields that the equational theory of N is decidable in exponential<br />time.

scholarly journals Hilbert Algebras of Fractions

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Christina-Theresia Dan
Keyword(s):  
Closed Subset ◽  
Sufficient Condition ◽  
Hilbert Algebra ◽  
Necessary And Sufficient Condition ◽  
Inductive Limits ◽  
Hilbert Algebras ◽  
Deductive Systems ◽  
Necessary And Sufficient

Let be a bounded Hilbert algebra and a -closed subset of . The Hilbert algebra of fractions is studied regarding maximal and irreducible deductive systems. As important results, we can mention a necessary and sufficient condition for a Hilbert algebra of fractions to be local and the characterization of this kind of algebras as inductive limits of some particular directed systems.

scholarly journals An algebraic approach to the spontaneous formation of spherical jets

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Milo Viviani
Keyword(s):  
Euler Equations ◽  
Large Scale ◽  
Algebraic Approach ◽  
Spherical Domain ◽  
Spontaneous Formation ◽  
Algebraic Properties ◽  
2D Euler Equations ◽  
Continuous Source

<p style='text-indent:20px;'>The global structure of the atmosphere and the oceans is a continuous source of intriguing challenges in geophysical fluid dynamics (GFD). Among these, jets are determinant in the air and water circulation around the Earth. In the last fifty years, thanks to the development of more and more precise and extensive observations, it has been possible to study in detail the atmospheric formations of the giant-gas planets in the solar system. For those planets, jets are the dominant large scale structure. Starting from the 70s, various theories combining observations and mathematical models have been proposed in order to describe their formation and stability. In this paper, we propose a purely algebraic approach to describe the spontaneous formation of jets on a spherical domain. Analysing the algebraic properties of the 2D Euler equations, we give a characterization of the different jets' structures. The calculations are performed starting from the discrete Zeitlin model of the Euler equations. For this model, the classification of the jets' structures can be precisely described in terms of reductive Lie algebras decomposition. The discrete framework provides a simple tool for analysing both from a theoretical and and a numerical perspective the jets' formation. Furthermore, it allows to extend the results to the original Euler equations.</p>

Notes on the Algebraic Approach to Dependence in Information Systems

1992 ◽  
Vol 16 (3-4) ◽  
pp. 263-273
Author(s):  
Jiří Novotný ◽  
Miroslav Novotný
Keyword(s):  
Information System ◽  
Information Systems ◽  
Algebraic Structure ◽  
Algebraic Approach ◽  
Complete Characterization ◽  
Dependence Relation ◽  
Abstract Setting ◽  
Dependence Space

The concept of the relation of dependence between sets of attributes of an information system is studied in a more abstract setting – in the algebraic structure called dependence space. Complete characterization of dependence relation in a dependence space is presented.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

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